Performance Analysis in Game Sports: Concepts and Methods: Concepts and Methods [1st ed. 2023] 3031072499, 9783031072499

Table of contents :
Preface
Contents
Abbreviations
List of Figures
List of Tables
List of Boxes
1: Basics
1.1 Definitions and Concepts
1.1.1 Performance Analysis
1.1.2 Competition, Training, and Athletes’ Abilities
1.1.3 Theoretical and Practical Performance Analysis
1.1.4 General Model of Sports Performance Structure
1.2 Performance Analysis in Game Sports
1.2.1 The Nature of Game Sports
1.2.2 Basic Problems of Performance Analysis in Game Sports
1.3 Approaches in Performance Analysis
1.3.1 Classical Performance Analysis
1.3.2 Notational Analysis
1.3.3 Sports Analytics
2: Action Detection
2.1 Assessment of Behaviour
2.2 Design of Observational Systems
2.2.1 Type of Observational Systems
2.2.1.1 Event Systems
2.2.1.2 Category Systems
2.2.2 Elements of Observational Systems
2.2.2.1 Observational Units
2.2.2.2 Observational Variables
2.2.2.3 Levels of Observational Variables
2.2.3 Complex Observational Systems
2.3 Validation of Observational Systems
2.3.1 General Framework of Validation
2.3.1.1 Reliability
2.3.1.2 Validity
2.3.2 Role of Observer
2.3.2.1 Observer Training
2.3.3 Methods and Statistics for Testing Observer Agreement
2.3.3.1 Agreement Matrices for Observer Training
2.3.3.2 Weighted Kappa
2.3.3.3 The Kappa Paradox
2.3.3.4 Inter- and Intra-observer Agreement
2.4 Examples for Studies Using Action Detection
2.4.1 Event Profiling
2.4.2 Detailed Event Observation
2.4.3 Hierarchical Categorial System
3: Position Detection
3.1 Functioning of Position Tracking
3.1.1 Position Detection Methods
3.1.1.1 GPS
3.1.1.2 LPS
3.1.1.3 Video
3.1.2 Signal Processing
3.1.2.1 Sampling Frequency
3.1.2.2 Smoothing
3.2 Validation of Tracking Systems
3.2.1 Gold Standards for Position Tracking in Sports
3.2.2 Design of Validation Studies
3.2.2.1 Measurement Site
3.2.2.2 Exercises
3.2.2.3 Levels of Analysis
3.2.2.4 Representation of Objects/Players
3.2.2.5 Data Processing Steps
3.2.3 Accuracy of Position Tracking in Sports
3.2.3.1 Video-Based Tracking (VBT)
3.2.3.2 LPS
3.2.3.3 GPS
4: Theoretical Performance Analysis
4.1 Statistical Approaches of TPA
4.1.1 Performance Profiles
4.1.2 Impact of Influencing Factors
4.1.3 Criticism of Statistical Approaches
4.2 Modelling Approaches
4.2.1 Methodological Aspects of Modelling Approaches
4.2.1.1 Types of Validation
4.2.1.2 Levels of Modelling
4.2.2 Direct Modelling of Game Behaviour
4.2.2.1 Ball Control
4.2.2.2 Ball Possession Episodes
4.2.2.3 Playing Style
4.2.2.4 Performance Indices
4.2.2.5 Fatigue
Alternative Explanations for Decreasing Performances
The Spectral Fatigue Index (SFI)
Individual Courses of Match Intensity
Transient Fatigue and Regression to the Mean
4.2.2.6 Within-Match Dynamics
4.2.3 Importing Models to PA
4.2.3.1 Network Analysis
4.2.3.2 Finite Markov Chains 
4.3 Dynamical Systems Theory Approaches
4.3.1 Dynamical Systems Theories
4.3.2 Complex Systems, Synergetics, and Relative Phase
4.3.2.1 History
4.3.2.2 Synergetics
4.3.2.3 Relative Phase
4.3.2.4 Applications of Synergetics in Sports Science
4.3.3 Ecological Psychology
4.3.3.1 History
4.3.3.2 Applications in Sport Science
4.3.4 Applications of DST in PA
4.3.4.1 Concepts
4.3.4.2 Goal Scoring and Chance in Football
4.3.4.3 Relative Phase, Synchrony, and Entropy in Sports
4.3.4.4 Perturbations
4.3.4.5 Ecological Psychology as Framework for PA
4.3.5 Outlook DST in PA
4.3.5.1 Recurrence Analysis
5: Practical Performance Analysis
5.1 Introduction
5.2 Concepts of PPA
5.2.1 Definition, Aims, and Research Strategies
5.2.2 Informational Coupling of Competition and Training
5.2.2.1 Step 1: Description
5.2.2.2 Step 2: Analysis
Step 2.1: Identification of Strengths and Weaknesses
Step 2.2: Identification of Performance Prerequisites
5.2.2.3 Step 3: Transfer to Training
Step 3.1: Assessment of Effective Trainability
Step 3.2: Integration into Training Process
5.2.2.4 Summary Informational Coupling
5.2.3 Comprehensive Performance Analysis
5.3 Methods of PPA
5.3.1 Qualitative Game Analysis
5.3.1.1 Qualitative Research Methodology
5.3.1.2 Qualitative Methodology in PPA
5.3.1.3 The Social Context
5.3.1.4 Qualitative Content Analysis
5.3.1.5 Communicative Validation
5.3.1.6 Steps of QGA
5.3.2 Development of Match Strategies
5.3.3 Video-Based Tactics Training (VTT)
5.3.3.1 Conceptual Foundation of VTT
5.3.3.2 Methodology of VTT
Aims of VTT
Methodological Decisions
Levels of Impact of VTT
Social Engineering and Reinforcement Techniques
VTT in Different Settings
Pitfalls of VTT
5.3.3.3 Scientific Evidence for VTT Methods and Effectiveness
5.4 Game Analysts in Professional Training Systems
5.4.1 Applications of Game Analysis
5.4.2 The Role of Game Analysts
5.4.3 Game Analysis Software
5.4.4 Club Information Systems
6: Outlook
6.1 Outlook on the Core Topics of PA
6.1.1 Basic Concepts
6.1.2 Action Detection
6.1.3 Position Detection
6.1.4 Theoretical Performance Analysis
6.1.5 Practical Performance Analysis
6.2 The Future of PA
6.2.1 Artificial Intelligence and PA
6.2.2 Sports Practice and PA
References
Index

Citation preview

Performance Analysis in Game Sports: Concepts and Methods Martin Lames

123

Performance Analysis in Game Sports: Concepts and Methods

Martin Lames

Performance Analysis in Game Sports: Concepts and Methods

Martin Lames Faculty of Sports and Health Sciences Technical University Munich Munich, Germany

ISBN 978-3-031-07249-9    ISBN 978-3-031-07250-5 (eBook) https://doi.org/10.1007/978-3-031-07250-5 © Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book is based on many years of teaching the subject of performance analysis as a master’s course at TU München, Germany. Even more influential, it is based on three decades of research in this area covering theoretical as well as practical aspects. Theoretical activities include the search for conceptual and methodological achievements in the analysis of game sports (a term for net games plus invasion games), including mathematical and stochastic modelling. Practical activities comprise the introduction of technological innovations, giving support in match analysis to top-level, mostly national teams, and deriving a conceptual framework for working in the practice of performance analysis based on these experiences. The scientific roots of this work lie in the discipline of sports science one could call “training and exercise science” as closest translation of German “Trainingswissenschaft”. The aim of this discipline of sports science is to provide scientific foundation for practical action in training and competition. Although it seems to be a quite narrow and merely applied perspective, a closer look reveals that this is by no means the case. To give a scientific foundation for practice it is, for example, necessary to understand the structure of the respective sports discipline. This, in turn, requires investigations of the type of basic research trying to establish general findings that for example explain success in competition. Also, it is necessary to identify properties of athletes as determinants of performance and to establish the relationships between them, what will altogether be called “theoretical performance analysis”. Nevertheless, scientifically founded support for practice remains the ultimate task that may only be solved by applying special and different methods and concepts: “practical performance analysis”. The book has six major chapters, starting with basic concepts, continuing with the two most important methods of data collection in performance analysis, action detection and position detection. Finally, concepts and methods of theoretical and practical performance analysis are presented. Chapter 1: Basics explains the underlying concepts and functions of performance analysis in the broader framework of training and exercise science. Special attention is given to—compared to other sports—the unique structure of game sports. The concept introduced to explain the nature of game sports is a dynamic interaction process with emerging behaviour. This concept will be substantiated in detail because it is the reference point of the whole book. Another basic concept is the distinction between theoretical and practical performance analysis that is introduced v

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Preface

and will be referenced to throughout the book as well. It is interesting to compare this concept of performance analysis with different approaches like notational analysis (UK) and sports analytics (USA). Chapter 2: Action Detection refers to the standard method of action recording with observational systems. It will derive the most common types of observational systems from concepts of behavioural assessment in psychology. Control of observer agreement is an important topic in this context to quantify reliability of observations either for examining data provided by external sources or to check/ improve one’s own observational systems. Finally, practical examples demonstrate power and flexibility of well-designed observational systems. In the recent two decades technological progress has made it possible to track the positions of athletes. Chapter 3: Position Detection starts with a brief introduction to the different technologies in use, GPS-, radio- and video-based systems. It then discusses methods to control the accuracy of tracking systems which used to be a surprisingly under-reported area. Only recently one has become aware of the complexity of validation studies and potential error sources in position detection. In Chapter 4: Theoretical Performance Analysis the different approaches to analyse the structure of sports are described in detail. It contains the classical statistical approaches and modelling approaches with the direct modelling of sports phenomena from action and position data and the valuable approach of importing models from other scientific areas and applying them to performance analysis. A special section is devoted to Dynamical Systems Theory with special focus on synergetics and ecological dynamics. All approaches are questioned critically whether or in how far they are capable of solving the problems of performance analysis. Chapter 5: Practical Performance Analysis is dedicated to explaining the concepts and methods of scientifically founded performance analysis conducted in practice. As the central method, qualitative game analysis makes use of qualitative methods; this research methodology not so common in performance analysis is briefly introduced. A more comprehensive view on performance analysis is advocated, including the collection of all information necessary for generating practical recommendations for training. Concepts and methods are described in depth and specific attention is given to main tasks in practical performance analyses such as identifying strengths and weaknesses of one’s own team and the opponent, developing a match strategy, and support tactical instruction and learning by video-based tactics training. At the end, Chapter 6: Outlook mentions the most interesting future perspectives for performance analysis and analysts. It is not speculative at all to expect a further progress in technological options for match analysis. Also, the role of performance analysts will change when working increasingly in “training systems”, a term expressing the tendency towards many experts from different areas being integrated in a professional support system of a team or an athlete. This book emphasizes a certain perspective on performance analysis. Always keeping in mind that the ultimate aim is to provide scientific foundation for practical action in sport it focuses on conceptual bases of performance analysis. Accordingly, the basic scenario for application is always sports practice. The most important

Preface

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methods and concepts for giving scientific support to practice are addressed in a systematic, comprehensive manner, whereas giving a review on existing studies in PA is not the priority. Readers of this textbook are scientists and students interested in a comprehensive, concept-driven overview of the scientific discipline of performance analysis, but also practitioners working in sports practice with an interest in conceptual backgrounds and a critical reflection of their daily work. Munich, Germany

Martin Lames

Contents

1

Basics����������������������������������������������������������������������������������������������������������   1 1.1 Definitions and Concepts������������������������������������������������������������������   1 1.1.1 Performance Analysis ������������������������������������������������������������   2 1.1.2 Competition, Training, and Athletes’ Abilities ����������������������   2 1.1.3 Theoretical and Practical Performance Analysis��������������������   4 1.1.4 General Model of Sports Performance Structure��������������������   7 1.2 Performance Analysis in Game Sports ��������������������������������������������   9 1.2.1 The Nature of Game Sports����������������������������������������������������   9 1.2.2 Basic Problems of Performance Analysis in Game Sports������������������������������������������������������������������������  12 1.3 Approaches in Performance Analysis ����������������������������������������������  14 1.3.1 Classical Performance Analysis����������������������������������������������  15 1.3.2 Notational Analysis����������������������������������������������������������������  19 1.3.3 Sports Analytics����������������������������������������������������������������������  21

2

Action Detection ����������������������������������������������������������������������������������������  23 2.1 Assessment of Behaviour������������������������������������������������������������������  23 2.2 Design of Observational Systems ����������������������������������������������������  25 2.2.1 Type of Observational Systems����������������������������������������������  27 2.2.2 Elements of Observational Systems����������������������������������������  31 2.2.3 Complex Observational Systems��������������������������������������������  37 2.3 Validation of Observational Systems������������������������������������������������  37 2.3.1 General Framework of Validation ������������������������������������������  38 2.3.2 Role of Observer ��������������������������������������������������������������������  40 2.3.3 Methods and Statistics for Testing Observer Agreement������������������������������������������������������������������������������  43 2.4 Examples for Studies Using Action Detection����������������������������������  53 2.4.1 Event Profiling������������������������������������������������������������������������  53 2.4.2 Detailed Event Observation����������������������������������������������������  54 2.4.3 Hierarchical Categorial System����������������������������������������������  56

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3

Position Detection��������������������������������������������������������������������������������������  59 3.1 Functioning of Position Tracking�����������������������������������������������������  60 3.1.1 Position Detection Methods����������������������������������������������������  60 3.1.2 Signal Processing��������������������������������������������������������������������  66 3.2 Validation of Tracking Systems��������������������������������������������������������  70 3.2.1 Gold Standards for Position Tracking in Sports ��������������������  72 3.2.2 Design of Validation Studies��������������������������������������������������  74 3.2.3 Accuracy of Position Tracking in Sports��������������������������������  79

4

Theoretical Performance Analysis������������������������������������������������������������  83 4.1 Statistical Approaches of TPA����������������������������������������������������������  84 4.1.1 Performance Profiles��������������������������������������������������������������  85 4.1.2 Impact of Influencing Factors ������������������������������������������������  88 4.1.3 Criticism of Statistical Approaches����������������������������������������  92 4.2 Modelling Approaches����������������������������������������������������������������������  93 4.2.1 Methodological Aspects of Modelling Approaches����������������  94 4.2.2 Direct Modelling of Game Behaviour������������������������������������  97 4.2.3 Importing Models to PA���������������������������������������������������������� 115 4.3 Dynamical Systems Theory Approaches������������������������������������������ 133 4.3.1 Dynamical Systems Theories�������������������������������������������������� 133 4.3.2 Complex Systems, Synergetics, and Relative Phase�������������� 136 4.3.3 Ecological Psychology������������������������������������������������������������ 144 4.3.4 Applications of DST in PA ���������������������������������������������������� 148 4.3.5 Outlook DST in PA ���������������������������������������������������������������� 167

5

Practical Performance Analysis���������������������������������������������������������������� 177 5.1 Introduction�������������������������������������������������������������������������������������� 177 5.2 Concepts of PPA ������������������������������������������������������������������������������ 178 5.2.1 Definition, Aims, and Research Strategies������������������������������ 178 5.2.2 Informational Coupling of Competition and Training������������ 181 5.2.3 Comprehensive Performance Analysis ���������������������������������� 188 5.3 Methods of PPA�������������������������������������������������������������������������������� 190 5.3.1 Qualitative Game Analysis������������������������������������������������������ 190 5.3.2 Development of Match Strategies������������������������������������������ 201 5.3.3 Video-Based Tactics Training (VTT)�������������������������������������� 204 5.4 Game Analysts in Professional Training Systems���������������������������� 214 5.4.1 Applications of Game Analysis���������������������������������������������� 215 5.4.2 The Role of Game Analysts���������������������������������������������������� 218 5.4.3 Game Analysis Software�������������������������������������������������������� 220 5.4.4 Club Information Systems������������������������������������������������������ 223

6

Outlook������������������������������������������������������������������������������������������������������� 227 6.1 Outlook on the Core Topics of PA���������������������������������������������������� 227 6.1.1 Basic Concepts������������������������������������������������������������������������ 227 6.1.2 Action Detection �������������������������������������������������������������������� 228

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6.1.3 Position Detection������������������������������������������������������������������ 229 6.1.4 Theoretical Performance Analysis������������������������������������������ 230 6.1.5 Practical Performance Analysis���������������������������������������������� 232 6.2 The Future of PA������������������������������������������������������������������������������ 233 6.2.1 Artificial Intelligence and PA�������������������������������������������������� 233 6.2.2 Sports Practice and PA������������������������������������������������������������ 234 References ���������������������������������������������������������������������������������������������������������� 237 Index�������������������������������������������������������������������������������������������������������������������� 255

Abbreviations

AI DMA DST EPTS FIFA GDR GNSS GPS IFAB LPS MLS NBA NTSC PA PAL PPA QGA RFID SNA TPA TU VBT VR VTT

Artificial intelligence Double moving average Dynamical systems theory Electronic performance tracking system Fédération Internationale de Football Association German Democratic Republic Global navigation satellite system Global positioning system International Football Association Board (rule commission of FIFA) Local positioning system Minimum least squares National basketball association (highest US basketball league) National Television Standards Committee (video norm) Performance analysis Phase alternation line (video norm) Practical performance analysis Qualitative game analysis Radio-frequency identification Social network analysis Theoretical performance analysis Technical University Video-based tracking Virtual reality Video-based tactics training

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List of Figures

Figure 1.1 Scientific subject of training and exercise science Figure 1.2 General structural model of sports performance Figure 1.3 General structural model of performance in game sports Figure 1.4 Hits in Google Scholar for “Performance Analysis Football” Figure 1.5 The general structural model for sports performances Figure 1.6 Empirical structure of performance in cross-country skiing Figure 2.1 Model projection Figure 2.2 General structure of invasion games and net games Figure 2.3 Criteria for selecting an observational variable Figure 2.4 Role of the observer Figure 2.5 Absolute and case-by-case agreement Figure 2.6 Compensation of objectivity Figure 2.7 Agreement matrix for observer training Figure 2.8 Matrix of agreement, matrix of weights, and weighted agreement matrix Figure 2.9 Type I agreement matrix for recording duels in match Figure 2.10 Start and end location of episodes (ball control periods) of the dominant and the inferior team in a Bundesliga match Figure 3.1 Two-dimensional Illustration of triangulation of a position given the distances from three satellites Figure 3.2 Calculation of area with sufficient elevation angle dependent on camera position Figure 3.3 Approximation of a trajectory by measurements of different frequency Figure 3.4 Simulated smoothing with moving averages Figure 4.1 Levels of modelling Figure 4.2 Percent of match duration of ball control categories in 11 matches of Bayern Munich Figure 4.3 Distance covered in m/min per 5 min-interval Figure 4.4 Distance covered (m/min) of teams visiting the teams with the lowest and highest season average in home games Figure 4.5 Match standings of 306 matches of Bundesliga season 2012/13 per min Figure 4.6 Spectral Fatigue Index over 5 bouts of 2 vs. 2 small sided game under fatigued and not fatigued conditions Figure 4.7 The course of distance covered in 5-min intervals in three selected matches and of the average of 36 matches xv

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List of Figures

Figure 4.8 ACF of distance covered for the mean of each 5-min interval and mean ACF the lags of all matches Figure 4.9 Z-values for playing time, total distance covered, and distance covered standardized with playing time for the 5-min interval with maximum intensity (max) and for max+1 Figure 4.10 Interaction graphs and minimum spanning trees for basketball, football, and handball Figure 4.11 Two plays, their network, and their adjacency matrix Figure 4.12 State-transition model for tennis Figure 4.13 State-transition model for table tennis Figure 4.14 Transition matrix of a tennis match Figure 4.15 Transition matrix of a table tennis match Figure 4.16 Relevance of tactical behaviours in tennis Figure 4.17 System dynamics of a damped and a driven pendulum Figure 4.18 A tennis rally of Justine Henin and Serena Williams with phase space trajectories of each player Figure 4.19 Illustration of Relative Phase for in-phase, anti-phase, and the general phase relation between two objects Figure 4.20 Coordination patterns in finger-waggling; positions of the two finger tips over time in Kelso’s finger waggling experiment; potential landscapes for coupled oscillators Figure 4.21 Conceptual model of a phase space in football Figure 4.22 Left: Basic nonlinearities in team and net sports Right: Nonlinearities in football matches Figure 4.23 Left: Goals shot in Bundesliga season 2019/20 plotted against shots at goal; Right: Plotted against goal attempts Figure 4.24 Proportion of “chance variables” and chance goals of all goals Figure 4.25 The rate of chance goals in scored and conceded goals by the first and last team and the four first and last teams of Bundesliga 2011–12 Figure 4.26 Distribution of results in a football match assuming two independent negative binomial distributions Figure 4.27 Team centroids of Italy and France in the World Championship final 2006 with Relative Phase Figure 4.28 Illustration of a rally in a net game as dynamical system Figure 4.29 Perturbation profile for two matches of Nadal and Federer, French Open 2007 Figure 4.30 Age-dependent course of critical goal situations (CGS) and perturbations per match and CGS per goal and perturbations per CGS Figure 4.31 Perturbation profiles of football teams of different age groups Figure 4.32 Colour-coded recurrence plot for a football match Figure 4.33 Recurrence plots of nine randomly selected football matches Figure 5.1 The informational coupling between competition and training Figure 5.2 Illustration of the concept of comprehensive performance analysis Figure 5.3 Illustration of the concept of considering interactions between match analyst and coach, staff, and athletes as being embedded in a social context

List of Figures

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Figure 5.4 Illustration of the analogy between Qualitative Content Analysis and Qualitative Game Analysis Figure 5.5 Steps of QGA Figure 5.6 Conceptual model of strategy development including feedback through strategy check Figure 5.7 The trimodal communication model of Merten Figure 5.8 Organizational sequence and results of video-based tactic test and match behaviour of service Figure 5.9 Different roles of match analysts in a sports club Figure 5.10 Design and user interfaces of a table tennis match analysis software Figure 5.11 Different roles in the staff of a professional football club Figure 5.12 Architecture of a club information system

List of Tables

Table 1.1 Comparison of TPA and PPA Table 2.1 Starting events of ball possessions leading to a critical goal situation in youth football Table 2.2 Examples for observational variables Table 2.3 Specification of an observational system for discrete, continuous, and enumerative variables Table 2.4 Frequency and duration of game stoppages in football per match Table 2.5 Expert ratings of OSPAF variables with mean and Aiken’s V and intra/ inter-rater kappa Table 2.6 Hierarchical observational system with game phases (categorial system) on first level and game phase specific variables on second and third level Table 3.1 Comparison between different tracking technologies Table 3.2 Assessment of the accuracy of LPS position tracking Table 3.3 RMSE for position, speed, and acceleration Table 4.1 Correlations between match intensity and teams’ average performances and product (interaction) of average performances for typical kinematic PIs; all correlations significant: min p = 0.007 Table 4.2 Descriptive statistics for the percentage of chance goals per team in Bundesliga and Premier League 2011–12 Table 4.3 Descriptive statistics of the recurrence parameters of 21 football matches Table 4.4 Inter-correlations between recurrence parameters and traditional PIs for n = 21 matches Table 5.1 Comparison of qualitative and quantitative research based on different criteria Table 5.2 The analogy between Qualitative Content Analysis and Qualitative Game Analysis

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List of Boxes

Definition Performance Analysis Anomy in the role of coaches Theoretical Performance Analysis Practical Performance Analysis The practical impact debate The structure of performances and ecological psychology Definition of game sports Performance indicators Traditions of observational studies Model theory Variants of observational systems Equivalence classes Action feeds Automated game observation Observer agreement for interval-scaled judgements Sufficient levels of measurement quality Problems with “pure” methodological concepts Performance Analysis and Technological Progress Commercial data providers Correlation as measure of agreement Is PA a science? Analysis of world top-level performances Modelling with regression functions Methodology of index building Spectral analysis in PA Importing a theory/a methodology to PA Laplace’s demon and football matches Hysteresis, critical fluctuations, critical slowing down A synergetic experiment in golf The agenda of DST modelling in sports Where is the ball 10 s after a corner? Expected goals and nonlinearity Practical Performance Analysis Practical experiences xxi

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Is giving feedback the central task of PPA? Norms for the required level of performance prerequisites Attitudes of qualitative researchers Qualitative Game Analysis Qualitative content analysis (Mayring 1994, 2014) Video-based tactics training Virtual reality for PPA? Is game analysis “big data”?

List of Boxes

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Basics

This chapter deals with basics of performance analysis embedded in a broader perspective of training and exercise science starting with central definitions and concepts. Although this is an arduous and tiresome, not at all easy-going start, these are necessary prerequisites not only for the course of the book but also to show the contrast to different approaches of performance analysis. After this, a paragraph outlines the particularities of game sports compared to other types of sports. It will be proven that in performance analysis literature, these differences are not sufficiently acknowledged, and sometimes even a tacit identification of sports and game sports is found. The chapter closes with a comparison of different approaches including UK’s notational analysis and US sports analytics.

1.1 Definitions and Concepts In a classical academic tradition, this textbook starts with definitions necessary for creating a common background of understanding. Sports science is not famous for being a very analytical science, but the roots of this approach can be seen in the conceptual systems going back to Soviet Union and GDR (German Democratic Republic) with their acknowledged strong definitions and systematics. In the field of performance analysis, these traditions meet an application field with completely different traditions, frequently associated with professional (US- and West European) team sports, specific head-coach personalities and scouts and analysts relying on gut feelings. As things have changed dramatically in modern professional team sports, nowadays being characterized by large, scientifically educated staffs, it is about time to raise the conceptual framework of performance analysis on a corresponding level, starting with a precise understanding of the terms used.

© Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5_1

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1.1.1 Performance Analysis A most interesting key term in a textbook on performance analysis (PA) is “performance analysis”. Studying the explanations of this term in the literature reveals an increase in activities and application areas being ascribed to PA over time. Traditional notational analysis only recorded events in competitions (Hughes and Franks 1997, 2004), whereas nowadays each method assessing any relevant aspect of a performance in sports is included. In earlier times, PA was mostly implicitly restricted to the analysis of game behaviour (McGarry 2009, p. 128); at present any type of sport is the object. O’Donoghue (2010, p. 2) has extended the area of investigations further to performances in training. This has led to the suggestion of a very comprehensive definition of performance analysis: Definition Performance Analysis

Performance analysis (PA) is the assessment of competition, parts of competition, and performance prerequisites with different methods for different purposes. A first comment must state that this suggested definition represents an “open” concept of performance analysis, open to different methods including modern machine learning approaches, but the grass-rooted coach’s out-dated gut feeling is still included (he for sure assesses the competition!). Purposes of PA range from establishing statistical laws on the structure of performances to supporting the football coach in deriving recommendations for tactical changes in the last 10 min with one goal behind. A second comment refers to the notion that PA is not limited to scientific activities. Assessing performances is something that happens in sports practice as well, and thus, a much broader framework is drawn. Differences and commonalities of PA conducted in academic and practical settings are issues that will turn up through the whole of this book.

1.1.2 Competition, Training, and Athletes’ Abilities As mentioned in the introduction, the scientific home of book and author is training and exercise science in the sense of German “Trainingswissenschaft”. This discipline of sports science aims at providing scientific support for practical action in sports (Hohmann et al. 2020). The scientific subject of training and exercise science consists of three areas: competition, training, and athletes’ capabilities including the interrelationships between them (see Fig. 1.1). The terms “training” and “competition” need no further explanation. With “capabilities”, personal properties of athletes are denoted that are required for acting

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Fig. 1.1  Scientific subject of training and exercise science. (With permission of Limpert-­Verlag from Hohmann et al. (2020))

successfully in competition and can be influenced by training. The term “performance prerequisites” means all personal properties that have an impact on performance including—besides the capabilities—those not being subject to training such as constitutional factors, for example, body height. To clarify the nature of the three areas, it is appropriate to refer to ecological psychology with constraints and affordances as basic concepts (Newell 1986; a detailed discussion of this approach is given in the section on dynamical systems modelling in Chap. 4). Being dispositions for action, capabilities may be termed structural organismic constraints and affordances of the athletes. Very much like environmental affordances allow a subject to do things (Glazier 2017), these internal affordances are prerequisite for an athlete to act successfully in competition, for example, a sufficient level in endurance, strength, and agility but also technical skills and tactical proficiency. Complementarily, if the level of capabilities is not sufficient, this constitutes individual organismic constraints in reaching goals in a competition. Studying the nature of the interrelationships between these three topics of training and exercise science reveals some basic insights in the conceptual background of performance analysis: • The purpose of training at least in elite sports is preparation for competition. • Success in competition is the ultimate criterion for every action taken in training. • The demands of performance in competition are the primary source for identifying the required levels of athletes’ capabilities. • Certain levels of capabilities are prerequisite for optimal performance in competition (performance prerequisites). • The required levels of athletes’ capabilities act as targets for training. • Training impacts on athletes’ capabilities with the intention to provide or optimize the required levels.

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A first conclusion on the nature of training may be derived from this scheme: The basic function of training, preparing athletes for competition, may be achieved only indirectly via impacting on the required levels of athletes’ capabilities. Only these capabilities have a direct impact on behaviour in competition, for example, my jumping capability allows me to accomplish a header after a corner. Using a belligerent metaphor, one could say: In training the weapons for the battle are sharpened, but the battle is decided on the battleground. This holds true to an even larger extent for game sports compared to other groups of sports as will be explained in the section on the nature of game sports below. Anomy in the Role of Coaches

Considerations on the subjects of training and exercise science (Fig. 1.1) and especially examining the interactions between them may also be useful for other purposes, for example, for understanding the role of coaches. Acknowledging direct impact of training on capabilities but not on success in competition refers to a basic problem in the role of coaches. The daily work and main responsibility of coaches is to organize training. On the other hand, the criterion mostly used to evaluate the quality of training is success in competition. This mismatch is a characteristic feature of the coach’s role: he is evaluated on behalf of a criterion that is not directly under his control. In sociology, a conflict between acknowledged aims and the means at disposal is called “anomy” (Merton 1949). Analysing the relations between the three big topics allows for identifying two main tasks of performance analysis (PA): First, PA has to identify determinants of success in competition and to support conclusions on required levels of athletes’ capabilities. Second, PA has to analyse behaviour in competition to identify strengths and weaknesses of the athletes. The latter is conducted with regard to deriving practical recommendations for training. These two different tasks give rise to the important distinction between practical and theoretical PA being introduced in the next paragraph.

1.1.3 Theoretical and Practical Performance Analysis One of the most important conceptual achievements in PA is the distinction between its two sub-disciplines: theoretical performance analysis (TPA) and practical performance analysis (PPA; Lames and McGarry 2007). Distinguishing between TPA and PPA does not only give an answer to most of the critical questions that were discussed in the last years in PA’s practical impact debate (see Box “The practical impact debate”) but also provides guidelines for the scientific founding of practical action in scientific as well as in practical contexts. The necessity of two different

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sub-disciplines of PA will become obvious immediately after determining precisely their respective aims and methods. Theoretical Performance Analysis

Theoretical performance analysis (TPA) aims at investigating the structure of sports performances. It searches for general laws describing behaviour in different sports (action and movement profiles, performance level comparisons, etc.) or quantifying the impact of determinants on competition behaviour, for example, winning or losing. In addition, a task of TPA is to find adequate models for sports competition reflecting its specific nature. Determinants of competition behaviour may be found in competition (e.g. time line, score line), in environment (e.g. weather, pitch conditions), or in athletes’ capabilities (e.g. endurance, strength). Finding an adequate model for the nature of a sport is a more demanding task in game sports than in other groups of sports as will be explained below. In order to attain general laws, TPA applies typical methods of behavioural basic research. Large, representative samples are used to ensure capturing typical structures of the game. Statistical evidence is looked for giving confidence intervals for behavioural norms as well as significance levels and effect sizes for law-like relationships between determinants and outcome. Using a reductionist approach diminishes the complexity of the subject under investigation and allows pointing out clearly the relationship under investigation. Recently, in addition to methods from behavioural research, methods from computer science are used to solve this task, for example, machine learning approaches. Chapter 4 is dedicated to a detailed presentation of TPA including the search for adequate models for game sports in the realm of dynamical systems theory. Practical Performance Analysis

Practical performance analysis (PPA) comprehends all performance analysis activities conducted in sports practice. It aims at supporting practice to achieve the respective goals of the club/team/athlete. In particular, performances in competition are analysed, that is, competitions of one’s own team to identify strengths and weaknesses as well as recent matches of the next opponent to develop a match strategy but also training exercises and athletes’ abilities. The general aim is to generate useful recommendations for practical action (practical impact). Methodologically, the analysis of particular competitions means that single-case studies are conducted. The research strategy applied is close to formative evaluation using scientifically approved methods, for example, observational systems or motor tests, to assess behaviour in competition and training. Conclusions are not drawn

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6 Table 1.1  Comparison of TPA and PPA Aim Research strategy Design Samples Criterion of effectiveness Qualitative methods Accounting for context Setting

TPA Establish general laws Basic research Descriptive studies Large, representative Statistical evidence Prohibited Reductionist approach Science, university

PPA Support for practice Evaluation research Process evaluation Single cases Practical usefulness Important Comprehensive approach Sports, sports facility

from statistical laws but from sound reconstruction of behaviour and interpretations relying on a broad information based on the whole relevant context, for example, game situation, opponent, one’s own tactics, preparation, motivation, and injuries/ rehabilitation. In Chap. 5, dedicated to details and methods of PPA, it will be explained why qualitative methods play an important role in this process. In the aspects discussed above and others (see Table 1.1), there are differences in many respects between TPA and PPA. These differences in aim, method, sample, setting, and design make a clear distinction more than appropriate. Especially what scientific methodology is concerned, differences cannot be underestimated. The distinction between TPA and PPA as two different research areas promises also to clarify many problems discussed in the so-called practical impact debate. The Practical Impact Debate

In 2013/2014, some papers were published that discussed the practical usefulness of PA results. Carling (2013) made clear that for practical purposes, PA findings on physical performance are mostly not relevant, for example, they fail to establish a link to success, prove significant but hardly relevant positional differences, and mostly fail to measure the degree of fatigue. He pleads for more pragmatism using results of PA in practice. Drust and Green (2013) state that although there is great progress in PA research and dissemination in sports practice, “the data available is frequently descriptive in nature and … of little impact in the ‘real world’” (p.  1380). They see a main reason for this in an insufficient distinction between basic and applied research and advocate for a research model specific to applied problems in sports science. Some issues earlier, Mackenzie and Cushion (2013) gave a review on research in PA and stated some general methodological problems such as sample sizes, operational definitions, and dealing with complexity. Also, they put the question of practical utility of PA results. They note that there has been not much research on PA in practice done yet and mention that a naturalistic and qualitative framework would be most appropriate here. Finally, Carling et al. (2014) wrote a letter to the editor commenting on Mackenzie and Cushion. They gave some explanations for the problems of

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maintaining methodological standards in PA and also plead for an opening towards PA in practice as a research subject of PA as scientific discipline. Of course, the practical impact debate is not finished yet. In a recent study on the use of PIs in practice, Herold et al. (2021) found out that old-fashioned, easy-to-observe PIs such as shots on goal are still dominantly used in practical settings. Finally, one must mention that there are areas in PA for which the ultimate aim of improving practice is not obligatory anymore. Examples are results of PA being used “only” for media enhancement or when data from PA is used for demonstrating the capabilities of visualization or artificial intelligence applications. Many of the issues brought up in the practical impact debate could be solved partially by omitting misunderstandings of the nature of scientific findings but most important by acknowledging the differences between the two sub-disciplines of PA, TPA and PPA! Nevertheless, it would create a wrong impression if these two areas were perceived as being totally independent. First, people engaged in PPA should have and usually have an education in TPA. Ideally, during their education, they are made aware of the differences between practical and scientific work concerning both conceptual and more hands-on aspects of each area. Second, there are specific relationships: Results of TPA provide a valuable background for doing even more informed PPA by giving, for example, a normative framework for analyses of one’s own team. On the other hand, because of its close connection to the “real world”, PPA should be the place where new hypotheses, new explanations, and new determining variables appear that are candidates for an investigation within the framework of TPA.

1.1.4 General Model of Sports Performance Structure Scientifically founded PA should start with a solid idea, concept, or model of its subject, that is, performances in sports. In Fig.  1.2, it is illustrated that athletes’ performance in competition is of top interest. Compared to environmental factors, the capabilities of the athletes are the primary influencing factor from a practical point of view, because they may become targets of training as shown in Fig. 1.1. In the following section, the model will be introduced more in detail before it will be tailored to game sports. Competition comprises the overall result as well as parts of performance. Parts of performance are obtained by the following: • A partition of the overall performance such as intermediate times adding up to the final performance in a running or racing event • Recording actions in competition, such as action profiles in a match or a free section in gymnastics, action chains leading to successful attacks or actions with their quality of execution

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Fig. 1.2 General structural model of sports performance

• Recording positions and derived aspects of competitions, such as movement kinematics, movement profiles, tactical configurations, and position-based mathematical models of performance in competition The capabilities of an athlete contain the relevant performance prerequisites for being successful in competition. A general systematics (Hohmann et al. 2020) distinguishes athletics, technical skills, and tactical capabilities. Finally, we have environmental determinants, whose influence on competition is very much dependent on the type of sports, for example, in outward bound sports such as skiing, adapting to the changing environment is quite decisive, whereas in sports with more closed skills such as gymnastics taking place indoor, the environment is held constant by standardized equipment. As mentioned above, a concept of PA just giving a description of competition behaviour would only give limited support to practice. It is of major importance to provide explanations of competition behaviour on the two levels shown in Fig. 1.2, environmental conditions and athletes’ capabilities. Identifying influential aspects of the environment such as opponents, home/away matches, spectators, referees, weather conditions, properties of sports equipment, and others contributes to the background knowledge of the sport or the event. Athletes’ capabilities play a different, even more important, role. Whereas environmental factors have to be more or less accepted and a good preparation should anticipate their influence on match day, athletes’ capabilities become, once identified by PA as explanation for inferior performance, target of training, and this is the most important link between PA and practice. Though arguing for a wide concept of PA, limits are reached when athletes’ capabilities in turn are subject to explanation. Typically this is done by identifying underlying determinants such as oxygen uptake and metabolism as explanation for

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endurance capabilities. Identification and diagnostics of determinants of endurance capabilities are clearly the realm of physiology. In the same vein, the origin of deficits in technical and tactical capabilities must be identified by psychologists, for example, motivation, vigilance, or aggressiveness, or by movement scientists when talking about determinants for perception, skill execution, and decision-making capabilities. Exercise science, on the other hand, deals with the search for appropriate interventions in training to cure these deficits. The Structure of Performances and Ecological Psychology

From a scientific perspective, it is very interesting and challenging to embed the frame concept for the general structure of sports performances in Fig. 1.2 into the theory of ecological psychology. The different types of Newell’s constraints (1986) fit excellently into this scheme: task and environmental constraints are nearly literally contained. Also, the notion of athletes’ capabilities as organismic properties constituting constraints and affordances is appropriate. Whereas weaknesses in an athlete’s performance may be explained by his personal organismic constraints, strengths in competition are most likely to be associated with structural organismic affordances. In Chap. 4 on TPA, ecological psychology will be presented in detail and also a critical discussion of its suitability as theoretical framework for PA may be found there.

1.2 Performance Analysis in Game Sports Since this book is dedicated to performance analysis in game sports, it is evident that commonalities in the structure of performance of game sports are of interest. Even within game sports we find sub-groups with (to a certain degree) different performance structures. The nature of game sports has important consequences for methods and concepts of PA in game sports. Finally, typical approaches of PA in other groups of sports will be mentioned.

1.2.1 The Nature of Game Sports What is a game sport? The term is not very common in English, where, for example, expressions like “team sports” or “individual sports” are more in use with team sports sometimes implicitly taken for game sports. But obviously, there are sports run by teams (rowing, relays) not being games and most net games are individual sports. The term “formal games” (consisting of net games, invasion games, and striking/fielding games) created by Read and Edwards (1992) and adopted by Hughes and Bartlett (2002) and Hughes and Franks (2004) was never popular and is nowadays reserved for serious games and eSports. Moreover, since PA deals also

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with other sports than game sports, it is a good start to look for a definition of these sports when aiming to point out the peculiarities of PA in game sports. Searching for a more apt definition of game sports, it is helpful to consider them as a group of sports (Aristotle’s genus proximum) with special characteristics (differentia specifica). From a PA perspective, it is convenient to distinguish groups of sports according to their leading determinant of performance. There is a suggestion by Thiess and Schnabel (1976), two leading sports taxonomists in GDR, comprising five groups of sports, that is, endurance and strength sports, game and combat sports, and technical sports, the latter with the sub-groups of artistic and drivingflying-shooting sports. What is the typical property of game sports as a group of sports? There is an early answer in the author’s doctoral thesis: Definition of Game Sports

“Game sports are a group of sports, where two parties (single, double, team) engage in a dynamic interaction process that is established by the parties in simultaneously trying to reach their aim and to prevent the opponent from reaching his one; the aim in a game sport is a symbolic action” (Lames 1991, 33). Explanations: • The definition follows the classical structure: Game sports form a group of sports with a distinguishing property from other groups of sports. • The distinguishing property of game sports is given by the specific way of interaction between the (two) parties. • The specific way of interaction is given by the simultaneous striving of the parties for their aim (offence) and by preventing the opponent from reaching his one (defence). • The only way to distinguish game sports from combat sports is connected with the different nature of the aims in these two groups of sports. While in combat sports the aim is a manipulation of the opponent’s body (hitting, kicking, stabbing, throwing on the mat, etc.), aims in game sports are symbolic acts performed with the game object (e.g. to throw the ball in a basket or to hit a winner). According to Read and Edwards (1992), three sub-groups of game sports with variants of the typical interaction process are distinguished: 1. Invasion games such as football codes (soccer, rugby, American, Australian, and Gaelic football), handball, basketball, and several others: The two teams are on the pitch at the same time (different: American football with only the special teams facing each other on the pitch!). The aim is to bring the game object (the ball) into a certain space, typically a goal or a basket, but also an “end-zone” marked by a line or through a “goal” built up by two posts and a bar. There are phases of ball possessions either finishing with rule-based events (goal, shot at goal, offensive

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foul, out of bounds, and others) or turnovers. There is physical contact between the two parties, and we typically have a back and forth on the pitch, because the players group themselves more or less around the playing object. 2. Net games such as volleyball, tennis, table tennis, and squash (the net is a wall here!): The game is made up of rallies ending with a point for one party. Rallies consist of alternating strokes (different: volleyball, a team net game!) by the two parties. The aim of the rally is to hit a winner or to force the opponent to hit an error. The parties being separated by a net (different: squash!) are not in physical contact. The sequence of alternating actions is the typical interaction in this group of game sports, making something such as “alternating strokes games” a better (there is a net in football as well!), but inconvenient, denomination. 3 . Pitcher/batter games such as baseball, cricket, and softball: In these game sports, we find a special interaction structure given by the fact that the aims of the teams on the pitch are not the same. For example, in baseball, the batter’s team tries to score runs and the pitcher’s team tries to avoid this and getting players out. These roles are changed in the second part of an inning. In the light of our definition, the teams are simultaneously striving for their respective aims, but these aims are different ones over certain periods of the match. Summing up these considerations on the nature of game sports, one may state that their constitutive property is interaction. From this basic statement, some further conclusions on their nature with important consequences for PA may be drawn: Achieving a symbolic aim against the resistance of the opponent requires a plan, a strategy how to do this. Such a plan has to take one’s own and the opponent’s capabilities into account. These plans may also be called the tactics of a player or a team, showing that in game sports, tactics is of outstanding importance compared to other groups of sports. In the case of team games, tactics is even more dominant since within-team cooperation demands for an additional dimension of planning or tactics. With respect to success, one may state that if a team makes an unsuccessful move, it will very likely try a different move to avoid failure thereafter. On the other hand, if there is a successful move or action, the opponent has every reason to change his behaviour. In sum, it is very unlikely to find a constant playing pattern all over a match; behaviour changes over time, and it is dynamic! Taken together with the constitutive aspect of interaction, the nature of game sports is best captured by treating them as dynamic interaction processes with emerging behaviour. This concept was suggested by several researchers in the area, already (e.g. Lames (1991), Passos et al. (2011)). The consequences for PA may hardly be underestimated. For example, the frequent practice in PA to describe a performance with summative statistics on the frequency of a certain behaviour during a match (“stats”) and taking it as a measure of the capability of one player or one team is a questionable method in the light of this concept, as the first practice does not reflect dynamics and the second does not reflect interaction! The resulting behaviour in a game perceived as a dynamic interaction process is only weakly connected to the levels of abilities of the players. It spontaneously

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Fig. 1.3 General structural model of performance in game sports

emerges from the interaction and is not repeatable and hard to predict (see Box “Where is the ball 10 s after a corner?” in Chap. 4). Emergence, the development of new structures from complex interactions between sub-systems, is a crucial concept for understanding game behaviour. This concept has already been introduced earlier (Kelso 1995; Glazier 2010; Duarte et al. 2013), and PA is still looking for appropriate methods to deal with it (see Sect. 4.3.1 in Chap. 4 on TPA).

1.2.2 Basic Problems of Performance Analysis in Game Sports Reflections on the nature of game sports like in the last section have far-reaching consequences for PA as already denoted. The general model for a performance in sports (Fig.  1.2) has to be adapted to reflect the conditions in game sports. In Fig.  1.3, the observable behaviour in competition is depicted as the result of the dynamic interaction of the two sets of athletes’/players’ capabilities. A problem caused by the nature of game sports is the fact that we only can “see” the result of the interaction process between the parties on the pitch and we do not directly perceive the capabilities of the parties. On the other hand, drawing inferences on players’ capabilities is a most important aim of PPA. In the light of the previous considerations, it is no surprise that it requires specially designed methods that allow looking behind the curtain of the interaction process (see Chap. 5 on PPA). Lames and McGarry (2007) compared the structure of performance in a game sport with the one of a 100 m sprint. The time scored in a 100 m sprint may be interpreted as an expression of the sprinter’s potential. It may even be conceived as a realization of his capabilities at the occasion of the performance under scrutiny. It is obvious that there is a very close relationship between his capabilities and his performance. It is a comparatively easy task for PA to identify strengths and

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weaknesses of a sprinter given the kinematics of his 100 m performance, for example, with reaction time, peak acceleration, peak velocity, and sprint endurance index. This does not hold true at all for performances in game sports. Since observable behaviour emerges from the dynamic interaction with the opponent, PA in game sports has to solve two basic problems: taking into account the changes in performance over time of a match and estimating the performance taking into consideration the behaviour of the opponent. Performance Indicators

As pioneers of performance analysis already mentioned (in Germany: Hagedorn 1972), performance in game sports is expressed by the frequency of actions either directly associated with reaching the aim of the game, for example, scoring or preventing a goal, or being supportive to this. Therefore, performance indicators, being single or combined action variables that describe some or all aspects of performance (Hughes and Bartlett 2002), are used to assess performance in game sports. O’Donoghue (2010) added necessary conditions for a variable becoming a performance indicator borrowed from business and engineering: it must have been proven to be a valid indicator for an important aspect of performance and possess three metric properties, namely, an objective measurement procedure, a known scale of measurement, and a valid means of interpretation. Confronting this notion of performance indicators with the nature of game sports, both constitutive properties, dynamics and interaction, create problems. A typical performance indicator consisting of (normalized) frequencies of actions in a match is first, a summative statistic and as such static and not dynamic, and is second, attributed to the performance of one player or one team and thus does not reflect the interaction. Sampaio and Leite (2013) mention this problem and optimistically state that continuing development is required in the forthcoming years, whereas the author sees it as a basic “dilemma of game sport research” (Lames 1991) and consequences are to be drawn concerning basic concepts of research strategies and methodologies to be explained in the remainder of this book. Of course, classical approaches in PA have perceived these problems as well. One way of dealing with the problem of dynamics is to refer to the “law of large numbers” that will cure dynamic changes in behaviour based on a large number of observations. This might seem to be acceptable in TPA, but in PPA, we are interested in the “true value” of a performance of one player in one game. This is one reason why in PPA qualitative research methodology is applied. What the influence of opposition is concerned, a suggestion in TPA is to introduce opponent’s strength as a confounding variable (O’Donoghue 2009; Lago 2009). One must state though, that this procedure is far away from analysing behaviour emerging from the interactions between the opponents. Instead, emergence

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means the situational mutual shaping of behaviour, which is hardly accounted for by introducing another summative, static variable “level of opponent”. For the purpose of PPA, a much deeper analysis of how the qualities of the opponent impact the performance of one’s own players is required bringing qualitative methods with in-­ depth reconstruction and interpretation into play (see Chap. 5 on PPA). Finally, it is worth noting that the impact of interaction and dynamics on performance in game sports varies between the different game sports. In net games, there is a tight interaction induced by the alternating sequence of strokes. Each stroke, except service, can be seen as highly influenced by or as an answer to the prior stroke. For a service, we must acknowledge that its impact strongly depends on the qualities of the return player as well. In invasion games, trying to invade a certain space against a defence implies strong interactions, too. In addition, it is maybe a good idea to distinguish between high-scoring games (basketball, handball) and low-scoring ones (soccer, field and ice hockey). In high-scoring games (basketball and handball roughly show around 40% successful ball possessions), attacks are more successful, and points are scored on a regular base with fewer opportunities for the defence to interfere to a well-­ planned and executed attack. In low-scoring games though, we have additional components that make the success of attacks unlikely, such as chance and instability or chaotic phenomena (see Chap. 4). In pitcher/batter games, actions are strictly sequential and frequently analysed in isolation (pitching game, batting game). Apart from the (crucial) pitcher-batter interaction, success depends to a great extent on individual skill. This means that in this group of sports, where performance is made up of sequential, rather independent actions (pitching, batting, catching, running), the connectedness of game behaviour and individual skill is comparatively close, and interaction is lower than in the other two families of game sports. In this light, it is not a surprise that the longest tradition in recording summative static PIs is found in baseball.

1.3 Approaches in Performance Analysis Performance analysis has a rather long history with respect to disciplines of sports science. Nevertheless, only in recent years technological developments have increased the potential of PA dramatically. This may be documented with the number of publications found in Google Scholar with the keyword “performance analysis in football” given in Fig. 1.4. There is an exponential growth until 2013 and a levelling off at a high level since then. The modelling method of using regression functions is discussed below in Sect 4.2 in Chap. 4. In the remainder of this paragraph, historically and actually relevant approaches of PA are described.

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Fig. 1.4  Hits in Google Scholar for “Performance Analysis Football”; from 1990 to 2013, an exponential trend fits data with R2 = 0.998

1.3.1 Classical Performance Analysis The term “classical performance analysis” is chosen here, because this is a relatively old approach of performance analysis but a basic one for more recent developments. It was established in the late 70ies/early 80ies of last century in the form presented here by Manfred Letzelter from Johannes Gutenberg University at Mainz, Germany. He merged analytical models on the structure of performances in sports with empirical research methodology, which was a big achievement for applied sports science in these times. There are three main characteristics of this approach: • Holistic perspective: All relevant parts of a sports performance as well as all relevant performance prerequisites are of interest to classical performance analysis. • Applied perspective: The ultimate aim of conducting a study under this paradigm is to generate useful information for training, specifically a list of performance prerequisites each weighted according to its impact on the complex performance. • Empirical perspective: The structure of performance is established in a strictly empirical way, that is, by operationalization, measurement, and statistical testing of the single elements of a sports performance and their relations. In his seminal paper, the method of classical performance analysis was described in three steps (Letzelter and Letzelter 1982):

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Fig. 1.5  The general structural model for sports performances. (With permission of Limpert-­ Verlag from Hohmann et al. (2020))

1. Theoretical modelling: A hypothetical structural model of the performance is developed using a general model (see Fig.  1.5) which is adapted to the sport under consideration by identifying the variables that should be addressed in a study on this specific sport. This theoretical model includes the complex performance, hypothetically relevant parts of this performance and hypothetically relevant performance prerequisites. 2. Examination of empirical structure: After the operationalization of the variables in the hypothetical model and their assessment in a large, representative sample for a certain sports setting, the empirical relations between and within the model components are studied with statistical methods, using, for example, correlation and regression methods or factor analysis. 3. Identification of targets for training: The impact of each variable on the complex performance is studied, and a “priority list” is generated giving the most important parts of performance and the most influential performance prerequisites according to weights obtained, for example, from multivariate regression methods or from structural equation modelling. A general structural model for sports performances is depicted in Fig.  1.5. It resembles very much the structure presented in Fig. 1.2, just giving more details and illustrating the idea of a “performance pyramid” with complex performance as the top and the lower levels being prerequisite to the upper ones. There is a distinction made between specific and general performance prerequisites with the former meaning stable properties needed directly in the execution of the sport, whereas the latter focus on determinants of these properties at a more general level, for example, a marathon runner needs a specific marathon endurance, which in turn depends on some physiological properties.

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Fig. 1.6  Empirical structure of performance in cross-country skiing. (Reproduced with permission of Philippka Verlag from Ostrowski and Pfeiffer (2007))

An example for step 2 of the above agenda of classical performance analysis, the examination of the empirical structure, is given in Fig. 1.6. This study on Nordic or cross-country skiing (Ostrowski and Pfeiffer 2007) shows the empirical relations between four levels of the general model. The complex performance is given by the running time on a cross-country skiing trail. Parts of performance are given by the time used for parts of the trail with different slopes (uphill, flat, downhill with and without use of arms). The level of specific performance prerequisites is represented by three capabilities, running endurance on a skiing treadmill and strength endurance on an arm-pull ergometer for diagonal and parallel pulls. Finally, physiological parameters such as heart rates, watts per kilogram bodyweight, and VO2 at certain intensities specified by lactate levels in the blood are given representing the level of general performance prerequisites. The small figures depicted in Fig. 1.6 show the respective R2-values of a regression with all variables from the lower level as independent variable and the construct on the higher level as dependent variable. One may see, for example, that skiing treadmill endurance performance is more determined by physiological variables than arm pull strength endurance obviously requiring specific skills. On the next level, it is interesting to note that only uphill and flat parts are substantially influenced by the capabilities under examination and that we have a substantial amount of unexplained variance. On the other hand, the time needed for these parts

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of the trail determines to a great extent the overall running time, with the exception of passive downhill that shows almost no impact. It becomes obvious from this example that results of a study performed under the paradigm of classical performance analysis create valuable background information for training, especially how to distribute efforts and resources to the many parts of the system. Despite its conceptional merits, there has been some criticism on classical performance analysis. First, there are some general methodological issues. Empirical models are based on empirical samples, that is, the athletes that happen to be in a sample “create” in a way the resulting model of the structure of performance. At this point, we run into the general problem of samples in top-level sports: at the very top, the samples are necessarily too small to allow for decent statistical evaluation. Especially when a differentiated performance model with many variables is to be filled with empirical content, this becomes an almost insurmountable problem. Ostrowski and Pfeiffer (2007) built their model on n = 31 athletes and several (nine) single regressions are run, because a more appropriate structural equation model does not work at this ratio of sample size vs. number of variables. Other critical aspects are the variables included in the studies. The claim of classical performance analysis is that all hypothetically relevant variables are included, which is very demanding. In practice, the selection of variables is less determined in a deductive manner, that is, all variables that are hypothetically relevant are included, but rather in an inductive way, that is, the variables one has at hand are included in the study. Ostrowski and Pfeiffer (2007) used the results of three tests applied in routine testing in Nordic skiing as representation of the performance prerequisites. Maybe the perceived gap with respect to explained variance between performance prerequisites and performances in different parts of the trail is due to missing skill or explosive power tests at the level of performance prerequisites. Another methodological concern is associated with the way statistical methods treat independent and dependent variables. The linear relationship typically assumed and assessed by traditional statistical methods may not be adequate for modelling some well-known relationships between performance prerequisites and performance, for example: • Threshold concepts, i.e., a certain level of a performance prerequisite that is to be achieved with no additional improvements beyond this level, • Optimal levels, i.e., when not enough and too much of a prerequisite both have negative consequences for performance, which is, for example, the case with body height in several sports. In addition to these rather technological problems, there are also conceptual issues in the criticism of classical performance analysis: • A covariation between variables does not reveal the basic mechanisms that are responsible for the statistical covariation. • Cases of biased correlations are discussed in research methodology, for example, correlations induced by moderator or mediator variables.

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Knowing the underlying mechanisms would be very helpful for practice for designing training interventions. In the same vein, one must admit that empirical results frequently show ambiguities, for example, is it really justified to devote more resources to a performance prerequisite that has a common variance of R2 = 0.55 with a complex performance than to one that correlates with R2 = 0.53, especially given the methodological problems mentioned above? The most severe objection against classical performance analysis comes from its basic assumption that performance is determined by the performance prerequisites of the athletes or teams. As explained in the paragraph on the nature of game sports above (see Fig. 1.3), this is not the case for game sports and combat sports, where performance must be considered as the result of the interaction process between the two parties. Moreover, aspects such as dynamics and emergence, both being constitutive of game and combat sports, are not an issue in classical performance analysis. Taken together, classical performance analysis was a great innovation for performance analysis at the time of its foundation. It was a big support in striving for academic dignity of applied sports science that was at stake in these times. For game and combat sports though, this is a conceptually inapplicable approach. Its merits are to be seen in individual sports, where overall performance is to a great extent determined by performance prerequisites, for example, track and field or swimming disciplines. Methodological improvements, for example, capturing nonlinear relationships with neural network methods or finding design solutions for the sample problem of top-level sports, will result in further valuable contributions of classical performance analysis to applied sports science.

1.3.2 Notational Analysis The title of two textbooks “Notational Analysis in Sports” (Hughes and Franks 1997, 2004) gave the name to a very early and influential school of performance analysis predominantly located in the UK. Hughes and Bartlett give a definition: “Notational analysis is an objective way of recording performance, so that critical events … can be quantified in a consistent and reliable manner. This enables quantitative and qualitative feedback that is accurate and objective” (2008, p. 9). From this definition, two aspects can be derived being characteristic for notational analysis. First, it is about event detection which is used to be the only relevant method of performance analysis for a long time. Only later, technological progress made position detection available for performance analysis, which since then is the second standard method in PA (see Chaps. 2 and 3 addressing these standard methods). The second aspect of interest is the purpose of notational analysis, which is seen in providing feedback about the events that took place in competition. Emphasizing the feedback function of notational analysis may be due to the impact of two research traditions, first, studies on coaches’ ability to correctly reproduce a match, and second, the investigation of motor learning processes in movement science.

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In very early studies, Franks and his co-workers were able to demonstrate that coaches’ memory of what had happened on the pitch is far away from being flawless (Franks and Miller 1986, 1991) and, in addition, coaches tend to be very confident in their judgements (Franks 1993). These proven perceptual weaknesses of coaches watching a match of course gave rise to a demand for accurate and objective feedback which was met by notational analysis. The second source of demand for feedback is to be found in movement science, where it is unanimously acknowledged that feedback, for example, intrinsic or extrinsic feedback, is essential for any motor learning process. Taking training in game sports as such a learning process, the importance of feedback becomes obvious. The position taken in this book is that feedback is of course important, but in Chap. 5 on PPA, the restriction on just giving feedback will be given up. In addition, the differences between a motor learning process and cognitive learning processes will be mentioned there with respect to consequences for the need and the structure of feedback in PPA. Instead of being restricted to merely giving feedback, the position taken in this book opens performance analysis to the derivation of practical measures as well. In notational analysis, deriving these measures is an exclusive task of the coach as it becomes clear in their early concepts of the coupling of athletes’ performance and practice (Maslovat and Franks 2008). The restriction on giving feedback made it hard for notational analysis to deal with some specific conceptual issues of game sports. The distinction between behaviour in competition and players’ capabilities, which is essential for practical performance analysis, is not important when one just aims at describing matches. Also, dynamics and interaction in game sports were initially not of interest to notational analysis and the search for summative PIs for the whole match prevailed (Hughes and Bartlett 2002; Nevill et al. 2008). In contrast to within-match dynamics, which was treated more or less only via modified score lines (Hughes 2004; Hughes et  al. 2013), match-to-match variability became more an issue (Hughes et al. 2001b). The desire for PIs that had “stabilized,” i.e., that match-tomatch fluctuation of PIs is below an acceptable level allowing to speak about a “normative profile” was expressed. A normative profile is required when inferences about strengths and weaknesses are to be made. A considerable number of studies were conducted to determine empirically the number of matches required to obtain a reasonably stable estimate for the mean values of PIs. O’Donoghue and Ponting (2005) made clear that this question could be answered also analytically by a probability estimation assuming the law of large numbers in statistics. It is interesting to see that researchers who have great experiences as players, coaches, or performance analysts and for sure have an excellent understanding of the structure of performances in game sports fail to adopt the corresponding concepts in their scientific work. Nevertheless, notational analysis is to be acknowledged as a pioneering approach in PA that has remained very influential ever since.

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1.3.3 Sports Analytics In US sports, especially in the professional clubs of the big five leagues (NBA, MLB, NFL, MLS, NHL), there is a long tradition of analysing sports data. The so-­ called sabermetrics (SABR, Society for American Baseball Research) in baseball, for example, go back until the early 1980s. They replaced the mere accumulation of baseball statistics, which may be traced back for baseball until 1845, when the box score was introduced (Lewis 2003). Interestingly, more advanced PIs from sabermetrics were first appreciated by fans and media and became a successful business model, for example, for STATS (Sports Team Analysis and Tracking Systems) Inc. and ESPN (Entertainment and Sports Programming Network) before the clubs took notice of it and applied it in their daily work (Lewis 2003). A breakthrough in this direction was the book Moneyball by Michael Lewis describing the successful use of sports analytics by manager Billy Beane from the Oakland A’s. Beane managed to arrive at great decisions, for example, in drafting new players, giving his team a position in competition that was much better than to be expected from the financial resources available. The standard book on sports analytics is Alamar (2013). He describes sports analytics as the search for patterns in sports data to optimize decisions in sports. A distinguishing feature of sports analytics in comparison to the two other approaches mentioned above is that it is not dedicated or restricted for use in sports practice (Miller 2016) but maybe even more relevant to media and club management (Fried and Mumcu 2017). In addition, there was hardly any formative involvement of sports science in the development of sports analytics, instead highly qualified experts from other sciences, especially informatics (typically being nerds in their respective sports), applied their knowledge and methods to sports data. Taken together, sports analytics has become a giant field of business (Harrison and Bukstein 2017; Link 2018). Link (2018) gives an impressively long list of stakeholders in sports analytics with their specific interests in it. This list contains large businesses that pursue special interests in sports analytics: • Media, entertainment industry: Sports analytics is used for media enhancement, that is, making media products more attractive. This gives a competitive advantage directly by increasing the audience, that is, the number of customers, and indirectly by becoming more attractive for advertising. • Data providers: Companies are engaging in recording match data and producing PIs with the aim of selling it to clubs, leagues, media, or fans. • IT companies: Big IT companies take sports analytics as showcases for demonstrating their capabilities, for example, SAP with their sports information system “Sports one” or Siemens with their digital twin initiative originally designed for industry 4.0. • Event management: Sports analytics is used for advertising matches, for in-event information enhancement, and for social media contacts to potential spectators.

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• Betting industry: Optimizing betting odds relies very much on sports analytics, but also betting frauds may be detected with it. • E-games: The e-game industry uses sports analytics to make tactical behaviour in their games as realistic as possible and/or to map individual or team characteristics onto their avatars. Besides the interests of business in sports analytics, recent developments in information technology have changed the way how sports data are used for decision support. Methods and concepts of other areas of analytics, including business analytics, are made available to sports analytics (Blobel and Lames 2020; Jayal et al. 2018). Machine learning and artificial intelligence (AI) (Araújo et  al. 2020) will have even more impact in future real-world performance analysis. These aspects will be dealt with in Chap. 6. Nevertheless, Alamar (2013) claim that good information cannot be produced from bad data holds true for sports analytics as well as for any other application field. This also means that scientifically founded domain knowledge, the target of this book on concepts and methods of performance analysis, is indispensable, no matter which kind of analytics will be used in the future.

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Action Detection

Historically, recording events in sports competitions is most likely the earliest activity in PA. In this chapter, action detection in PA is put in the tradition of behavioural research as a relatively recent development. As notational analysis may be seen as a special case of behavioural observation, this link opens a broader perspective on the issue. All observational methods share two important properties: they are limited to the perceivable surface of behaviour and the measurement instrument is the human observer. Based on these commonalities, a paragraph is dedicated to the design of observational systems in sports. Dealing with the central methodological issue of agreement between the human observers requires introducing some special techniques that maybe are not common in a typical methodological education in sports science. Finally, examples of observational systems for action detection in sports are given. One might ask why to treat observational methods in a special chapter in a textbook on performance analysis in the age of data providers, action feeds, and artificial intelligence. The simple answer is that one is relying on competency in these methods in case there is a deeper interest in details than provided by action feeds or when there is no coverage by data providers either because of a too low performance level or in game sports that are not commercially attractive for data providers. Moreover, pursuing an AI approach in sports does not absolve from testing data quality, in the case of event data typically applying observational validation methods.

2.1 Assessment of Behaviour Textbooks of notational analysis often do not mention that methods and designs of notation systems for sports analyses must be seen as a special case of observational methods. This perspective, though, allows making use of decades of methodological developments and considerations that have led to a complex body of knowledge.

© Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5_2

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Traditions of Observational Studies

The big tradition of observational methods in behavioural sciences starts with the advent of behaviourism in the first decades of the last century (Watson 1913). Behavioural responses to stimuli were investigated typically in laboratory settings rendering control in experimental studies of behaviour. This was the cradle of observation as a scientific method. Another branch developed investigations in sociology focusing on examining behaviour in natural settings. Famous examples are Margarete Mead (1928) introducing the ethnographic method; the Marienthal study on unemployment by Jahoda et al. (1933); and the Chicago school of sociology conducting among others studies of the “street corner society” (Whyte 1943). A very important development dates back to 1950 with Bales’ “interaction process analysis” introducing category systems for observing behaviour in small groups. In pedagogical research, this approach was extended to the analysis of classroom behaviour (Flanders 1960) using the time interval method. Most of the actual problems we are struggling with in observational systems designed for action detection in game sports are already dealt with in these studies, for example, observer agreement, observer training, and design and structure of observational systems.

On the other hand, when comparing the observational task in game sports to those in other settings, we find favourable conditions in “our” area. In a typical natural setting of behaviour research, for example, the unemployed in the Marienthal study or street scenes in the slums of Chicago, observations are idiosyncratic in nature. We do not know why an individual appears at this place at this point in time nor the intention pursued with the behaviour, not to speak about the person’s preferences for different options of behaviour. From a methodological perspective, this makes it difficult to define a category system for behaviour and even more for action chains, because sequences are hardly predictable. Almost the opposite is true for behaviour observation in game sports: • Matches have a well-defined temporal structure; beginning and end are well known and even indicated for a public audience. • Actions are samples from a well-defined set of possible actions that are in principle all known beforehand. • Matches take place at a certain location with well-defined extensions and are easy to observe (the location is even constructed for convenient viewing!). • Each team has a clearly defined aim and each player plays a specific, but in principle well-known role to achieve it. • Expected behaviour in most situations is well known, for example, we know what a goalkeeper and the shooter should do in a penalty situation.

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Behavioural options are comparatively constrained by rules, for example, how to move (with) the ball, which zones of the pitch may be entered, and which kind of behaviour is termed fair or foul. In sum, we find comparatively very favourable conditions for observational methods in game sports. This is the reason why observational systems have proven to be very appropriate and successful methods in analysing performance in game sports. Specific adaptations of observational methods from behavioural sciences to the demands of performance analysis in game sports were made already some decades ago, for example, in Spain by the group around Anguera, in the UK by notational analysis (Hughes and Franks 1997, 2004), and in Germany by the author’s monograph on “Systematische Spielbeobachtung (systematic game observation)” from 1994. Anguera started off from behavioural assessment in psychology (1991) and arrived after behavioural studies in physical education at performance analysis in game sports (Anguera 2009) by delivering a comprehensive methodological framework for observational systems in game sports (Anguera and Mendo 2013). A comment on the British approach of “notational analysis” was given above in Chap. 1 introducing this influential school of PA. In Germany, Lames (1994) focused on the specific structures of game sports and on designs for observational systems that allow to answer questions of performance analysis. Taken together, knowledge from behavioural sciences, their adaptations to the special conditions in game sports, and experiences from notational analysis allow setting up a methodological framework for designing observational systems in the specific area of performance analysis in game sports.

2.2 Design of Observational Systems Designing an observational system requires several methodological decisions. These decisions are to a great extent determined by taking into account the purpose of the system, that is, the kind of information that it should provide. As a first, more or less trivial consequence one may state that there is no single observational system, for example, for football, serving all purposes. Rather, for each problem under investigation, a specific observational system has to be designed underlining the importance of this chapter. A more important consequence is to regard an observational system as a model of a game built for a special purpose. Lames (1994) introduces general model theory to evaluate the appropriateness of observational systems designed for different purposes. Model Theory

Stachowiak (1973, 1983) developed a “general model theory” that was widely adopted in German sports science because it provides a framework for model building and evaluation. Modelling may be conceived as projecting an original on a model for a special purpose. This projection—very much in a

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Fig. 2.1 Model projection

mathematical sense—has some properties (see Fig. 2.1) that should be subject of model validation: • Projection: Are all relevant attributes of the original projected to the model? • Reduction: Are all non-relevant attributes of the original not projected to the model? • Abundance: Does the model contain abundant attributes that interfere with the purpose of modelling? As becomes clear from these properties of model building, the most important aspect is whether the purpose of the model is achieved. As a consequence, the respective purpose of a model should be pointed out in advance, and model validation consists of scrutinizing critically its achievement using the three properties above as criteria for validation.

The benefit of using the theoretical framework of model theory for designing observational systems is not only disposing of criteria for the design and validation of observational systems. As any observational system may be considered being the result of model building, one will not be able not to use this framework but only to use it unknowingly, which is for sure only the second best option. Implicit modelling not only abstains from the systematic way of validation provided by the modelling framework; it is frequently even characterized by not caring for validation at all. Many problems with inappropriate interpretations of the results from observational systems could have been prevented in the past by using model theory as framework instead of starting with ad hoc observations. For example, drawing conclusions on the quality of a player from static, summative statistics (“stats”) does not pass a validity check of model theory. When a game is modelled by a set of stats,

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this does not project its nature of a dynamic interaction process. How can we assume to directly observe something like a “true value” of a player’s quality by looking at emergent behaviour being brought about by a dynamic interaction process? Considering an observational system as a model of the original game sports means in turn that designing observational systems for performance analysis requires thorough reflections on one hand on the nature of game sports (see sections above) and on the other hand on the respective purpose or informational claim of the observational system.

Variants of Observational Systems

Besides the specific decisions that are to be made designing an observational system for game sports, each textbook on observational methods mentions some general decisions that must be made beforehand concerning the appropriate choice of a specific observational system out of a set of variants. Mediated - live observations: Is the behaviour recorded live or recorded on a medium and assessed only later? Live observation is fast but error-­prone, mediated observation is slower but more reliable. Modern action feeds in sports are recorded live for live statistics but typically undergo checks based on mediated observation resulting in the final statistics. Active - passive - no interaction: Is the observer actively or passively involved in the interactions of the players (coach, assistant coach: active; analyst: typically passive)? Does this lead to changes in behaviour? Knowing – unknowing: Are the players informed of being observed? This could create ethical problems in settings other than top-level sports, where observation by media and spectators is constitutive. Here, players know that they are observed by their own and several other analysts. Open - standardized: To which degree are the observed variables fixed in advance? Is there total or no advance fixing or is a mixture preferred requiring a set of fixed variables but leaving room also for spontaneous observations (appropriate for scouting of teams and players)?

2.2.1 Type of Observational Systems A first and basic decision in designing an observational system for game sports is on the type of the observational system used. The most important alternatives here are event systems or category systems. In event systems, the occurrence of pre-defined events is recorded, whereas in category systems at each point in time, the current state of a system is indicated. The term “category system” is a little bit confusing as the term “category” is used very widely. The relevant notion here is that there is a set of states that describes comprehensively the possible states in a match (see box below). More formally, a category system may be seen as a partition of the set of all

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possible situations in a match given by a finite number of states each being an equivalence class for a certain variable. Equivalence Classes

In mathematics, an equivalence class is formed by elements in a set when for each element in the class the equivalence relation holds true, being defined by the properties of reflexivity (object A is equivalent to A), symmetry (if A is equivalent to B, then B to A), and transitivity (from A equivalent to B and B equivalent to C follows A equivalent to C). In the context of observational systems, the set is made up of all possible states in a match, and an equivalence class is a sub-set of it, for example, a certain rally in a match or the level of an observational variable like “backhand”. For the design of an observational system, some properties of all these sub-sets each being an equivalence class are very important: • The equivalence classes form a partition (in the mathematical sense) of a set, that is, every two equivalence classes are either equal or disjoint. • One object of a set belongs to exactly one equivalence class, that is, at least one and only one. Equivalence classes with their properties are a useful construct in designing category systems and specifying the levels of an observational variable. There are other types of observational systems besides event and category systems, for example, rating scales, where — by expert judgements — comprehensive assessments of the performance of players and teams are obtained. In performance analysis, though, rating scales play only a marginal role because one is interested in recording the “real” behaviour, “actual sports performance” as O’Donoghue (2010, p. 2) puts it, and only to a lesser extent expert opinions on it. Sometimes, though, rating scales are used as criterion variables to check the relevance of observational variables.

2.2.1.1 Event Systems Designing an event system requires exact definitions of the events of interest, for example, “A corner in football is ...”. Then, observers record each occurrence of an event that meets the definition. A certain event may correspond to no, one, or even more than one definition of the events of interest. This can be demonstrated with a corner in football. If the observational system’s event definitions do not contain corners, for example, in an event system on free kicks, the corner will not be registered. In this case, the corner did not “happen” in the sense of the event system. If the event definition of a cross does not exclude set plays and merely requests a ball played from the side into the penalty box, for example, a corner meets the definitions of two events of interest: corner and cross. If the definition of a cross does not

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Table 2.1  Starting events of ball possessions leading to a critical goal situation in youth football (Schmalhofer 2016, courtesy of Alexander Schmalhofer) Age group U15 U17 U19 U23 Total

Turnover oppenent half n % 64 41.6 51 38.3 35 29.9 25 22.9 175 34.1

Turnover own half n % 37 24.0 32 24.1 27 23.1 24 22.0 120 23.4

Position attack n % 23 14.9 13 9.8 20 17.1 25 22.9 81 15.8

Clearance opponent n % 4 2.6 3 2.3 7 6.0 4 3.7 18 3.5

Set play n % 26 16.9 34 25.6 28 23.9 31 28.4 119 23.2

contain set plays, the corner will be registered exactly once. This ambiguity can be seen as a weakness of event systems. A typical application of event systems is performance profiling. In this case, we are interested in frequency distributions of certain events providing, for example, an overview on the technical and tactical repertoire of a team or a player overall or limited to a certain match situation. Table 2.1 shows a typical example. Based on these profiles, youth development programs could be informed about required technical or tactical skills, for example. In performance analysis, event systems are very common. They are simple in handling and usually an economic choice, because they allow focusing on the events of interest. Prerequisites are just definitions of events that are recorded in a sample of matches. Frequently, these are contained in routinely provided “match statistics” or “stats”. On the other hand, one may critically ask whether the relevance of events is captured with this method as frequency is not a sufficient condition for relevance. Also, event systems do typically not provide the action chain the event was part of. Questions like “What did lead to the corner?” or “What was the most successful preparation for the volley winners?” are not answered by this type of observational system. Another objection from the point of view of modelling is even more severe. An event system tacitly assumes that a game is modelled by frequencies of certain events. Therefore, the constitutive aspects for game sports, interaction and dynamics, are not at all captured by event systems. Taken together, event systems may not claim validity for giving the strength of a player or team nor for being a projection of the interaction. They may, however, claim validity for the frequency of certain events occurring during a match, no more and no less.

2.2.1.2 Category Systems The principle of category systems is to model a match as a gapless chain of events. This means that at each point in time, a certain event is going on in the match. The meaning of “event” here is a little bit different from its meaning in an event system where it denotes just a perceivable action. In a category system, events form a continuous chain, requiring a starting and ending point in time. The latter should be adjoining to the starting point of the next event. For example, in a net game, a stroke

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Fig. 2.2  General structure of invasion games and net games

would start at the contact of the ball with the racket and end when the ball hits the racket of the opponent. Invasion games may be perceived as a continuous chain of ball possessions of a team (note that this will be discussed critically in Chap. 4). This category system may be extended to a more detailed level of elementary actions such as pass, dribble, or shot. On this more detailed level, one could define a category system as well, by specifying mutually exclusive elementary actions, where at each point in time one of these actions is going on (see Fig. 2.2). A similar structure holds true for net games. They can be conceived as a continuous chain of rallies. Again, we have a more detailed level of single strokes. The first stroke in a net game is the service and the last one is either winner or error. It must be mentioned that a stroke-based category system is quite demanding, very much like an elementary action-based category system in invasion sports, because a tennis match may consist of 1.500 strokes, for example. It becomes obvious that for the purpose of game observation with category systems, the term “gapless” is not meant in a mathematical sense but in a pragmatic way. Although the next action after a winner or an error in a net game is not the next serve, but everything that is happening between rallies, this is neglected without too much loss of information relevant to performance analysis. In category systems for invasion games, we typically ignore phases with ball not in play. After a successful shot at the basket, the next elementary action is the inbound pass. Everything between these two elementary actions is ignored, although especially in football with a net playing time of around 60%, these ball-not-in-play situations are quantitatively important, and case-by-case analyses of game interruptions reveal interesting insights (Siegle and Lames 2012; Zhao and Zhang 2021). At this point, it should be mentioned that in behavioural sciences, a different technique of designing category systems is known. Sometimes, instead of the event chain technique just explained, the time interval technique is used, for example, in Bales’ interaction analysis (1950) or Flanders’ studies of classroom behaviour (1960, 1970). With this method, continuous chains are obtained by specifying time intervals, for example, 3 s in Flanders’ observational system for teaching behaviour. For each interval, observers record the presence of a certain behaviour from a set of

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defined behaviours (equivalence classes). Since in game sports, we usually have well-defined and relevant event chains, observational systems making use of the time interval technique are very scarce. In fact, the only suggestion in sports science known to the author for this technique is from Pavičić (1991) in water polo. He defines “pictures” that are taken at a certain frequency and a comprehensive set of variables is recorded for each picture. “Actions” are obtained by taking the differences between pictures. Finally, one must stress the conceptual advantages of category systems that were not perceived to their full extent in the past. A continuous observational system allows reconstructing, in principle without gaps, the behaviour in the match. That means, we know the behavioural context of actions since we know the actions before and after. Also, dynamical changes that are typical for a game may only be traced with category systems when applying appropriate methods.

Action Feeds

The increasing media interest in professional game sports has made it the business idea of some companies to compile so-called “action feeds” of matches. This requires besides an elaborated book of definitions several observers for live recordings. Action feeds contain at a very fine-grained level elementary actions such as passes, dribbles, duels, and other events. It is interesting to note that for action feeds, being event systems by nature, the notion of a category system applies as well, if the fine-grained actions collected are taken as a continuous action chain. Thus, fine-grained action chains blur the difference between event systems and category systems. In case our questions may be answered with the information contained in the action feeds, we are in a comfortable “big data” situation with a wealth of information from many matches and many seasons of several leagues being readily at hand. Nevertheless, using action feeds for TPA and PPA does not release from validity/relibility checking (see below) usually not provided with commercial action feeds. In addition, action feeds are only available for top leagues/tournaments in professional sports and not for youth and amateur sports. Moreover, when addressing a question that may not be answered by the events of an action feed either because the action of interest is not contained or not contained in the required detail, one must still create one’s own observational system (see example of detailed penalty analysis in football at the end of this chapter).

2.2.2 Elements of Observational Systems In this paragraph, the necessary decisions to specify an observational system are outlined. As mentioned above, it is prerequisite to be very precisely aware of the purpose of the observation and the information to be collected to achieve this purpose. Moreover, the decision on the type of observational system to be employed is

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assumed to have taken place beforehand. After this, an observational system can comprehensively be defined by specifying three elements: 1. observational unit, 2. observational variables recorded per unit, 3. levels for each variable with their operational definitions.

2.2.2.1 Observational Units In behavioural sciences, the issue of observational units is critical because of the idiosyncratic nature of human behaviour. Human behaviour is in principle a continuous process from cradle to grave; a certain behaviour can arise from different intentions; interpretations are often ambiguous. The pioneering psychologists Cranach and Frenz (1969) define an observational unit as “the element of behaviour that is taken as smallest event that does not need to be further dissected in the eyes of the examiner” (translation by author). Fortunately, game sports differ in many respects from natural behaviour as mentioned at the beginning of this chapter. There are only a limited number of alternatives for observational units as becomes clear from the general structure of invasion games and net games in Fig. 2.2. In event systems, the observational units are easy to decide on. Since we have one or a list of events of interest, these make up the observational units. Each event is generally described by a specific set of observational variables, which in turn are given with their respective levels and operational definitions. In category systems, defining observational units is not a too difficult task, either. Since we have a continuous chain of actions, these actions are taken as the observational units. In the case of invasion games, we have either elementary actions (ball contacts) as observational units or—on a higher level of abstraction—ball possessions. In net games, observational units are made of single strokes or rallies, respectively. To sum it up, a decision for an observational unit usually does not create a big problem in performance analysis of game sports. Due to the rule-based behaviour and the well-known structure of game sports, we may specify a small set of candidates that apply for almost any observational system in the domain. The choice of granularity depends on the purpose of the observation. 2.2.2.2 Observational Variables Specifying observational variables reflects the specific aims of an observational study. As the variables to be observed depend to a great extent on the specific interests of the study, these interests should be clear beforehand. We have a great variety of options and it is not always a simple consideration which variables we choose. Table 2.2 gives a general overview of the type of variables that may be taken into account for an observational system, each with some examples. The question remains, which observational variable to choose and why. Here, a more general, abstract view on the problem might help. From a conceptual point of

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2.2 Design of Observational Systems Table 2.2  Examples for observational variables General variables Player team Result of observational units Score line

Temporal variables Time evolved Net playing time Time left Start/end/ duration of observational units Period of match

Spatial variables Location of start of observational unit Location of end of observational unit Position of actions on pitch Positions of opponents/team mates Hitting areas in goal

Technical variables Category system of techniques Handedness Velocity Direction Spin

Tactical variables Tactical action of player before ball possession Tactical action of player in ball possession Tactical action of player after ball possession Tactical action on group level Tactical action on team level

view, there are three inclusion/exclusion criteria that should be taken into account and be balanced: relevance, resources, and observability (Lames 1994). Relevance: This is of course the first and most important criterion. If an observational system is a model of a match with the purpose of satisfying specific needs for information, all relevant variables should be included. One should be aware that there are different aspects of relevance, for example, to give an optimal description of the observational unit, to allow for valid statistical inferences, or to give a classification variable facilitating tailored analyses. Resources: Recording an observational variable is inevitably associated with creating costs. These might be time resources, technical resources, or financial ones. Observational variables differ greatly in this respect. Score lines may be recorded almost incidentally, players are identified at one glance by an experienced observer, but technical or tactical variables sometimes require repeated analyses or even employing technical devices, for example, quantitative assessments of spin rates in tennis or table tennis. Another good reason to be economical with the number of variables recorded per observational unit is the large number of units, for example, the already mentioned up to 1.500 strokes in a tennis match require 1.500 additional observations and recordings per additional variable. Observability: Some variables that are usually considered to be relevant to game sports are in principle not accessible by observational methods. As observation is restricted to the observable surface of behaviour, we are not able to record physiological variables like heart rate or fatigue and psychological variables like anxiousness or self-confidence. In addition, since observability is not always a yes/no property, variables are typically observable only with a certain precision (see section below on observer agreement). The degree of observability might affect the relevance of a variable (one should refrain from in-depth interpretations of a variable with only low observability), or the invested resources must be increased to

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Fig. 2.3  Criteria for selecting an observational variable

achieve sufficient observability (e.g. using high-frequency cameras instead of normal ones). The last considerations make clear that adding a variable to an observational system cannot be decided by evaluating each of the three criteria by itself. It is rather the interplay of them that allows a final decision (see Fig. 2.3). The only thing that is for sure is that variables indispensable for achieving the purpose of observation must be included. If observability and/or expenditures speak against it, this study must be abandoned. In practice, though, a number of compromises may be made as follows: • Assessing a variable with high relevance justifies the use of more resources (e.g. for the time-consuming analysis of the spin of a table tennis serve that sometimes requires repeated observation with slow motion as the server tries to hide the spin to the opponent), because observability must be optimized in this case. • Problems with observability may induce compromises concerning the relevance of a variable, as it is not a good idea to put the central focus of a study on a variable with restricted observability. On the other hand, observability demands for resources as it may be increased with a higher investment in temporal, technical, and/or financial resources (e.g. using more expensive highfrequency cameras). • Finally, the available resources sometimes force to make compromises concerning the assessment of relevant variables, because non-sufficient resources lead to either dropping the variable or to accept a lower level of precision.

2.2.2.3 Levels of Observational Variables After having determined the observational unit and made a list of observational variables, designing an observational system requires the specification of the levels of observational variables. For example, if we scrutinize tennis strokes (unit), we want to know at which side (variable) it was hit and introduce the levels “forehand” and “backhand”. The specification of levels of observational variables is sometimes as natural and simple as in this case; sometimes it requires more reflections on granularity and exhaustiveness of recording the behaviour of interest. From a methodological perspective, specifying the levels of an observational variable means to

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define a category system of levels in the sense that each observation may be projected into one and only one category as a mathematician would put it. The importance of fixing levels of observational variables is that they create equivalence classes (Link and Ahmann 2013; Anguera and Mendo 2013; see box “equivalence classes” above). This means that all units being assigned to a certain level are treated uniformly. A stroke is either a base-line backhand or it is not. This may be alleviated by combining variables, for example, examining base-line backhands with and without pressure, from far outside, outside or from mid-court, etc., but the principal problem remains that we are describing a number of strokes with a common label knowing that, from a movement science perspective, each stroke is a singular event. There are criteria for category systems of levels of observational variables that must be achieved for a methodologically sound treatment (Lames 1994). Completeness: Each possible variation of the variable that may occur in a match must have a corresponding level that it can be projected on. In other words, for each observational unit, one level of the observational variable has to apply to the behaviour. Sometimes it is quite natural to enumerate exhaustive levels, for example, handedness of a throw/pass/shot: right or left. Typically, we encounter more problems with technical and tactical variables because there may be many variants and alternatives. In this case, we can proceed either deductively, deriving levels from an accepted taxonomy which is quite frequent in textbooks on game sports, or inductively, recording behaviour in a reference sample and trying to classify all registered variants. Uniqueness: Each observational unit may fit only into one of the levels of the observational variable. In other words, the levels must be mutually exclusive. This is easily met when we have naturally distinct categories, like handedness coming with left or right as mentioned above. In case of more complex categories, this could create a problem, for example, is a clearance also a pass or is a corner also a cross? Achieving uniqueness is one of the tasks of operational definitions. Operational definitions: An operational definition is a definition of a level of an observational variable by a measurement procedure. In observational systems, operational definitions are given by listing observable levels for each level of the observational variable. For example, for a volley in tennis (unit), the height (variable) may be distinguished with three levels: low, middle, and high. Operational definitions of these levels would be for “low”, ball is hit below the knee; “middle”, ball is hit between the knee and shoulder; and “high”, ball is hit above the shoulder. These definitions employ body parts and hitting points of the ball as observable items and “below”, “between”, and “above” as observable relations. Thus, we formally have logically unique and complete levels meeting the demands of a category system. Whether or not these definitions work in practice, meaning whether actually one and only one category is recorded per observational unit must be verified by testing inter-observer agreement. Granularity: Especially in the context of observational variables recording spatial and temporal properties but also in some technical variables (e.g. technique of service in table tennis), we may specify category systems of different granularity,

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that is, levels of detail. For example, the point, where the ball hits the table in table tennis, may be given with the levels left and right half, with the four combinations of left/right and short/long, or with an (almost) arbitrary high granularity if xycoordinates of hitting-spots are available. To arrive at an appropriate decision on the granularity with which a variable is recorded, it is at first a good idea to record at the most detailed level, because it is always possible to aggregate detailed levels at a higher level, for example, the event time of an action recorded in the min:sec format may easily be aggregated to first half/second half or 5 min interval. Nevertheless, defining the optimal level of granularity is a question of the relevance of the variable, the costs for going to more detailed levels, observability and operational definitions, and the natural complexity of the variable under scrutiny. In practice, it is quite frequent that even after thorough definitions of variable levels, there are events that do not fit into any of the specified categories. Examples are events that are not observable due to overlay or video footage temporarily not showing the behaviour. Also, it might happen that something totally unusual or unprecedented, not fitting to any category, happens, for example, a tennis player hits after a fall in a lying position. For instances like that, it is generally advisable to introduce a residual category in the sense that the level of the variable was not observable, unclear, or not fitting into the suggested categories. Summing up the statements on designing observational systems for game sports, one arrives at concrete requirements for their specification. After the type of observational system is decided upon (category or event system) and the observational unit is fixed (structural units or events), observational variables and their levels with operational definitions have to be specified (see Table 2.3).

Table 2.3  Specification of an observational system for discrete, continuous, and enumerative variables Observational variable Discrete variable

Height of volley Continuous variable Position of volley; distance to net Enumerative variable Player ID

Level Level 1 Level 2 Level 3 Low Middle High Range of values 0–11.89 m Enumeration 1–33

Operational definition Operational definition 1 Operational definition 2 Operational definition 3 Ball hit below the knee Ball hit between the knee and shoulder Ball hit above the shoulder Operational definition (if not trivial) Shortest distance to net from vertical projection of hitting point Operational definition (if not trivial) Shirt number

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2.2.3 Complex Observational Systems So far, only observational systems with a “flat” structure (unit, variables, levels of variable) were introduced. In practice, however, we frequently find the need for more complex systems, for example, hierarchical systems with nested specifications and more than one observational unit. Under this aspect, multi-event systems may be considered as several parallel observational systems. We find very much the same structure when we deal with conditional levels for a variable. For example, if the stroke type is “service”, we may use a category system for the variable technique with the levels flat, slice, and kick. If stroke type is “base-line” though, the technique may be described by the levels topspin, slice, and drive. A common case of more complex observational systems is having observational units on two structural levels. For example, information is recorded on a first level “match” (observational unit 1), and on the second level, each rally (observational unit 2) is described with observational variables of a “flat” observational system. Variables on match level are of particular interest as independent variables for studies aiming to performance profiles, for example, level or ranking of teams or players and match conditions. Hierarchical systems—in a more literally sense—frequently come into play when a comprehensive modelling of the structure of a sport is aimed at. Aiming to construct a category system, for example, in football, on a first level, we might apply match phases like ball possession team A, ball possession team B, ball not in play, and no-control phase. For each of these phases, one could design an event or a category system with a more detailed specification. These could in turn be hierarchical systems by themselves, for example, when a ball possession period is differentiated in starting event, follow-up events, and ending event each with a specifically designed event or category system (see section with examples for observational systems below). Hierarchical systems allow for more detailed analyses, but the complexity of the analyses is increased as well. The respective reference values must always be clearly presented. For example, for the percentage of team A’s ball possessions with shot on goal, one could take as reference all ball possessions of team A or all ball possessions of team A ending in opposite third with the latter one providing a more specific estimate for offensive effectivity.

2.3 Validation of Observational Systems Observational systems are instruments for assessing or measuring human behaviour. For measurements in behavioural sciences, the concept of validation is crucial. It deals with questions like: How precise is the measurement, how trustworthy are its results? Validation of observational systems has a different meaning for different stakeholders in game analysis. A sports scientist designing an observational system is

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well aware that reliability and validity must be demonstrated before any conclusions drawn from data with this system will be accepted. Sports data companies offering match statistics or “action feeds” might not feel this obligation to the same extent, because their main interest is to sell the products. On the other hand, scientists usually are not able to compete with the amount of data these companies are collecting, and so it is a good idea to make use of these large data sets (sometimes referred to as “big data in sports”) for scientific purposes, but then the question of validation remains open! Sports practitioners sometimes show blind trust in data presented to them. They take each figure given as granted and do not see it in a framework of measurements with errors being a common issue as scientists do. This is not appropriate, because typically, severe decisions (Who will play? What will be our tactics in the next match? Which player will be drafted?) are made based on these data and one should be at least aware of the error margins. This section on validation of observational systems gives a general framework for validation discussing reliability and validity. Then, the specific conditions for validation in observational systems are analysed focusing on the role of the observer. Finally, an overview on standard statistics and methods for assessing observer agreement is given.

2.3.1 General Framework of Validation A general framework for the validation of observational systems is found in behavioural research. Since observational systems are measurement tools for human behaviour, they are extensively discussed in psychological research methodology. The measurement criteria relevant to validation are reliability and validity.

2.3.1.1 Reliability Reliability is the measurement criterion that denotes the precision of a measurement. It means the degree we can rely on the results in the sense that they are reproducible or trustworthy. Three main sources of threats to reliability must be considered: inconsistent measurement instruments, instable variables, and instable conditions (Lienert and Raatz 1998). Consistency of instrument: A measurement cannot be reliable when the measurement instrument is inconsistent. This could mean, for example, that the scale of the measurements is not fine-grained enough, that the error of the instrument is too large, or that the results of the instrument change over time (drift). In the case of observational systems, we have the specific problem that our instrument is a human observer. This leads to special sources for errors as well as special statistical methods for testing consistency that both are dealt with in the next sections. Stability of variables: A measurement cannot be reliable when the observed variable shows by its nature large fluctuations. For example, when there is learning from

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trial to trial, performance may not be measured reproducibly. Another example is simple reaction time that has a high natural fluctuation and hence cannot be measured reliably. Test literature recommends taking the mean of up to 40 tests (test prolongation (Lienert and Raatz 1998)) for a reliable measure of basic reaction time. With respect to game sports, the dynamics of behaviour was denoted in the first chapter being typical for their structure of performance. Players change behaviour to optimize success. This means that behavioural variables are not stable which in turn creates fundamental problems in achieving reliable measurements of match behaviour. Stability of conditions: A measurement cannot be reliable when its results depend on changing conditions or environmental factors. The most important and constitutive environmental factor in game sports is the opponent. If behaviour in game sports is conceived as spontaneously emerging from the interactions between players, this indeed is a threat to reliability in the sense of reproducible measurements of behaviour. Summing up this discussion about different aspects of reliability, we must acknowledge that only for instrumental consistency we might hope for reliable measurements when working with appropriate methodological diligence. The two other aspects (stability of variables and conditions) are in conflict with the nature of game sports as dynamic interaction processes. This is well known to sports practice and reflected in a statement such as “You play just as good as the opponent allows you to do!” It is a good advice to accept variability of behaviour in game sports as a part of its nature—and to look for appropriate methodological answers, see Chap. 5— rather than “complaining” about regrettable large “errors” of match performance variables or ignoring the problem at all. Some researchers draw different consequences. O’Donoghue (2010, p.  158f) sees the problem that match performances are not stable by nature, too. He draws the consequence that only the recording process is subject of reliability testing, that is, a specific notion of reliability in performance analysis is created. Hughes et al. (2001b) introduce “normative profiles”, that is, “stable” behavioural profiles of a player or team. Starting from a variation of behaviour in single matches that is obviously inacceptable for practical as well as scientific purposes, they investigate how many match profiles have to be averaged to “stabilize” to a normative profile. Gregson et al. (2010) describe high fluctuations in high-intensity running performance. For researchers they draw the conclusion that individual capacities are not to be detected by single observations and advice to adjust the sample size for experimental proofs of effective training measures. For practitioners, they underline the importance of knowledge of this variability to arrive at informed decisions. In the latter cases, this imposes the impression that the authors see variability in game sports behaviour as a handicap that has to be overcome by appropriate statistical measures, mostly increasing sample size, rather than seeing it as a part of the nature of game sports.

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2.3.1.2 Validity Validity is the measurement criterion that denotes whether the intended object of measurement is captured (Lienert and Raatz 1998): “Do we measure the things we claim to measure?” From this definition, it becomes immediately obvious that validity is relative to the objective of a measurement. The same measurement may be valid for one objective, but not for an other one. Regarding the nature of game sports again, we must be sceptical to grant validity to behavioural observations if they claim to assess performance capacities of players. Of course, the observed behaviour is influenced by the capabilities of a player/a team, but what is observed at the behavioural surface may not serve as a direct assessment of his capabilities if match behaviour is perceived as emergent result of the dynamic interaction of players. Empirical findings on the large behavioural variation in game sports like the ones quoted above only bear witness for this notion. Quite the opposite holds true when we discuss validity of our observational systems for recording behaviour that has occurred in the field. This is the primary purpose observational systems are designed for, and there is no reasonable doubt that they—in general—may achieve this aim. Hence, unlike for assessing capabilities of the players, for the objective of protocolling behaviour in the field validity may be ascertained—at least when all methodological issues are obeyed. What are the consequences of these insights in measurement criteria of game behaviour? First, performance analysis as a scientific discipline is still looking for appropriate methods to deal with the intricate nature of game sports. This will be referred to in Chap. 4 on theoretical performance analysis. Second, for practice, where momentary capabilities of players need to be assessed for generating recommendations for training (see Chap. 1), the consequences of the considerations just made are that in addition to observational data, further methods must be employed to arrive at conclusions with practical relevance. Appropriate (qualitative!) methods will be dealt with in Chap. 5.

2.3.2 Role of Observer The standard research method for assessing human behaviour is observation. Alternatives such as interviews, questionnaires, or physiological and biomechanical measurements each have considerable disadvantages when it comes to recording behaviour in natural settings. For this reason, observational systems are the preferred method for performance analysis in game sports, because in this group of sports, action plans and their execution and hindering are the core of performance. In a match, players with their capabilities and plans enter the interaction with a behavioural outcome that is subject to observational methods. The constitutive property of the method of observation is the measurement instrument, which is the human observer. As pointed out above, an observational system requires the projection of observed behaviour onto one of the system’s behavioural categories. This process deserves a short philosophic consideration

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since what is demanded is to denote perceptions with a term. This is nothing else but the basic philosophical problem of comprehension. In Kant’s version, for example, comprehension is the synthesis of sensual experiences from the external world with concepts of the mind (“Thoughts without content are empty, perceptions without concepts are blind!” Critique of pure reason). For our purposes, it is sufficient to acknowledge that denoting an observation with an observational category makes use of the human capability of comprehension, which is the basic reason why we rely on human observers (see Box “Automated game observation”). Automated Game Observation

Recent developments in information technology, especially in the field of machine learning, have led to a realistic perspective for an automated analysis of match behaviour based on positional information of players and ball. These methods are working on a very large data base of annotated (declared by an observer) events, “learns” the underlying rules for attributing spatiotemporal configurations to certain events, and finally should be able with an acceptable error margin to automatically identify game events. Notwithstanding the fact that success in automation benefits from the rather simple structures of events in game sports, this is a great perspective. It will be interesting to see how progress will evolve in the future. Given the great variety of observational variables, the degree of automation should be dependent on the nature of the variables, some requiring for sure additional information than just positional ones, for example, service technique in tennis may be inferred only from recording movement details or ball trajectories. Nevertheless, a great future for automated game observation may be expected, especially because it offers considerable savings if human observers could be replaced by algorithms. The model presented in Fig. 2.4 illustrates the role of a human observer in an observational measurement (Lames 1994). There are three critical transitions in the information flow that may lead to specific errors. It is worthwhile to study these potential sources of errors, because in case of problems this is the starting point for improvement. The first transition of information is from reality into a sensory representation with some specific error sources: • The observed match behaviour may pose problems for observation, for example, when things are happening very fast, relevant aspects show only minor differences, or many aspects are relevant at the same time. A good example here is service in table tennis, where top players are able to create different spins with very similar movements. This is meant to create problems for the receiver, but it does so for the observer, too.

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Fig. 2.4  Role of the observer (with permission of Philippka Verlag from Lames (1994))

• The observational conditions may cause trouble such as occlusion, bad viewing angle, or large distances. Using video recordings allows for repeated inspection in slow motion or even frame by frame, thus alleviating many of the problems of direct observation. But especially when we are interested in events without media coverage and must work with self-recorded videos, we frequently achieve only suboptimal conditions for observation. • The observer himself could create problems at this transition. As a well-designed observational system should not pose challenges to sensory thresholds, the quality of a sensory representation may primarily be challenged by the observer’s vigilance. It takes much experience to follow a live match and to stay attentive for an hour or more. But also with analysing matches on video we face challenges as usually this takes much longer than live recordings, because typically more variables are collected in higher detail. Also, most studies require the analysis of many matches increasing the demands on vigilance or sustaining motivation of the observer only further. The second transition is from a sensory into a mental representation. Here, a perception is denoted with a category what was just called comprehension in the sense of Kant. For example, a base-line stroke in tennis is perceived, and from certain movement characteristics of the arm while hitting, from the trajectory of racket and ball, and from its bouncing behaviour, an observer familiar with tennis may conclude that there is backspin and he will label the observation with the term “slice”. It is obvious that at this point that the degree of expertise of an observer comes into play. A complete layman would not be able to make the connection between sensory input and the tennis specific label for it. Nevertheless, for achieving reliable and valid measurements, it is a good advice not to rely too much on the expertise of observers. Finally, the mental representation of an event has to be transferred to the observational system. For this, it is helpful that the categories of the system contain the usual technical terms of the game. The purpose of operational definitions is to facilitate the transfer from mental representations to the observational system. For example, when a volley was hit at the height of the player’s hip, the operational definition (between the knee and shoulder) would label it being “middle height”. Errors at this step may occur when the observer is not familiar with the observational system and its exact operational definitions. But problems may occur also when the registration process is too demanding which may happen in live recordings when there is not

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enough time. Moreover, the handling of the—mostly computer-based—system may be too complicated. A frequently underestimated demand for the ergonometric design of computer-based observational systems is the option for quick revisions of false data entries (see Chap. 5, Sect. 5.4.3).

2.3.2.1 Observer Training One consequence from the manifold sources of observer errors mentioned above is the necessity of observer training. Observer training is a systematic routine for reducing observer errors and increasing observer agreement when using an observational system. Observer training is an issue in data companies, who are recruiting and training permanently a large group of observers for their routine services, in sports science, when new observational systems are developed and studies are conducted, and also in sports practice, when a game analysis department wants to ensure the consistency of match observations made by different observers. Basically, there are two alternatives for observer training: first, the operational definitions are taught and/or a training set of observations is evaluated under supervision (deductive method). The observational system is presented to the future observers mentioning frequent pitfalls like, for example, specific definitions that deviate from common usage of technical terms in sports practice. This is not uncommon, because technical terms in sports practice are sometimes ambiguous and standardised definitions are rather the exception. The second way is to conduct observations in practice and discuss judgements among the observers (inductive). This method is the appropriate choice when there is not a binding catalogue of definitions and adherence to this catalogue is to be made sure (companies), but in cases when the search for a common interpretation and understanding is dominant, for example, in a research project or within the PA staff of a professional club. Observer training aims to increase observer agreement in the sense that observers name similar behaviours with the same category. It may well happen, even if observers are great experts in the sport, that there are different opinions, for example, on the necessary amount of spin for labelling a stroke “topspin” instead of “drive”. Observer training then aims at achieving sufficient agreement on thresholds for subjective discrimination between categories. It must be noted that in data companies supplying, for example, action feeds in real time, observer training plays a big role, of course. There is a thorough recruiting of candidates, an extensive training phase, and in production mode, there are several levels of supervision that are involved in case of doubt or overload. In addition, statistics assessing the agreement, which will be dealt with in the next section, should be calculated (and ideally published).

2.3.3 Methods and Statistics for Testing Observer Agreement Measuring the agreement between observers in categorical judgements is a specialised field of research methods in behavioural sciences (see also Box “Observer Agreement for Interval Judgements”). There are books dedicated to this specialty

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Fig. 2.5  Absolute and case-by-case agreement (constructed data)

(e.g. Wirtz and Caspar 2002; Gwet 2012), and no textbook on research methods dealing with observational methods omits this topic. A set of statistics was developed to meet the demands of behavioural sciences for a sound quantification of observer agreement. Before introducing the most relevant of these, three design principles for testing observer agreement are explained. A first principle of an appropriate assessment of observer agreement is the caseby-case analysis of judgements. This means that each single judgement of an observer needs to be compared to the corresponding judgement of the other observer. Frequently, only summative agreement is reported, that is, the number of observations per category like, for example, the number of drives, slices, and top-spins for tennis baseline strokes from observers 1 and 2. In this case, only the differences between the numbers for each category are interpreted as deviation. This is logically not correct since mathematically, there may be total agreement in the number of observations per category and no single identical judgement. This is illustrated in Fig. 2.5, where on behalf of the deviation between judgements duel won (duel+) and duel lost (duel-), it is demonstrated that there may be perfect agreement in absolute numbers but poor agreement at the case-by-case level. Whereas the absolute frequencies for duels lost and won are identical (n = 20 each) for the two observers, they actually agreed only in 10 out of 40 cases. As a consequence of this principle, it is not possible to control for objectivity in a sufficient way when data are only available as summative frequencies. Deviations between frequencies of categories generally overestimate true observer agreement (O’Donoghue, 2010, 161). The second principle may be associated with research ethics. When the purpose of agreement testing is to give an honest estimation of the reliability of the observations, agreement testing should be done only for corresponding judgements, that is, on the judgements per variable. Otherwise it is possible to “cure” poor agreement in one variable by excellent values for another one as is demonstrated in Fig. 2.6. Here, we have a maybe acceptable overall agreement of 60 out of 70 judgements, but the perfect observability of throw-ins hides the problem with clearances (only 10 agreeing judgements out of 20 judgements overall). For the sake of clarity, the example is a constructed one, but in literature, we sometimes find very large tables of agreement providing excellent overall results making use of the method criticised (e.g. Liu et al. 2013). A third principle of an appropriate assessment of observer agreement is to acknowledge that we in general have a two-step process. Only after the two observers have both identified the occurrence of an observational unit, their agreement in

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Fig. 2.6  Compensation of objectivity (constructed data)

attributing the levels to the observational variables can be judged. This means we typically have a type I error of agreement, that is, the rate of commonly identified units, and a type II error of agreement, the agreement in attributing the levels of an observational variable to these units. Type I: Did the two observers record a pass at time-stamp 22:43? Type II: If so, did they judge it a low/middle/high pass in agreement? Since the type II error can only be assessed if there is no type I error, reporting type II agreement alone overestimates objectivity because it does not contain cases not reported by one of the observers. Type I errors are quite likely to occur in event systems with many events in a tight sequence (e.g. a pass sequence in football) or when recording the mere occurrence of an event requires some judgement (e.g. a duel). In category systems, where the game is structured as a continuous chain of events, it may, for example, be doubtful whether there was a complete stroke or elementary action; a stroke in observational systems is typically only recorded when there is a direction intentionally given to the ball with the racket, which on rare occasions leads to ambiguities. On this occasion, it is interesting to note that the meaning of an ace in tennis is different in a category system in tennis compared to sports stats. Whereas in media reports, it is required for an ace that there is no contact between ball and racket of the return player, in performance analysis, an ace is a direct point with the service, that is, without a return. Whether or not the ball has hit the racket in an uncontrolled manner (frame, rebound) is not of importance to PA. In the following, the statistical assessment of observer agreement will be explained for the case of two observers and a nominal-scaled observational variable with k levels, which is the standard case in observational systems in sports (see also Box: “Observer agreement for interval judgements”).

Observer Agreement for Interval-Scaled Judgements

The agreement between judgements in the case of interval-scaled variables, for example, two physical education teachers measuring the long-jump performances of the pupils in a PE class (independently), is assessed by the “coefficient of objectivity” that is given by the Pearson-Bravais correlation r between the judgements. A more specific statistics is the intra-class

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correlation (ICC) that is suited for more than two raters and may be chosen from a variety of variants, each with a specific indication (Wirtz and Caspar 2002; Gwet 2012). By definition the calculation of r requires a pairwise, case-by-case data organization and may be calculated only for pairwise non-missing data. Barrow and McGee (1979) recommend to apply a threshold of r > 0.90 for sufficient objectivity. Interval-scaled variables are typically obtained when the measurement is a physical procedure such as measuring the length of a long-jump, whereas observational measurement procedures working with category systems for variable levels generally result in nominal-scaled variables. It must be noted that measuring agreement is a much wider field than can be discussed here, there are whole textbooks on the issue (Wirtz and Caspar 2002; Gwet 2012) presenting numerous statistics, for example, for multiple experts, or nominal, ordinal, or interval-scaled judgements. The assessment of observer agreement starts with an “agreement matrix”: a quadratic table with columns for the levels of the observational variable recorded by one observer and rows for the ones recorded by the other (see Figs. 2.5, 2.6, 2.7, 2.8 and 2.9 as examples for agreement matrices). An agreement matrix for an observational variable with k levels consists of k2 cells. For each single occurrence of the observational unit, the judgements of the two observers are recorded in the appropriate cell of the matrix. Cell frequencies may be denoted with zi,j, that is, the number of entries in row i and column j. A zi,j value in an agreement matrix means the number of judgements, where observer 1 assigned level i to an observational unit and observer 2 assigned level j to it. Then, agreements are in the diagonal cells of the agreement matrix zi,I; deviations in judgement occur in the non-diagonal cells zi ≠ j. Very intuitively, a good and common measure for agreement is the percentage of the sum of the diagonal cells, that is, the identical judgements of the two observers, compared to all judgements, the per cent agreement: i 1



% Agreement  100   zi ,i / N k

Though being simple and intuitive, there is some criticism with per cent agreement. Assume two people tossing a coin at the same time and record each result in a four-cell agreement matrix (heads or tails, observers 1 and 2). If the coins are fair and on the long run, we expect to have 25% of all tosses in each cell. Calculating per cent agreement, we find a value of 50%. This means we have 50% agreement when tossing a coin, the classical chance experiment. If two observers would just toss a coin when there is a duel and assign the winning team according to head or tail without even watching the match, we would find a 50% agreement. This type of

2.3 Validation of Observational Systems

47

agreement is called chance agreement, and it is inevitably included in per cent agreement. The criticism is not only that one would not like to include chance agreement in a valid measurement of agreement but also that the amount or extent of chance agreement depends on the number (and distribution) of levels of the observational variable. For example, if two observers each throw a dice, expected per cent agreement (=chance agreement) would be 1/6 or 16.67%. Thus, it is a good idea to characterize observer agreement with a statistics that eliminates chance agreement. The most commonly used statistics with this property is Cohen’s kappa: Kappa 

PO  PE 1  PE

i 1



PE   pi ,.  p.,i k

with: PO = observed agreement, PE = expected agreement; pi,. = relative frequency of entries in row i; p.,i = relative frequency of entries in column i. A closer look at this formula shows that kappa means the ratio between “observed agreement minus chance agreement” and “total agreement (=1) minus chance agreement” which is quite intuitive. Cohen’s kappa calculates chance agreement as sum of the k category agreements. A category agreement is the product of the relative frequency of observer 1 assigning category i and observer 2 assigning category i. This is straightforward also, because it expresses the independent coincidence of two chance events, for example, when tossing a coin we have a 0.5 chance for tail, and the product 0.5 × 0.5 = 0.25 is the probability of two coins showing tail in independent trials. The sum over the categories tail and head is expected or chance agreement: PE = 0.25 + 0.25 = 0.5. Cohen’s kappa is the standard statistics for evaluating observer agreement. By convention, a value of kappa = 0.80 is acknowledged as sufficient agreement for nominal variables in observational systems (Lames 1991; Frick and Semmel 1978: 0.75–0.80; Flanders 1960: 0.85). This is partially not in line with other conventions published for Cohen’s kappa. For example, Altman (1991) gives a table with much lower levels required for acceptable kappa, for example, 0.4–0.6: “moderate”. This may be appropriate when kappa is used as a measure for correlation between two categorial variables and one is interested in examining whether there is a correlation at all. This is different from testing observer agreement, though, which means to check whether agreement is high enough to achieve trustworthy measurements (see Box “Sufficient levels of measurement quality” below). In this case, it is a good idea not to work with gradations such as poor, fair, or moderate (Altman 1991) but to apply a strict threshold, for example of 0.80, instead.

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Sufficient Levels of Measurement Quality

Sufficient levels for statistics (benchmarks) characterizing the quality of a measurement, for example, coefficients of objectivity and reliability or statistics for observer agreement, are of big practical interest. The question whether a measurement is acceptable or not has to be answered (positively) before reporting results or drawing conclusions from a study. One seemingly obvious option—and at the same time the most frequent pitfall—is to test these statistics for significance typically resulting in a p-value. This p-value, though, denotes in almost every case the error probability for rejecting the null hypothesis that the statistics obtained is equal to zero. For example, in the case of a significant Cohen’s kappa, one has proven that its value is above zero, that is, that there is agreement at all. But this is not the question! We want to know whether there is sufficient agreement. This question is not addressed by significance testing! Searching for suggestions for acceptable thresholds for agreement given by experts in the field typically leads to confusion, because of different levels given by different authors. Sometimes the authors obviously mean effect sizes of rejecting the null hypothesis and not thresholds for acceptable agreement (Altman 1991). Differences may also occur because of technical reasons as most statistics depend on sample size and/or number of category levels (Wirtz and Caspar 2002). The most severe objection against a binding convention is that a reasonable threshold should depend on the severity and difficulty of the judgement, thus being rather strict for critical or easy measurements and more tolerant in noncritical or difficult measurements. The recommendation for a Cohen’s kappa benchmark of 0.80 given above must be seen in front of this background. Nevertheless, searching the literature until one has found a recommendation for an acceptable kappa level that fits one’s own data may not be tolerated.

2.3.3.1 Agreement Matrices for Observer Training In Fig. 2.7, it is demonstrated how an agreement matrix may be used for observer training. The idea is to calculate not only the global %Agreement (85.0%, Fig. 2.7 left) but also the %Agreement for each level separately. This is done by collapsing the corresponding cells as demonstrated in Fig.  2.7 right for the level “topspin” resulting in a %Agreement (topspin) of 64.5% (result for level “slice”, 97.4%, and for level “drive”, 45.5%). This means that the problem is located at the distinction between the levels “drive” and “topspin”, whereas the judgement of level “slice” is very satisfactory. But in addition, we see also that the most severe problem in agreement is the discrepancy in judging drive or topspin with observer 1 tending to see “earlier” a topspin when observer 2 still judged “drive” (ten times, the opposite happened only once!). Thus, we may derive direct and very concrete recommendations for observer training from an agreement matrix. In this case, increasing the threshold between

2.3 Validation of Observational Systems

49

Fig. 2.7  Agreement matrix for observer training left, complete matrix, and right, collapsed matrix for level topspin

drive and topspin by observer 2 and/or decreasing this threshold by observer 1 would be most promising for increasing overall agreement and could be targeted at in observer training.

2.3.3.2 Weighted Kappa There are cases where we have variables with discrete levels of a continuous variable such as areas on the football field indicated by lines on the lawn (e.g. offensive half, defensive half). Because here we have adjacent levels, it may happen that one is simply not able to decide whether level k or level k + 1 is the correct observation. Practically spoken, if an event happens exactly on the border between areas k and k  +  1, there is an inevitable ambiguity on the location, for example, a kickoff is performed exactly at the midpoint and it could be assigned to either offensive or defensive half. Academically spoken, when we have adjacent discrete levels of a continuous variable, the differences between the two levels may become arbitrarily small; at least they may fall below any perception threshold (This implies for example that there is no objective offside judging in football!). In some of these cases, we would not like to assign the label “no agreement” to two observations where the exact value is not assessable without ambiguity. (This does not necessarily hold true for the kickoff above, because among the many overall ball contacts in a football match, the few ones with natural ambiguity between defensive and offensive half may be neglected.) For solving this problem, we have the option of using the weighted kappa statistics (kappaw). We may weigh an observation at a neighboured level not as disagreement (weight = 0, usual kappa procedure) but with a value between 0 and 1 (e.g. weight = 0.5, weighted kappa procedure). The result will be a higher level of agreement, which is justified in some cases like the depicted one, but must, of course, be considered only with caution and always from the perspective of critical reliability testing. An example is given in Fig. 2.8. In an observational study measuring the height and the volume of splashes in board diving (Wolle et al. 2003) with a four-level Likert scale (variable “volume of secondary splashes”), 42 jumps were controlled

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Fig. 2.8  Matrix of agreement (top left), matrix of weights (top right), and weighted agreement matrix (bottom) for the height of splashes in board diving

for observer agreement. The ordinary (unweighted) matrix of agreement is given in Fig. 2.8, top. Agreement statistics are not sufficient. Since the nature of the variable does not allow to provide discriminating operational definitions and we have adjacent discrete categories describing a continuous phenomenon, the prerequisites for weighted kappa are met. Figure 2.8, top right, depicts the matrix of weights, with a weight of 0.5 for adjacent levels. The weighted matrix of agreement (Fig. 2.8, bottom) is obtained by multiplying each cell of the matrix of agreement with the matrix of weights. After this, each entry is treated as agreement (non-diagonal cells: weighted agreement); the sum of all cells is observed agreement. Expected agreement and weighted kappa is then calculated quite straightforward. Since there were only deviations between observers in adjacent levels, expected agreement increases by introducing weights, but to a much greater extent, this holds true for observed agreement. Taken together, weighting lifts kappa to a much more acceptable level which may be seen as is justified in this case, because indications for weighting are met.

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51

2.3.3.3 The Kappa Paradox Another problem with kappa arises when we want to test for the type I error mentioned above, that is, agreement on the occurrence of an event. In Fig. 2.9, we see a (constructed) matrix with the agreement of two observers on recording duels during a match. In 140 cases, there was agreement, but observer 1 recorded five duels, which observer 2 did not record and vice versa. %Agreement is 93.3% and looks fine. But when we calculate Cohen’s kappa, we face a surprise: kappa = −0.03! This phenomenon is discussed, for example, by Feinstein and Cicchetti (1990). They named it the “kappa paradox” because we obtain small kappa values although there is high per cent agreement. The reason for this paradox is found in the imbalanced marginal totals or sums (145 vs. 5). The relevance of the kappa paradox lies in the fact that we must expect imbalanced marginal sums each time we check for type I error, because typically we expect much more events to be recorded by the two observers in agreement than in disagreement, and most importantly, the frequency in cell no event/no event is always zero by definition/design. Both effects in sum care for imbalanced marginal totals. For these cases, Gwet (2002, 2008, 2012) recommends the AC1-coefficient (Agreement Coefficient 1) with a modified calculation of chance agreement, in our case AC1 = 0.93. Thus, type I agreement should be controlled using AC1 instead of Cohen’s kappa! AC1 

PO  PE 1  PE

PE  2 p1 1  p1  p1 

p

1,.

 p.,1  / 2 N



with: PO = Observed agreement, PE = Expected agreement;p1,. = relative frequency of entries in row 1; p.,1  =  relative frequency of entries in column 1; case of two observers (Gwet 2002, p. 4).

Fig. 2.9  Type I agreement matrix for recording duels in match (constructed data)

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2.3.3.4 Inter- and Intra-observer Agreement A last issue to be mentioned here is the difference between inter- and intra-observer agreement. Inter-observer agreement depicts the case of two independent observers, which is usually required in assessing agreement (O’Donoghue 2010). Intra-observer agreement is obtained when one observer does the analyses twice with a certain amount of time between the assessments to wash out memory effects. Typically and plausibly, intra-observer agreement is higher than inter-observer agreement. For example, in the study of Wolle et al. (2003) depicted above in Fig. 2.8, the (unweighted) kappa values for agreement for 42 jumps were kappa = 0.367/0.468 for inter-rater agreement for height/volume of splashes and kappa = 0.897/0.867 for intra-rater agreement. Obviously, the failure to provide suitable operational definitions for the levels of the variables (very high, high, low, very low) led to these unsatisfactory results between observers, whereas the judgements of a single observer seem to be to a great extent reproducible. It must be clearly stated that observational studies that do not test inter-observer agreement using appropriate, critical procedures and/or do not meet the benchmarks for observer agreement are not acceptable for scientific purposes. On the other hand, it is well known that in sports practice, one is frequently satisfied with sufficient intra-observer agreement because here, the relevant experts care mostly for their results being reproducible and not for results of other experts. May this be reasonable or not, it constitutes a difference to the requirements in scientific studies. There is no doubt though that observational data provided by data companies should undergo and pass strict tests for observer agreement, because many other users of the data from sports practice, science, and media rely on it. Although knowledge of appropriate methods and statistics to validate observational systems in sports is widespread since a long time (e.g. Lames 1994), we still find studies and reports without or with doubtful validation. This may have several reasons, for example, a lack of knowledge of principles of the design of validation studies, the use of inappropriate methods and statistics, and simply unawareness of the necessity to conduct a validation. A special case is made up of situations where there is no interest in critical, strict testing. This attitude is prevalent in commercial providers of observational data, which is quite understandable from their point of view. As long as clients especially from clubs, leagues, and federations but also from science do not ask for proofs of validity, they have good reason to continue. A rather new application field for validation procedures of observational systems is the validation of the so-called action feeds, that is, very fine-grained event systems that are made commercially available by data providers (see Box “Action feeds”). Stein (2021) validated the game interruptions in two action feeds with video observation as gold standard and found 28 problems in 171 relevant events (16.4%) such as time stamp too late or wrong player/team recorded. Especially machine learning approaches rely on validation techniques for observational data, because they conduct their studies on “big data”, that is, very large samples, where veracity (see Box “Is Game Analysis Big Data? “in Chap. 5) is constitutive and must be verified.

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2.4 Examples for Studies Using Action Detection 2.4.1 Event Profiling A first example of an observational system is an event system for a profiling task of PA (Siegle and Lames 2012). The events are all game stoppages in a football match (16 Bundesliga matches) with the main variable “type of stoppage”. Football rules enumerate all possible stoppages, thus providing the different levels for this variable. Other variables recorded per event are starting and end time, location (here given by lawn stripes), match time, and score line.

Problems with “Pure” Methodological Concepts

A methodologically interesting problem in case-by-case analyses of game stoppages is given by the events “injury” and “substitution” both taking place when the game is halted for another reason, for example, for a free kick. This means that the same stoppage may be a free kick and a substitution at the same time, thus violating strict requirements for a categorial system: one event must not meet two levels. At this occasion, one may realize that a pragmatic approach is always to prefer, keeping in mind the intended aims of a study. The alternatives giving priority to the pure methodological concept would be either to ignore substitutions and injuries as specific stoppages and just record the initial reason for the stoppage (e.g. free kick or throw-in) or to “overrule” the initial reason when there is a substitution or an injury. The former is not viable due to the specific nature (e.g. duration) of stoppages including an injury or a substitution, and the latter would result in a biased number of events of the initial stoppage, for example, the number of free kicks in a match. A solution in this case is to record these stoppages twice and being aware of this fact in frequency counts. Profiling results are, for example, frequency and duration per type of stoppage (see Table 2.4). The purpose of event profiling is to give an overview on the frequency distribution of events (throw-ins and free kicks are the most frequent reasons for stoppage; the total number of stoppages is more than one per minute playing time) and other variables recorded with the events (longest durations for injury, kick off, referee ball, and substitution, very high variability in duration per type of stoppage). Several other interesting things may be studied in addition when having caseby-case recordings of match stoppages. These reach from a detailed understanding of the intermittent nature of playing load to an investigation in how far a team tends to play the clock down by significantly longer stoppages in case of a lead in the last part of a match. It must be mentioned that this specific type of study, event profiling, is greatly facilitated by the so-called action feeds that are recorded and made commercially

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Table 2.4  Frequency and duration of game stoppages in football per match (with permission of Taylor and Francis from Siegle and Lames (2012)) Type Throw-in Free kick Goal kick Corner kick Substitution Kick off Injury Referee ball Penalty Total

Frequency (n) Mean 39.69 32.56 17.38 10.00 3.69 3.19 1.25 0.19 0.13 108.06

sd 6.72 9.03 4.27 2.78 0.87 1.76 1.18 0.54 0.34 13.02

Duration (sec) Mean 8.56 19.38 19.19 23.13 40.13 52.87 79.09 42.50 51.00 18.31

sd 5.80 12.46 7.72 15.85 14.62 11.74 40.48 17.79 15.56 16.04

Min 1 1 3 8 19 5 33 28 40 1

Max 42 64 45 205 85 76 179 63 62 205

available by data providers. This allows for much larger samples to be investigated as has been done by Zhao and Zhang (2021) examining stoppages of a complete season in five leagues (1826 matches).

2.4.2 Detailed Event Observation As example of a study, where a new observational system has to be designed when being interested in deep details of behaviour, is the observational system OSPAF (Observational System for Penalty kick Analysis in Football) of Pinheiro et  al. (2021). The aim of OSPAF is to describe penalties in a most comprehensive way with a special focus on the strategies used, that is, goalkeeper dependent or independent by the penalty taker or taker dependent or independent by the goalkeeper. At the very beginning, the authors state that the only method to study penalty shooting from a practical perspective is match observation, because in laboratory settings (e.g. Dicks et al. (2010), the specific pressure of a penalty in a real match may not be imitated, and the preferred way a player executes a penalty is overlaid by experimental instruction. The same holds true for penalty studies in training settings with players being instructed to use a certain technique or strategy, for example, goalkeeper dependent or independent strategy (e.g. Noël et al. 2015). The investigated behaviour in these settings will always lack ecological validity: first, because it is forcing players to execute penalties in a way they usually do not prefer, and second, because in real matches, one may assume that only players with a certain specialization execute penalties. A methodologically interesting aspect in the study of Pinheiro et al. (2021) is the comprehensive involvement of an expert group for the selection of observational variables. Table  2.5 shows the results for each variable in the final OSPAF.  It becomes obvious that a number of variables (24) are needed to adequately describe penalty shooting on a behavioural level. Three criteria were applied for admitting an

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Table 2.5  Expert ratings of OSPAF variables with mean and Aiken’s V and intra-rater/inter-rater kappa (Pinheiro et al. 2021) Variable Run up speed Run up fluency Approach angle Number of steps Kicking technique Ball speed Foot used to kick Non-kicking foot orientation Penalty taker gaze behaviour Goalkeeper initial posture Deception by penalty taker Anticipation movement Goalkeeper tactical action Goalkeeper performance Moment of the match Location of the match Momentary result Momentary result Match importance Penalty kick direction Penalty kick height Penalty kick outcome Penalty taker strategy Goalkeeper strategy

Agreement Mean 4.10 4.38 3.86 3.76 4.38

V 0.77 0.85 0.71 0.69 0.85

Adequacy Mean 4.00 4.14 3.76 3.81 4.29

V 0.75 0.79 0.69 0.70 0.82

Univocity Mean 0.90 1.00 0.76 0.95 1.00

V 0.90 1.00 0.76 0.95 1.00

Intrakappa 0.81 1.00 0.85 0.89 0.91

Interkappa 0.76 0.80 0.80 0.82 0.82

4.19 3.67 4.24

0.80 0.67 0.81

4.10 3.86 4.00

0.77 0.71 0.75

0.81 1.00 0.90

0.81 1.00 0.90

0.84 1.00 0.75

0.79 1.00 0.81

4.38

0.85

4.43

0.86

0.81

0.81

0.78

0.78

3.90

0.73

3.86

0.71

0.95

0.95

0.84

0.84

4.19

0.80

4.24

0.81

0.86

0.86

0.92

0.81

4.29

0.82

4.24

0.81

0.90

0.90

0.86

0.78

4.14

0.79

4.24

0.81

0.90

0.90

0.77

0.70

4.76

0.94

4.71

0.93

1.00

1.00

0.86

0.83

4.48

0.87

4.14

0.79

1.00

1.00

1.00

1.00

4.00

0.75

3.95

0.74

1.00

1.00

1.00

1.00

4.29

0.82

4.19

0.80

1.00

1.00

1.00

1.00

4.24

0.81

4.10

0.77

0.95

0.95

1.00

1.00

4.38

0.85

4.14

0.79

0.90

0.90

1.00

1.00

4.29

0.82

4.33

0.83

0.95

0.95

1.00

1.00

4.29

0.82

4.29

0.82

0.95

0.95

0.95

0.90

4.67

0.92

4.71

0.93

1.00

1.00

1.00

1.00

4.81

0.95

4.57

0.89

0.95

0.95

0.75

0.73

4.52

0.88

4.33

0.83

0.90

0.90

0.79

0.75

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observational variable. In this case, the agreement between the experts (n = 20) was assessed using Aiken’s V: 1. Agreement: the degree of general acceptance of the variables to be included in the observational system (five-point Likert scale). 2. Adequacy: the level of pertinence and importance of the variable (five-point Likert scale). 3. Univocity: the clarity of the definition of a variable (two-point Likert scale). A second innovative aspect is an expert rating of the optimal viewing angle of a penalty. 71.4% of the experts indicated the angle Behind the penalty taker, aerial view as appropriate; 18.2% the angle Behind the penalty taker, pitch view; and 10.4% the angle Behind the goalkeeper, aerial view. The other four angles investigated received lower support from the experts. Optimal viewing angles have—although obviously being relevant—only rarely been the focus of observational studies. It would be interesting to see whether results differ dependent on viewing angle. This example shows that for some studies—typically studies with a very detailed interest in a certain event in a game—information available from routine analyses, for example, event and position streams of data providers, are not sufficient to answer very specific questions, in addition to the fact that routine analyses typically are not available for youth and amateur events or game sports with less media interest. Thus, one may assume that designing appropriate observational systems will remain a skill of performance analysts also in the future, although we may expect much progress in automatic event detection as well (see Box “Automated game observation”).

2.4.3 Hierarchical Categorial System As was said above, there exist more complex observational systems than just a number of events or categories with observational variables and their levels. The example given here is referred to again in the section on modelling of game behaviour in Chap. 4 (Table 2.6). We have a classical categorial system with the four observational units episode team A, episode team B, no-control, and stoppage. The term episode is chosen to distinguish this variable from the usual variable ball possession period, which is frequently taken for a binary variable, that is, either team A has the ball or team B. This is not appropriate because when a player’s ball possession is defined as being able to control the subsequent direction of the ball (Pollard and Reep 1997), which is not always the case, a state no-control must be added. Episode as phase where a team exerts control over the ball means something different than ball possession usually does. This structure is modelled with a hierarchical observational system where on the first level we have the four observational units. Second level variables introduce a new hierarchical level of observational units (begin, course and end of an episode) and on the third level we have the observational variables for all units. Figure 2.10 illustrates that interesting features of a match may be revealed using a hierarchical observational system. For two teams, the location of the beginning and the end of their episodes are given. It shows interesting details on where the ball was brought in possession and how far the ball was advanced once being in

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Table 2.6  Hierarchical observational system with game phases (categorial system) on first level and game phase-specific variables on second and third levels (Prüßner 2016, courtesy of René Prüßner) First level variable (game phase) Second level variable Episode Begin of A or B episode

Course of episode

End of episode

No-control episode

Stoppage

Third level variable Time Location x Location y Begin event Passes Direct passes Back passes Side passes Dribbles Minimum x Maximum x Time Location x Location y End event Time of begin Time of end Event list Time of begin Time of end Event list

Operational definition mm:ss 5 levels 4 levels Enumeration Number Number Number Number Number 5 levels 5 levels mm:ss 5 levels 4 levels Enumeration mm:ss mm:ss Enumeration mm:ss mm:ss Enumeration

Fig. 2.10  Start and end location of episodes (ball control periods) of the dominant (left) and the inferior (right) team in a Bundesliga match (Prüßner 2016, courtesy of René Prüßner)

possession. For example, the dominant team (Fig.  2.10, left) won the ball much more often in its offensive zone and also managed to enter the offensive zone much more often than the inferior opponent (right) no matter where the ball was won. The inferior team, though, was in a majority of its ball possessions starting in its own half and only capable to advance to the middle part of the pitch, thus indicating successful offensive pressing of the dominant team.

3

Position Detection

Around the year 2000, it became possible to track players’ positions in game sports during match. This was a revolution in performance analysis (PA) because from then on, we had a totally new family of data at our regular disposal. Before that, in the very beginnings of PA as scientific discipline, it was only in principle possible to assess positions of players on the pitch, for example, in projecting a motion picture or video frame by frame, mark positions manually on a table, read the marks, and transfer the marks to a coordinate system (Winkler 1985). Another method used by PA pioneers was to watch players’ motions in a film or video and trace it with a pencil on a football pitch drawn on a sheet of paper. Distance covered was then assessed with a nowadays forgotten device that was called curve ruler. A further approach was so-called time-motion analysis (Reilly and Thomas 1976). Methodologically, these approaches have more in common with observational systems than with modern tracking technologies. A human observer records the location (including distance) and type of a player’s movements on the pitch. Although there was more and more support by electronic devices, these time-motion analyses remained error-prone and very laborious, because each player had to be “tracked” separately based on video footage (Bloomfield et al. 2007). There was no way for a regular use of position data in practice, whereas today we have GPS (Global Positioning System)-, radar-, and video-based position detection at work in several professional game sports, in Europe dominantly in football and handball. Performance Analysis and Technological Progress

The example of position detection shows very clearly that our capabilities in performance analysis depend on the state of the art of available technology. Technological progress contains several sub-processes, such as enhanced performance of technical devices, for example, Moore’s law on computing power (Moore 1965), miniaturization, and cost reduction, all of which have led to the new technologies becoming of value for performance analysis,

© Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5_3

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finally. Technological innovations are the result of a continuous process that is by no means driven by sports science. Instead, car industry, entertainment industry, and of course military are the most powerful drivers. Nevertheless, we may expect from technological progress a continuous stream of innovations and experience shows that we may expect some of them showing potential for performance analysis. It is the task of sports science to track technological progress, to identify developments with potential for PA, to conduct pilot studies, and eventually to introduce the innovation in practice on a routine base. National scientific support systems for top-level sports may be evaluated by the degree they stimulate and promote activities aiming to bring innovations to work in sports practice (Lames et al. 2016). For sports science as well as for its discipline performance analysis this means that technological progress will keep us continuously busy in the future and also that today’s methodological options, not so much the concepts, presented in this book will be called outdated in some future. This chapter starts with an introduction in the different technologies nowadays in use for position detection in game sports. The focus here is only on technical details of raw data acquisition and signal processing that are relevant to practical decisions in performance analysis. Intricate details from an engineering perspective are left apart. Nevertheless, much like in action detection, caring for reliability and validity of position detection is a relevant issue for performance analysis as well and treated in a second section. The focus here is on specific problems, for example, with appropriate gold standards or compatibility of position data obtained from different systems/ technologies. Several examples for position-based studies may be found in Chap. 4.

3.1 Functioning of Position Tracking 3.1.1 Position Detection Methods As mentioned above, at the current state of performance analysis, three major technologies are used for position detection of players and/or ball: GPS-, radar-, and video-based tracking (VBT). The presentation of these technologies will give a rough idea of their technical functioning and then specify the requirements and limitations for each system for sports analyses and finally line out typical use cases in sports.

3.1.1.1 GPS GPS (Global Positioning System) is a satellite-based position tracking technology. Actually, there are several systems with global position tracking capabilities (GLONASS, Russia; Galileo, European Union; BEIDOU, China; Japan and India only regional) besides NAVSTAR/GPS, which is the US system. Since the US GPS

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was the first one, it is open to each user and the most used system internationally; GPS has become a synonym for satellite-based position tracking, although the correct label would be GNSS (Global Navigation Satellite System). The central feature of GPS is a network of orbiting satellites. A minimum of 25 satellites at 20,000 km height with inclined trajectories ensures that at least 8 satellites are “visible” at most points on the earth’s surface (Hofmann-Wellenhof et al. 2012). The satellites are equipped with an atomic clock and high-precision position measurement devices. They are continuously emitting radio signals with a fixed and documented structure, containing roughly spoken their ID, their actual position and a time stamp. GPS sensors are able to receive these signals from “visible” satellites, that is, they require a direct “line of sight” to them. By triangulation, each receiver is able to calculate its position on the earth’s surface. This works in principle quite simple, because if the time a signal has travelled from a certain position in space to a position on earth is known, one may calculate the distance to this position and hence conclude that the receiver is located on a sphere around the satellite with a known radius. If two of these spheres are known, one’s own position is located on a circle formed by the intersecting spheres. Finally, the intersection of the first two spheres with a third sphere mathematically gives the exact point of the receiver’s location. As one might assume already, in practice, things are not as simple. Electromagnetic radio signals emitted by the satellites travel with speed of light (about 300,000 km/s), the satellites themselves travel with very high speed, and gravitation has also a relativistic influence on the measurements. Although mathematically the minimum requirement for a precise triangulation in space is 3 satellites (see Fig.  3.1), the many sources of lacking precision require a fourth satellite for appropriate time

Fig. 3.1  Two-dimensional illustration of triangulation of a position given the distances from three satellites

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estimation and an abundance of further visible satellites to improve accuracy. Typically at least 8 visible satellites are required. The precision of standard GPS is given with an upper 95% limit of 7.8 m with an RMSE of 4 m. Therefore, in sports, we typically use differential GPS that requires an additional receiver with a fixed and known position typically close to the pitch. With the help of the signals of this stationary receiver, one is able to clean the signal and get a better spatial resolution down to some centimetres. A big improvement in the accuracy of speed data obtained by GPS came when Doppler effect in the satellite signals, that is, an increase/decrease in wave frequency when the sensor is approaching/receding from the source of the signal, was exploited for assessing speed and direction of the moving sensor. At this point, it becomes obvious that only with the advent of highly sensitive electronics and only in the recent years, one has become able to conduct the sophisticated measurements associated with GPS. First applications of GPS in sports came quite early for navigation in outdoor sports, such as sailing, for example. For jogging and golf, there are successful GPS tools as well. In the last years, we saw an increasing measurement frequency for GPS devices in game sports starting from modest 1 Hz to 15 Hz and more (but in some devices only obtained by interpolation from real measurements!) nowadays. This increase and the advent of differential GPS and Doppler speed made GPS-­ based position detection in game sports competitive to other technologies. GPS performance is hindered by anything that prevents the receiver from getting the satellite signals properly. Electromagnetic waves cannot penetrate metal or concrete structures. Therefore, GPS position detection is not suited for indoor events. Although there are some technical remedies under way, this remains a strong limitation for tracking sports events, not only indoor events but also the very relevant outdoor events that take place in bowl-shaped or even roofed stadia. This is unaffected by the option of collecting data from GPS sensors equipped with Inertial Measurement Units (IMUs) that provide indoor data, also. When using GPS outdoor, there still might be problems caused by so-called multipath effects; that means a signal from a satellite is reflected by rocks, buildings, metal constructions, or wet surfaces, and a receiver gets two interfering signals reducing accuracy. Optimal conditions for GPS are given by a flat plane with unobstructed view to the sky and no metal or concrete or wet objects around. One may assume, for example, that GPS works better on a training pitch than in a football stadium. In a recent study (Shergill et al. 2021), the quality of the GPS signal was investigated over 50 matches in 24 stadia in English Championship league (second league). It found on average sufficient conditions, for example, the number of satellites visible, their distribution (HDOP = horizontal dilution of precision), but an average of 11 min of playing time was measured regularily, where the recommended signal quality thresholds of the provider were not met. Also, there were significant differences in results depending on the quality of the GPS signal. Moreover, a requirement for GPS-based position detection is a receiver attached to the tracked object. In recent years, these receivers became very small and light and can be easily worn in a pocket of a bra-like harness typically between shoulders (line

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of sight!). Problems occur when the ball must be equipped with a GPS sensor or when only sub-­optimal fixation (hips, below protecting sports harness) is available. A big advantage of GPS for applications in sports is its ready-to-use property. As soon as receivers are attached and the base station is plugged in and records data from the receivers, the system provides data. Also, GPS is comparatively cheap, although costs increase with increasing accuracy demands.

3.1.1.2 LPS Local Positioning Systems (LPS) work similar to GPS. The decisive difference is that LPS do not work with satellites but create their own reference system by distributing so-called base stations around the pitch. These base stations receive signals from a sensor worn by the tracked object. Unlike GPS sensors, LPS sensors receive and actively emit signals. They are called transponders (transmitter/responders) or RFID (radio-frequency identification) chips. Again, the position of the transponder is obtained by triangulation of time-of-flight information from several base stations. Since a typical time of flight is now only some nanoseconds (1 ns = 0.000,000,001 s), several electronic measures must be taken to achieve sufficient accuracy, including an additional stationary transponder and the reference transponder, with a known position. These systems are also called “radar”- or “radio”-based position detection systems, because typically the frequencies of their signals are located somewhere between radar and radio in the frequency spectrum of electromagnetic waves. First applications of LPS in sports started in the first decade of this century (Stelzer et al. 2004). Initially, it was used for race car tracking and motorcycle tracking in moto-cross events. Soon, LPS was applied in soccer, speed skating (Drawer 2008), and several other sports, too. The precision of LPS, at least the one given by the manufacturer, is usually quite high, for example, an error rate of 5–10 cm is reported (www.inmotio.eu). Another big advantage of LPS compared to GPS is the sampling rate. Typically, we have a basic sampling rate for a system (e.g. 1,000 Hz) that must be divided by the number of the sensors in the field. Tracking 22 football players thus is possible with roughly (reference sensors, substitutes) 1,000 Hz/22 = 45 Hz. Ball tracking with LPS requires the equipment of a ball with a sensor which remains quite a challenge and has reported to be successful by only a few manufacturers with only some documented reliability studies so far (Seidl et  al. 2016; Blauberger et al. 2021). Nevertheless, ball tracking via LPS is available for football, basketball, and handball and will enhance diagnostic options in the near future. The practical requirements for a LPS allow indoor position detection. There are considerable space requirements because base stations need to be installed around the pitch with a sufficient distance to the pitch; thus measurements in smaller indoor halls may create problems. Moreover, the positions of base stations and reference transponders must be known exactly. Both requirements, mounting and measuring of base stations give a preference to fixed installations. Mobile measurements require the setup of base stations and determining their position with a tachymeter with a precision of some millimetres. Since the technology used is more demanding, costs for LPS are typically higher by a factor of 2–3 compared to GPS.

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3.1.1.3 Video Video-based tracking (VBT) is a completely different technology compared to GPS and LPS. It relies on video images of the match taken by one or more cameras. A video frame consists of rows and columns, which are represented digitally by their colour value. For example, the pioneering VGA standard had 640x480 pixels with 262,144 possible colours. More modern standards are full HD (1.080 × 1.920 pixels) and 4 k or ultra HD (4.096 × 2.160 pixels). VBT solves the task to determine the positions of objects based on colour information of thousands of pixels per frame (VGA: 307,200 pixels; 4 k: 8,847,360 pixels) entering the system at a frame rate of typically 25 Hz (PAL; NTSC: 30 Hz). Object identification is addressed by making use of several image processing technologies that became only available in the last decades due to progress in the capacities of relevant hardware and to theoretical innovations in image processing. The basic process may be described—very simplified—with four steps: video recording, world-to-pixel transformation, object segmentation, and pixel-to-world transformation (Beetz et al. 2005). The quality of video recordings is a decisive prerequisite for the quality of VBT. We need a full-pitch coverage allowing the identification of the objects of interest. First, the tracked objects must be represented with a sufficient number of pixels to make it possible for the algorithms to detect the object. This might be achieved by using highresolution video (e.g. 4 k), but this used to be limited in the past by the amount of data to be processed in real time. Although it is in principle possible to analyse videos from a swaying, tilting, and zooming camera, typically several fixed cameras are used to cover the whole pitch. We know systems with two cameras as well as systems with 20 or more cameras, the latter solutions again touching technological limits of data handling. A second problem may at present only be alleviated, not solved: occlusions, that is, one object (player) appears in front of a second one in the video image. Thus, the cameras should be distributed around the pitch, and also their mounting position should provide a reasonable angle of sight to the pitch so that the number and degree of occlusions are minimized (see Fig. 3.2). The next step consists of the world-to-pixel transformation f: world  →  pixel. This means that for each camera, the location of each point on the pitch in the pixel matrix has to be established by a calibration process. For this purpose, objects with known location are identified in the pixel matrix. In football, typically the lines on the field are used with their known (middle circle, penalty box, penalty point, goals) or assessed (length and width) dimensions. Problems that may occur at this step are optical bias of the camera lenses and a non-flat surface of the pitch, the latter being generally the case because for reasons of water drainage, the elevation of the pitch may be up to 0.5 m higher in the middle compared to the corners. The central step of VBT is the identification of the objects of interest (players and ball) in the pixel matrix. For this purpose, several techniques of pattern recognition are at hand (Beetz et al. 2005). For example, background subtraction allows identifying so-called blobs, that is, potential locations of players, by subtracting the current pixel matrix from an average value per pixel obtained from several frames (background). The most important cues are the dress colours of players of the two teams, which must also be “learned” before the analyses. A player model consisting, for example, of head, shirt, trousers, and legs/socks with the respective colour

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Fig. 3.2  Calculation of area with sufficient elevation angle (orange line) dependent on camera position (blue). Parameters are elevation angle (here: 12°), camera’s distance to pitch (15 m), and height above pitch (20 m)

values is fitted to each blob. With this player model, the pixel with the best representation of the player’s position on the pitch (usually a vertical projection of the player’s estimated body centre) is identified. The world xy-coordinates of the player are obtained by making use of a pixel-to-­ world transformation, which is the inverse of world-to-pixel transformation that was established initially f−1: pixel → world. It must be mentioned that these four steps are a very simplified description of the process. In practice, information from previous frames and from the other camera views is necessary to establish a good position estimate, and several more techniques of pattern recognition are involved (Beetz et al. 2005). As already mentioned, a problem in VBT is video quality. In a field setting, we find unfavourable or changing light conditions with sharp and changing light/ shadow contrasts. Depending on elevation angle, there is more or less background interference. Weather conditions such as rain, fog, and snow should hamper VBT as well. Also, colours of player’s dresses may change with ground contact especially on muddy playgrounds. The extent of influence on measurement results of these effects is unknown since there is no study so far that has investigated the impact of these problems. The biggest and remaining problem for VBT is occlusion. This means that a blob contains more than one relevant object. Although one tries to care for this as much as possible by camera positions and blob analysis, occlusions are in some situations inevitable when players approach each other very closely like, for example, in front of the goal during corners. Even less relevant situations may lead to occlusion, for

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example, hugging players after a goal scored. Intervention of human operators is needed to reassign the player’s identity to the segmented objects. In contrast to the automatic GPS and LPS, VBT is only a semiautomatic technology, requiring human intervention typically some hundred times per match in the first years. A big advantage of VBT is that it works without sensors carried by the objects. Up to 2015, when IFAB and FIFA started to develop standards for electronic performance and tracking systems (EPTS), any electronic sensors were prohibited in football, thus video-based systems being the only alternative for recording positions in football. The same situation is found in basketball where in NBA players were not allowed wearing LPS sensors until 2017 when wearable technology was in principle admitted. The sampling frequency is identical to the video frame rate, that is, 25 Hz with PAL standard. In principle, it would be possible to use high-frequency video, but as with high-resolution video, this is limited by data processing capacities. Accuracy faces additional problems in comparison to other technologies like distance to the cameras or direction of movement relative to the camera axis (moving perpendicular or in line with the camera axis) (Siegle et al. 2013). The business model is different from GPS and LPS. While with GPS and LPS a customer may purchase and run a system, VBT is typically offered as a service of specialized companies. Typically such a company is contracted to supply a whole league or event with position data as VBT is much more demanding what technological (data network) and personal resources (correction of occlusions) is concerned. Since there are high demands concerning the quality of video footage, the practical use of video-based tracking is mostly limited to competitive matches in professional leagues in large stadia. There is also a tradition of VBT-based indoor position tracking since around 2010 in NBA. Only recently, systems enter the market that do tracking from broadcast video or use drone-based videos thus becoming independent from fixed cameras at elevated positions. In Table 3.1, a short comparison of the three tracking technologies is given. Each category is roughly characterized with a four-level scale.

3.1.2 Signal Processing Each of the three technologies mentioned above delivers as raw data continuous streams of xy-positions of the relevant objects at their respective sampling frequency. This raw data is typically still quite noisy and needs further processing to Table 3.1  Comparison between different tracking technologies (− problem, 0 neutral, + positive, ++ very positive) Tracking technology GPS LPS VBT

Hz − + 0

Accuracy − 0 −

Handling ++ 0 −

Mobility ++ 0 −

Sensor − − ++

Outdoor ++ ++ 0

Indoor − + 0

Costs + 0 −

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obtain meaningful trajectories. This process is called smoothing or filtering. Most of the tracking systems deliver only post processed, that is, smoothed data to the client. The client does not come in touch with raw data. Ogris et al. give the rare opportunity to have a glance at raw data, in this case from a LPS (Ogris et al. 2012, Fig. 3.3). It is very impressive to see the great extent of raw data scattering and the heavy corrections imposed by smoothing, in this case by a Kalman filter. Only after smoothing, the trajectory becomes comparable to the gold standard trajectory at all. Nevertheless, since post processing may be responsible for errors, especially in certain types of movements, some aspects of it need to be mentioned here to create a good understanding of the functioning of position detection in sports. In the following, the impact of sampling frequency and degree of smoothing will be made aware of. Again, the focus is not on the technical details but on consequences for position detection in performance analysis.

3.1.2.1 Sampling Frequency The impact of the sampling frequency, that is, the Hz rate of the measurements (1 Hz is one measurement per second), on the precision of measurements is best illustrated graphically. In Fig. 3.3, the approximation of an original movement trajectory (red) by measurements of different frequencies (blue, turquoise, green) is illustrated. It is easy to perceive that the lower frequencies are not capable to pursue the original movement satisfactorily and thus not capable to give accurate estimates, for

Fig. 3.3  Approximation of a trajectory by measurements of different frequencies

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example, for the distance covered by a player on this trajectory. One might also arrive at the conclusion that the necessary frequency depends on the original movement. If this is a less curved line, like a jogging track, measurements with lower sampling rates would yield good estimates, also. In signal theory, the minimum necessary sampling rate is given by the Nyquist-Shannon sampling theorem (Shannon 1949). It says that this is twice the maximum frequency of the frequency spectrum of a signal. This works only for signals given as a mathematical function, because there is no upper limit for a spectral frequency in a natural noisy signal. There are some conclusions for the practice of position detection in sports, though. Movement trajectories including sharp turns and high accelerations require higher sampling frequencies than linear movements with lower accelerations. Thus, a low-frequency GPS may be sufficient for monitoring the trajectory of a jogger. Competitive football, though, is—at least concerning actions close to the ball— characterized exactly by the demanding properties mentioned above, sharp turns and accelerations. This issue will be addressed again in the next section on validation of position detection.

3.1.2.2 Smoothing Since raw data from position detection are quite noisy (Ogris et al. 2012), they must be mathematically processed before a reasonable trajectory of the object on the pitch is obtained. If one would not do that, totally absurd values for distances travelled, speed and especially acceleration would be reported. Smoothing is justified especially when taking into account that each point of raw data is actually the most likely estimate for this point with other estimates having a similar probability. There are several options available for smoothing, the most popular ones are the following: • Curve fitting: If we know that the movement is determined by a mathematical function, we can determine the parameters of this function, for example, slope and intercept of a linear function, by a “minimum least squares” (MLS) estimate. • Moving average: For each point, the smoothed value is the mean value of some points before and after that point. The number n of these points indicates the degree of smoothing using moving averages, for example, MA(i, 25) gives as smoothed value for point i the average of points i−12, ..., i + 12. • Spline regression: Splines are a series of cubic polynomials that interpolate a signal with a curve of minimum curvature. In spline regression, a certain tolerance interval around each point is allowed for obtaining an even smoother curve. The size of this interval determines the degree of smoothing with splines. • Filtering: This is a large family of smoothing methods that all have in common that they work with the frequency spectrum of a signal. A frequency spectrum is the result of a Fourier transform of a signal. A Fourier transform is a decomposition of a signal into sine or cosine waves of different frequencies. Lower frequencies represent components of the signal that change only over longer periods, whereas higher frequencies represent rapid, rather discontinuous changes. In our case, trajectories may be represented as frequency spectrum with lower frequen-

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cies standing for the amounts of long-range movements such as basketball players moving between the two baskets in the rhythm of the ball possessions of their own and the opposite team. Higher frequencies in this spectrum are caused by rapid changes in the trajectory, either “natural” ones, such as changes of direction and speed, or the changes from measurement to measurement due to measurement error. With a high-pass filter, we may eliminate all frequencies higher than a certain threshold from the signal and thus get a smoothed (filtered) signal by applying the inverse Fourier transform. The threshold for the high-pass filter determines the degree of smoothing. As was pointed out, with each of the most common smoothing methods, there is in each case a parameter determining the degree of smoothing. This degree is a compromise between reducing measurement error (“noise”) as far as possible on the one hand and on the other hand preserving the “real” trajectory. There is no general optimal solution for this problem. Viable solutions depend on the amount of noise and on the characteristics of the real trajectories. Especially if the latter ones contain abrupt changes in speed and direction, like in many game sports, it is difficult to find a compromise. Figure 3.4 illustrates this dilemma with a simulated example. The blue line is the original movement, for example, the lateral displacement in one turn of a slalom run. The grey signal is the blue line plus normally distributed random noise of a certain amplitude added; standing for the raw data, one obtains as a concrete measurement. The orange line is the smoothed grey signal (here a moving average over 25 measurement points was applied).

Fig. 3.4  Simulated smoothing with moving averages

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What we see is that smoothing gives (in this case) a fine approximation of the original movement, but also, that in the surroundings of extreme values, here the change of direction, smoothing leads to flattening the original peaks. This systematic problem tends to become bigger with stronger smoothing and more extreme peaks in the original movement. Summing up, one has to acknowledge that signal processing is an important part of position tracking. Typically, the applied methods are hidden to the users of tracking data. Nevertheless, it is useful to realize that there is no best way of signal processing, and the optimal procedure depends on the error rate of the measurements and the properties of the examined movements. Together with knowledge of the strengths and weaknesses of the different tracking methods, this is a prerequisite for conducting adequate studies using position tracking data.

3.2 Validation of Tracking Systems Applied sciences like PA often face problems meeting academic standards. Especially the validation of tracking systems may be criticized in this respect; details will be given explicitly below. Typically, when new measurement devices are introduced in academics, validation studies come first to demonstrate reliability and validity of the assessments. In sports psychology, for example, one sometimes may have the impression that there are as many papers on validating new questionnaires as papers with results obtained using these questionnaires. Performance analysis is dealing with positional data from professional sports competitions. These are in general not collected by the researchers themselves but by commercial data providers (see Box “Commercial Data Providers”). This frequently leads to the situation that data without sufficient prior validation are available. Of course, it is seducing for a scientist—including the author—to start analyses without a validation when data are at hand. Also, it is understandable that there is not too much effort in ex post validation of widely introduced procedures. Instead, methodologically poor “fig-leaf” validations are quoted, for example, Di Salvo et al. (2006) with a validation of Prozone have 306 quotes according to Google Scholar and Zubiaga (2006) with a validation of Amisco has 63 (a dissertation in Spanish!). Nevertheless, an unsatisfactory academic level of validation studies is not only a problem for the scientific discipline of performance analysis; it may lead also to validity problems with the results of the studies and—very important for an applied discipline—it could lead to inappropriate decisions being taken in the day-to-­day work in practice. Commercial Data Providers

When position tracking was introduced in the last two decades, this gave rise to a growing industry of data providers. As this is a business, the products delivered are designed primarily to meet the demands of the clients. Originally, the primary clients of data providers were media, though. It is the media that pay for the information provided, in general via the owners of the proprietary rights, such as clubs, leagues, or federations.

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Since scientists do not act as direct customers of these companies, it is no surprise that scientific standards do not play a big role for commercial providers: • There is no interest in publishing the signal processing procedures involved, because these are hidden from competitors as intellectual property. • There is no interest in publishing the underlying definitions of the observational systems, because this gives rise to never-ending discussions and justifications. • There is no interest in objective, high-quality accuracy checks of position tracking, because quality control may be achieved with internal testing as well and above all without creating problems in case of bad results. Taken together, there are good reasons why the companies in the past did not care primarily for scientific standards, which in turn created methodological and ethical problems for researchers. On the other hand, more and more clubs started to use tracking information for practical purposes in training, thus relying on reliable data, and the FIFA EPTS initiative (https://www.fifa. com/technical/football-­technology/standards/epts) heads in the same direction as well. At present, the accreditation of EPTS by FIFA has become a routine, despite some open problems in EPTS validation mentioned below. At this point, it must be mentioned that practical demands require not only single systems to be tested for accuracy, but also methods must be derived making positional data from different source systems comparable. Why is this a relevant problem? Typically and historically, match analyses are conducted by VBT. As explained above, the requirements for VBT are frequently not given in training either for organizational reasons (employ tracking companies) or for technical ones (camera positions). As a consequence, position tracking in training and on training pitches is conducted using LPS or GPS. If training pitches are equipped with stationary LPS, it is even possible that sessions not accessible to LPS (different pitches or other locations, for example, training before away matches) are tracked with GPS.  In sum, we have at least two, sometimes even more, tracking systems/technologies working for assessing movement profiles in competition and training. Moreover, as the purpose of training is preparation for competition, movement intensities and other characteristics of exercises in training are frequently determined with respect to match characteristics such as overall intensity and duration or number, intensity, and duration of interval bouts (Buchheit et  al. 2014) but also passing speed and number of ball contacts. Taking these two aspects together—the use of different systems and the need for cross-referencing between systems—gives rise to the demand for not only validating individual EPTS but in addition also investigating the compatibility of different position tracking systems. Some naïve approaches (Buchheit et  al. 2014) using linear transformations between the data of two systems resulted in very unsatisfactory agreement between

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systems. It became clear that deviations between systems are different for trajectories with different characteristics, for example, linear jogging with low speed vs. sharp turns with maximal acceleration. Linke and Lames (2019) found out that considerable differences between systems originate in the different ways a player’s body is represented, for example, sensor at the centre of shoulders (typical for GPS, mostly LPS) or the centre of pelvis (sometimes LPS). VBT takes the centre of the detected player model which corresponds to the centre of the pelvis. Taken together, comparability studies between EPTS pose a specific methodological problem of their own. This chapter continues with a decisive aspect of position tracking validation, the employment of appropriate gold standards. As validation studies make up a special kind of scientific studies, the next section is dedicated to questions of designing validation studies in the sense of a general methodology. Finally, the present state of knowledge of the accuracy of position tracking for different systems and different items is depicted.

3.2.1 Gold Standards for Position Tracking in Sports The International Organization for Standardization (ISO; www.iso.org) defines a criterion standard or gold standard as a value or measuring method that serves as an agreed-upon reference for comparison, which is derived as a theoretical or established value based on scientific principles. A gold standard is an indispensable ingredient for a validation study, because something like ground truth is needed to compare the results of the tested systems with (Luteberget and Gilgien 2020). The most appropriate gold standard does not only depend on technological options but also on the kind of validity that is demanded. Should the measurement be valid for whole body movements or just centre of mass, are we interested in elementary movements such as linear runs or in real football movements, and do we need validation of performance indicators or of each xy-position? Taken together, it still is to be considered an art to find an appropriate gold standard for a validation of a tracking system. Despite these remarks underlining the necessity of gold standards in validation studies, there are also studies that primarily compare results from different systems and do not use a gold standard (e.g. Randers et al. (2010) and Harley et al. (2011)). In these cases, one is not interested in the absolute accuracy but in a relative comparison of different tracking systems. It might be a little bit unsatisfactory in cases of deviations between the systems not to be able to tell which system is responsible for the (larger part of) errors, especially one is not able to recommend a superior system. As an important result, both studies demonstrate impressively that there are problems with comparisons between different systems (although this becomes not obvious in the discussion sections). Randers et  al. (2010) examine four different systems and give results that allow calculating the percentage of the lowest mean compared to the highest mean (set to 100%) obtained from the four systems. In

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detail, this is 87.8% for total distance, 60.8% for high intensity running, and only 54.8% for sprinting distance. In a further paper on the topic, Buchheit et al. (2014) try to solve the problem of incompatibility of data from EPTS employing three different technologies by introducing linear transformations to adapt measurements from one system to the others. Because of lacking agreement between the systems, this has to be done separately for both different performance indicators and different pitch sizes. The literature on validation of position tracking in sports knows several different gold standards that were used in the past (Luteberget and Gilgien 2020): • A very commonly used gold standard is a predefined movement circuit with known spatial extensions (Frencken et al. 2010), for example, 5 m straight, 90° turn, and 5 m straight. Here, we may compare the “real” dimensions of the distance to cover (in the example: 10 m) with the distance provided by the tracking system. The problem with this kind of gold standard is that we are not sure whether the players actually perform the prescribed path exactly. In the case quoted above and in several similar ones, there remain doubts, because the trajectory is— mathematically spoken—not continuously differentiable, and it is physically not possible to run this path exactly at constant speed (infinite angular acceleration required in turning point!). • Timing gates are widely accepted as a high precision criterion measure; they provide precise measurements of the time needed to travel from gate 1 to gate 2. As speed reference, they are only of limited use (Aughey 2011; Redwood-Brown et al. 2012), because one must again assume that the athlete actually performs the prescribed path (which is a problem with nonlinear paths, for example, not continuously differentiable paths with “corners”) and one must be aware that timing gates only provide estimates of the average speed between the two gates. If one is interested in the precision of xy-measurements, which is a quite natural question in testing tracking devices, timing gates fail to answer it. • Momentary xy-positions may be assessed using radar- or laser-based distance measurement devices. These devices, e.g. Laveg, emit radar or laser beams and receive the reflection of a beam from the object very much like police does with cars in traffic control. At a closer look, this gives only the distance of the object, but as this is done at about 100 Hz, this provides a good estimate of momentary position and speed as well. In tracking validation studies, this gold standard was applied, for example, by Varley et al. (2012) and Siegle et al. (2013). The restriction here is on linear movements. There may be acceleration or deceleration, but as only distance is actually assessed, valid measurements are only obtained for movements directly towards or away from the camera. • Finally, the most advanced gold standard at present is “imported” from laboratory research. Marker-based systems for high-precision movement assessment are standard in lab-based movement analysis such as gait analysis. Technically, most of them are working with infrared cameras and infrared-reflecting markers attached to the object. In a lab setting, eight or more fixed cameras are installed, and a typical measurement volume in a movement science lab is about

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5 × 5 × 3 m. As this technology is meant primarily for indoor use, transferring it to outdoor settings is quite hazardous, for example, because sunlight “blinds” the infrared sensors of the cameras and rain or even humid grass may give rise to reflections that may distort marker detection. At present, there are only few studies known using an infrared movement analysis system as gold standard under outdoor conditions. Duffield et  al. (2010) and Vickery et al. (2014) validated GPS using exercises from tennis, cricket, and agility training, while Ogris et al. (2012) and Stevens et al. (2014) tested the accuracy of LPS both using soccer-specific movements. Linke et al. (2018a, 2020) used soccer-­ specific exercises also and tested GPS, LPS, and VBT systems. These studies are characterized by using different numbers of infrared cameras and different measurement volumes. The problem with infrared movement analysis systems such as Vicon as gold standard for EPTS is the confined space of the measurement volume. Duffield et al. (2010) use 22 cameras for (half?) a tennis court, Vickery et al. (2014) use the same system for exercises with 21 m maximum length, Ogris et al. (2012) use 8 cameras for a 26.5  ×  24  m rectangle on a soccer pitch, and Stevens et  al. (2014) had a 10-camera system controlling exercises in a 30 × 3 m and a 15 × 6 m rectangle, whereas Linke et  al. (2018a, 2020) used 33 cameras for a 30  ×  30  m square. A similar method (25 x 25 m?) was adopted for FIFA’s EPTS validation. A question that is frequently not addressed is controlling the accuracy of gold standards (Merriaux et al. 2017). Frequently, it is not sufficient to report the manufacturer’s specification instead of conducting measurements by oneself. Especially marker-based tracking systems typically need to be installed in a field setting prior to each study. This requires sophisticated calibration procedures, and thus even gold standard results are prone to errors. As a consequence, the accuracy of the gold standard over the whole measurement area should be demonstrated with a special investigation (Linke et al. 2018a, 2020). A persisting problem up to now concerns the validation of EPTS in football. One would like to be able to control position measurements all over a whole football pitch (FIFA norm: 105 × 68 m) with players performing a football match. The desire for a full-pitch gold standard is not an aesthetic one, but we see maximum speed and acceleration values in the limited measurement volumes that are much lower than in real matches. To make it even worse, these high-intensity values are most error-­ prone for tracking and provide the most important information for sports practice. Regrettably, one must state that in the studies published so far, there is no gold standard allowing for full-pitch validation.

3.2.2 Design of Validation Studies Conducting an EPTS validation study requires several methodological decisions, which can be made more or less appropriately. Some of these are mentioned here to facilitate a critical reception of validation studies. These decisions depend on the intention or purpose of the validation (e.g. system optimization, system comparison,

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demonstrating benchmarks) and thus are by no means trivial. The main sources for the following sections are Linke et al. (2018a, 2020). As actual validation studies are conducted almost exclusively in football, adaptation of the validation methodology to other sports is not discussed.

3.2.2.1 Measurement Site The measurement site should provide optimal conditions for the tested systems as well as for the gold standard. A second criterion is ecological validity; the systems should be scrutinized under conditions similar to their practical application. These claims together create problems when EPTS using different technologies—GPS, LPS, and VBT—are to be validated at the same time. The fact that each system has its specific optimal site (indoor, outdoor, stadium, see Table 3.1) leads to compromises required when all systems are to be tested at one time and—consequential— in one place. Buchheit et al. (2014) compared three technologies using an open roof stadium and report non-optimal conditions for VBT. Linke et al. (2018a) conducted their study in a wide stadium with only few spectators’ stands. They erected an additional scaffold for VBT ensuring the required conditions (here: viewing angle). The second study (2020) was performed in a professional soccer stadium (ESPRIT Arena, Düsseldorf, Germany) for testing two VBT systems. The stadium’s roof was closed to allow daytime testing with the infrared cameras of the gold standard system. Moreover, since studies have shown an influence of the location on the pitch on the precision of the measurements (Siegle et al. 2013), one either could choose a more difficult or more easy location in the pitch for the tested devices. For VBT, a difficult condition is a location with a maximum distance to the nearest camera and exercises conducted in a movement plane in direction of the relevant camera’s line of sight. LPS might be hampered by concrete or metal constructions beneath the pitch, whereas GPS could be affected by occluded line of sight to the satellites, for example, by the tribunes of a stadium. As mentioned above, the choice depends on the intention of the study; easy conditions show the full potential of a system, whereas difficult conditions demonstrate its capability to scope with unfavourable conditions that might occur in field settings. 3.2.2.2 Exercises There is a broad range of exercises that could be chosen for EPTS validation. Typically one will work with a spectrum of exercises each selected for assessing specific aspects of position tracking. These aspects could be to examine elementary movements vs. football movements, aiming in the first case to pin down performance of the EPTS to controlled elementary conditions such as standing still, moving with continuous speed at different levels, accelerations and decelerations, or continuous or accelerated curved runs. On the other end of the spectrum, there are typical training exercises or (small sided) football games. Another idea is to use exercises to be assessed more easy or more difficult by the EPTS. For example, one might provoke occlusions to give VBT a hard job (Siegle et al. 2013). Above all, as there is the limitation that we do not know a gold standard covering a full football pitch yet, it is impossible at present to employ the most relevant exercise, an 11 vs.

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Table 3.2  Assessment of the accuracy of LPS position tracking by RMSE based on results for 2 min bouts of a small sided game as example (Linke et al. 2018a) Distance covered Total (m) At 1–6 km/h (m) At 6–15 km/h (m) At 15–20 km/h (m) At 20–25 km/h (m)

Ground truth 153.38 34.11 106.87 13.74 5.91

RMSE 6.05 2.73 6.59 2.98 2.59

RMSE% 3.95 7.99 6.16 21.67 43.77

11 full-pitch football match. This is regrettable not only for reasons of ecological validity but also because of the fact that high-intensity running is reduced on a limited pitch (Casamichana et al. 2012). High-intensity exercises in turn are most error-­ prone for position detection (see Table 3.2 below) and, above all, most relevant to physiological assessments!

3.2.2.3 Levels of Analysis The most basic information that is provided by EPTS is the xy-position of the tracked object. This information is given at a certain measurement frequency specific to the system. Obviously, it is a good idea to check for the precision of this basic information. On the other hand, there are other variables derived from this information at an intermediate level such as speed and acceleration, which are typically derived from xy-positions with the exception of GPS using Doppler shift for direct speed assessment. As these data require additional data processing and are subject to different measurement problems, it is recommended to account for this intermediate level in a validation, too. Finally, performance indicators (PIs) are derived from tracking data such as distance covered or number, distance covered, and duration of stays in certain intensity intervals. Checking the validity of PIs performance analysts in practice are working with then is also a required level of analysis. 3.2.2.4 Representation of Objects/Players Position tracking systems allege to assess the position of an object, mostly the players on the field. This position is given as a point estimate (xy-coordinate), whereas in reality, a player is a three-dimensional object, of course. The question arises then, which xy-point is chosen to represent a player position. GPS and LPS locate the position of the player with the position of the sensors typically attached to the centre of shoulders. VBT detects a model shape of the player and projects the centroid of this model to the pitch as xy-position. Conducting a validation study, it is a methodological consideration which point of the player captured by the gold standard is actually compared to the EPTS. Each gold standard provides different points for comparison, respectively different options. Whereas light barriers are shut by the first body part moving through it, laser distance measurements track one point of the surface of the body (ideally; with a proficient operator only!). Studies using Vicon typically put a marker on the sensor, thus validating the sensor position. Linke et al. (2018a, 2020) attached five markers in their studies allowing to assess not only the centre of shoulders but also the centre of the pelvis,

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which is most of the time close to the centre of mass. In a special paper dedicated to the representation problem, Linke and Lames (2019) found significant differences in the results from both locations. This means, for example, that there will be differences between the results of EPTS that are due merely to the fixation points of sensors. As a result for EPTS validation methodology, we have two alternatives to test a system vs. a gold standard: The gold standard tracks the system’s sensor positions, which is the fairest procedure from the system’s perspective, or the gold standard tracks the centre of mass of the players and compares this to the results of the tested system, which puts the accent on ecological validity.

3.2.2.5 Data Processing Steps Last but not least, validation of EPTS is demanding with respect to the data processing required to perform this task. Initially, we have xy-data streams from the systems under scrutiny and the gold standard. • Re-sampling: As systems have their individual measurement frequencies, the data streams must be re-sampled (either up-sampled or down-sampled) to a common or pairwise common sampling rate. • Space synchronization: As each system has a specific origin and coordinate system (e.g. GPS comes with the geographic coordinates of latitude and longitude), spatial positions must be synchronized. This is done with a set of linear transformations (e.g. rotations and translations), for example, with a generalized Procrustes analysis (GPA; Gower and Dijksterhuis 2004). • Time synchronization: The measurements must start at the same point in time to be comparable. This may be achieved by event triggering, by electronic synchronization of the devices, or by cross correlation synchronizing of the data using the best fitting time lag. • Smoothing: Typically, the xy-positions the systems provide have undergone an internal smoothing, already. At the level of xy-data, it is a good idea just to compare the output of the systems. At higher levels though, results such as speed and acceleration may be obtained only after smoothing the positional data again. Since this leads to differences in the results, for example, heavily smoothed trajectories are shorter than mildly smoothed ones, a methodological consideration here is to treat each data set with the same smoothing procedure. This provides a higher internal validity to the comparisons, but practice may sometimes expect a comparison of the net results of a tracking system stressing ecological validity. • Performance indicators: Sometimes the systems make use of different definitions of performance indicators. This may especially be the case with those that employ speed thresholds for intensity intervals. These have to be homologized, of course, prior to be able to conduct comparisons at the level of performance indicators. After having made the data comparable with the above steps, a statistics assessing the differences between the results of two tracking systems is needed. When one system is accepted as gold standard, we may call this difference the error of a

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tracking system. In the literature, we find several statistics used to characterize errors. The classics in the field (Di Salvo et al. 2006; Zubiaga 2006) used correlation, for example. This may be done only with caution; see Box “Correlation as Measure on Agreement”. Correlation as Measure of Agreement

“Correlation is an instrument of the devil!” (Hilgard 1955, p. 228). Although this statement was given with respect to a certain problem in personality psychology, the pitfalls of correlation are in place until today as, for example, Aggarwal and Ranganathan (2016) mention! Early classics in EPTS validation correlated velocity data obtained from timing gates and the tested device. Because they merged results for different velocities, on one hand, they obtained excellent correlations; on the other hand, they fell into the pitfall known as correlations with heterogeneous subgroups. Simply spoken, the different running velocities (differences over 10 m/s) make the errors appear small (large per cent errors, but 34 m and zone 1: zone in front of goal) by a maximum of 0.5, which is in turn obtained from a combination of control, pressure, and density: Dangerousity = Zone × (1 − (1 − Control + Pressure + Density ) / k ) The operational definitions of the constructs express very straightforward their intuitive meanings. This includes the notion of “control” as decreasing with increasing relative speed of ball and acting player, although in the sense of the overarching construct dangerousity, practitioners might feel that direct play (despite lower control) frequently leads to dangerous situations, because it increases the tempo of the attack. Also, the fact that non-zero values for dangerousity may only be obtained having entered the 35  m zone may be disputed as well as the concept of a non-­ steady function for dangerousity only being defined when a player (and team) is in ball possession (imputation by interpolation?). Once established, dangerousity allows for defining interesting PIs like an action value, that is, the difference of dangerousity before and after a player action, and team dominance, that is, the difference of summed up dangerousity between the teams, for a match interval or the whole match. An outstanding feature of this study is its extensive empirical validation. First, there is an expert rating of dangerousity of 100 situations not only used for calibration of model parameters but also for construct validation with convincing results. The low Fleiss’ kappa of 0.32 underlines the problems with practitioners as experts and threshold values for agreement (see also Box “Sufficient levels of measurement quality” in Chap. 2). A second empirical validation is the correlation between team dominance and “winning probability”, that is, the betting odds prior to the match, which may be taken as expected outcome prior to a match. Here, the dangerousity-­ based indicator or team dominance clearly outperforms all other PIs examined and shows relevant inter-correlations with shots at goal, pass accuracy, and ball possession. Although the authors mention that there is need for further validation (no item analyses  conducted!), the approach sets a standard for transparent modelling of game constructs based on positional data.

4.2.2.5 Fatigue One of the most important consequences of kinematic match data becoming available is the option of assessing the physical load during matches and training. This presumably opened a perspective to assess fatigue, what has built a bridge between PA and training physiology potentially increasing the impact of both areas on decisions in practice. Nevertheless, despite these excellent options, there are some conceptual and methodological problems in assessing fatigue from match data, and one must admit that some early approaches were not aware of these problems.

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One of the most robust findings in PA on football matches is the decreasing intensity between halves (first half >second half) and within halves (early periods > late periods) as is found in many studies and shown in Fig. 4.3. So it is suggestive to take these decreases as fatigue, as “declining performance after prolonged exercise” is close to a common notion of fatigue. On the other hand, applying modelling methodology, there is a contradiction between the nature of game sports as interaction processes with emerging behaviour and the interpretation of kinematic dynamics as direct expression of underlying physiological processes. In other words, physical activity during a match should primarily be perceived as induced by the necessities of the interaction process with the ultimate aim of winning the match and therefore only indirectly as indicator for the endurance and sprinting abilities of the players. Actually, the conclusion of this paragraph on modelling fatigue in PA will be that decreasing running performance may not at all be interpreted as exclusively  resulting from fatigue. This is because the dynamic interaction processes give rise to several other factors than fatigue having impact on running performance.  lternative Explanations for Decreasing Performances A One alternative explanation of decreasing performances within half-times is the “first-five-minutes effect” meaning the very robust finding that maximum intensities are found in the first 5 min in football matches, sometimes also in the first 5 min of second half (see Fig. 4.3). It may be assumed that at the very beginning of the half-­ times, teams are very attentive and very reactive to any movement of the opponent.

Fig. 4.3  Distance covered in m/min per 5-min interval; 51 Bundesliga matches (792 players) of season 2012–2013 and 2013–2014. (Data from Linke et al. (2018b))

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Furthermore, a frequent tactics is to start with a very high effort in the halves either to force an early goal or as Carling (2013) has put it: “the recognised frantic nature of the former [the starting phase] when teams wish to ‘engage’ and ‘register their presence’ with the opposition” (p. 661). It must be mentioned that the shape of this part of the general course of match intensity given in Fig. 4.3 is not in agreement with an accumulation of fatigue leading to decreased performance. Rather, the shape of the course of the intensity might be interpreted as a reduction of increased efforts in the first parts of the half times to normal levels in the end. Pacing may be seen as the intentional regulation of match intensity induced by tactical considerations. A possible pacing strategy might be to start with a very high intensity for psychological or tactical reasons mentioned above but also trying to score an early, frequently decisive goal. But also a cautious start, putting emphasis on ball control and less on creating scoring opportunities with high-risk actions is an imaginable pacing strategy. Perceived or expected fatigue may have an impact on pacing also (Noakes et al. 2005; Tucker 2009), for example running performances of matches within congested fixtures might be affected  by this. Players might unconsciously reduce their efforts assuming a lower running capacity after matches played recently or save resources for the next matches. Empirical evidence for pacing behaviour is given by Bradley and Noakes (2013). They found higher reductions in running performance for players starting  with higher intensities compared to players starting with lower ones in the first half except for sprinting. Regrettably, this effect was only demonstrated descriptively rather than statistically, for example, with an interaction term of an ANOVA. There is support for the notion that observable match intensities are negotiated between the interacting teams. Partially, this is evident from plausibility considerations: when one team decides to play with a high intensity, the other team cannot stay abstinent and play with a lower one. Empirical evidence is given by Spandler (2015) showing that away teams perform significantly below their away average when visiting the team with the lowest running performance at home (Bundesliga season 2011/12: t  =  −2.672, p  =  0.016, d  =  0.630; Bundesliga season 2012/13: t = −2.788, p = 0.013, d = 0.657; Fig. 4.4, left side). Also, teams perform above their away average when visiting the team with the highest running performance at home (Bundesliga season 2011/12: t = 3.586, p = 0.002, d = 0.845; Bundesliga season 2012/13: t = 5.680, p 5 m/s) Sprint distance (>6.3 m/s) 0.607 0.353 0.272 0.482 0.310 0.244 0.143 0.253 0.261 0.244 0.236 0.167 0.629 0.447 0.389 0.554 0.399 0.304

These findings suggest that there is a negotiation of match intensities on the spot with highest impact of the home team’s pacing but also with a specific contribution of the away team. Nevertheless, the only moderate to medium correlations found (all being highly significant, p  A. In an extreme case, a midfielder losing each ball he gets from his defence and playing many balls he wins from the opponent to his offence but not playing a single pass connecting defence and offence would earn high betweenness values denoting him as a playmaker.

Fig. 4.11  Two plays, their network and their adjacency matrix. In this example, players A, B, and C would all receive the value of 1 for betweenness (Korte et al. 2019)

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The problem here originates from the difference between the meaning of “betweenness” in a passing chain in team sports, that is, a player receiving the ball from a teammate passes it to a teammate, and the definition of betweenness in network theory. The technical reason is that network parameters are calculated from adjacency matrices containing only (frequencies of) edges between two nodes (Freeman 1979). Ramos et al. (2018) introduce the idea of temporal networks with intervals corresponding to attacking plays. Korte et al. (2019) suggest to calculate “flow betweenness” based on play-by-play networks in football. They modify the calculation of flow centrality suggested by Fewell et al. (2012) for basketball in the sense of the notion of playmaker in sports, that is, extracting passes of intermediate players. Results show that this leads to a reduction of conventional betweenness values to a degree specific for playing positions with goalkeepers showing largest reductions. Also, the bias introduced by successful ball possessions preferring more advanced playing positions is reduced by flow betweenness. Although the correlation per player between flow betweenness and conventional flow centrality is overall quite high (r = 0.89), this does not hold true for matches with a low average number of passes per possession, for example, r = 0.56 for matches with less than three passes on average per possession, showing the general relevance of the introduced play-by-­ play calculation of betweenness parameters. From a more general perspective, making use of social network theory and methods for PA is paradigmatic for introducing new theories and methodologies in PA (see Box “Importing a Theory/A Methodology to PA”). It requires a deep and correct understanding of the original theory to evaluate the potential of its application. After first modifications allowing for applying the theory to sports, a structural validation of these modifications and an empirical validation is needed. Eventually, modifications required for a correct description of sports have to be done, which in turn may enrich the original theory, for example, when the type of “intermediate” betweenness analysed by Korte et al. (2019) is to be scrutinized in other application fields of social networks, too.

4.2.3.2 Finite Markov Chains 1 This section introduces the application of special stochastic processes, discrete finite absorbing Markov chains, to PA of net games such as tennis or table tennis. We will see that they do not only provide apt descriptions for net games but they might as well be used for answering typical questions of PA using simulations. Also, there will be an outlook of applying variants of Markov chains to team sports. The basic idea of finite Markov chains is to describe a process by a finite set of discrete states and the transition probabilities between them (state-transition modelling). If the Markov property may be assumed, several interesting variables can be obtained by rather simple calculations based on the transition matrix between  Parts of this section are reproduced from the chapter “Markov Chain Modelling and Simulation in Net Games” (Lames 2020) in the book Science Meets Sports: When Statistics Are More Than Numbers edited by Christophe Ley and Yves Dominicy (2020). 1

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states. What makes this model appealing to applications in sports is that variables of high relevance in PA are dealt with such as winning probabilities or rally lengths. One general prerequisite for successful modelling is to understand the nature and properties of the model and in how far these reflect properties of the original, here net games. A Markov process is a stochastic process that satisfies the Markov property (described below). A finite Markov process is a Markov process with a finite number of states. A Markov chain is a Markov process with transition probabilities independent of n, the position of the states in their sequence (this—sometimes disputed—and all other definitions from Kemeny and Snell (1976)). This “chain property” denotes time invariance or stationarity when the process steps are given by discrete time intervals or have a natural temporal succession. The most common metaphorical paraphrase of the Markov property is “memorylessness”. That means that the probability of the process being in state si in the n-th step depends only on the state it was in the step before. Mathematically, the conditional probability that the process is in state si in the n-th step given all the states before n (0,...,n−1) equals the conditional probability of being in state si in the n-th step given only the state before n. Another paraphrase of the Markov property: the future depends only on the present and not on the past! Finite Markov chains constitute a class of stochastic processes with certain specific properties making them very appropriate, simple, and useful models for net games and many other real-life processes (examples in Kemeny and Snell (1976)). It is very instructive to distinguish between certain types of states of finite Markov chains: starting states, transient states, and absorbing states. Starting states are possible states for n = 0, that is, states where the process under consideration may start with. In the case of net games, this is the service of player A or B (Service A/Service B). Typical starting vectors in net game studies are 0 for all states except the services. They may either contain an initial probability of 0.50 for Services A and B (appropriate for table tennis because of alternating service) or the empirical relative frequencies of services from A and B (more appropriate for tennis, because number of services may differ considerably). If only rallies with service from either A or B are to be studied, they respectively are given a starting probability of 1. Transient states are states to which the process may never return once this state has been left. The same holds true for transient sets of states; once this set of states is left, the process may never return to it, but while still being in the set, the process may reach any state in the set. Examples in tennis are Second Service or Return for transient states; there is no way to return to the state Return in a tennis rally. In table tennis, long rallies end up in the transient set of states >fourth stroke A and > fourth stroke B and may stay in this set for some strokes until the rally ends with a point or an error. Absorbing states are most relevant from a sports point of view. The formal definition of an absorbing state is a transition probability of pi,i = 1. This means, once entered in an absorbing state, the process is trapped, it will remain forever in this state. In net games, these absorbing states are the ultimate aim for each player in a rally, making it end up in either Point A or Point B.

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Fig. 4.12  State-transition model for tennis. (Reproduced with permission from the chapter “Markov Chain Modelling and Simulation in Net Games” in the book Science Meets Sports: When Statistics Are More Than Numbers edited by Christophe Ley and Yves Dominicy (2020))

The particular structure of net games as series of alternating strokes of different categories (=equivalence classes of strokes like service, return, etc.) gives rise to modelling net games with state-transition models (see Figs. 4.12 and 4.13 for state-­ transition models for tennis and table tennis). Each stroke category makes up two discrete states (one for each player) with the absorbing states Point A or B added. The transitions between these states are given by the relative frequencies of successor states for each state and may be depicted by a transition matrix (see Figs. 4.14 and 4.15 for transition matrices for tennis and table tennis matches). These transition probabilities may be obtained by observational methods from real matches. State-transition modelling is for several reasons very applicable to net games. The alternating strokes take place in classes of situations that give rise to equivalence classes of states of each net game in a very natural way. We have clear transitions literally the crossing of the net. Dynamics and interaction, the constitutive elements of game sports (net sports and team sports), are contained here in the sense that both players want to reach their favourable absorbing state and each stroke is devoted to this task. Their tactics and success of doing so are reflected in the transition probabilities. Figure 4.12 shows a state-transition model for tennis. We have the starting state Service A (states for player B serving are symmetrical). Then, two transient states follow, second Service A and Return B. After this opening of the rally, a transient set of states is entered. This set contains four states of open play, base-line strokes, attack strokes (player at net, opponent at base-line), defence strokes (player at

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Fig. 4.13  State-transition model for table tennis. (Reproduced with permission from the chapter “Markov Chain Modelling and Simulation in Net Games” in the book Science Meets Sports: When Statistics Are More Than Numbers edited by Christophe Ley and Yves Dominicy (2020)).

Fig. 4.14  Transition matrix of a tennis match Clijsters vs. Capriati, Australian Open Half Final, 2002; 7–5/3–6/6–3. (Reproduced with permission from the chapter “Markov Chain Modelling and Simulation in Net Games” in the book Science Meets Sports: When Statistics Are More Than Numbers edited by Christophe Ley and Yves Dominicy (2020))

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base-­line, opponent at net), and net strokes (both players at net). The arrows between the states of this transient set make clear that, at least in principle, there may be a transition from each state to each other, if the side condition of alternating strokes is respected. For example, if in the net state a lob is played, the match may continue with a defence stroke (lobbed player at base-line, lobbing player stays at net) or even a base-line stroke (both players at base-line). The absorbing states Point A and Point B may be reached from each state, that is, each stroke may be a winner or an error, except Point B from Service A, because in tennis in case of a service error, a second service is granted. The state-transition model for table tennis (see Fig. 4.13) is very much related to the number of the strokes. Implicitly, we have tactical meanings there with the first stroke being the service and the second stroke being the return. The depicted model is based on the modelling of the performance analysis team of the Chinese table tennis federation (Fuchs et al. 2018) where first plus third and second plus fourth strokes are important stroke classes made complete by longer rallies with more than four strokes. From a mathematical perspective, it is interesting to note that the chain property of Markov processes is acknowledged here in a way that earlier strokes in a rally have specific transition probabilities, whereas after four strokes, these probabilities are assumed to be invariant thus giving a sports specific answer to the problem of stationarity. Figures 4.14 and 4.15 depict examples for a transition matrix from real matches in tennis and table tennis. These matrices give appropriate descriptions of the match, of course only at the given level of abstraction. The transition matrix describes a “super rally” including each single rally in its transition probabilities. For sports experts, it is quite obvious from the transition matrix what was going on in a match and where the winner took most advantage. In the tennis matrix in Fig. 4.14, we see that Jennifer Capriati showed a more aggressive service with more first service errors and double faults. Obviously, this provoked the high return error rate of Kim Clijsters. Moreover, it becomes evident that the most prevalent course of the rallies was the base-line duel with only low transition rates to the net. The net was approached exclusively from base-line strokes meaning that both players never played serve-and-volley. Finally, we see that the match was very tight (result!), because there is no obvious advantage for the winner (Clijsters) in the transition probabilities. In contrast to this tennis match, in the table tennis example, the dominance of the winner becomes quite clear. Whereas in service and return, Ma Lin shows a weaker performance committing more errors in service and return, his strong strokes are #3 and #4 provoking dramatic error rates of Wang Hao. Longer rallies are more balanced again. The dominance in strokes #3 and #4 resulted in a clear victory as the majority of the rallies finished in this phase. Besides the informative, but purely descriptive use of the transition matrices, one may obtain interesting performance indicators from variables calculated assuming the properties of Markov chains. For example, the expected rally length given an arbitrary starting state depicts an important aspect of tactics, that is, the capability to maintain the rally after a certain

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Fig. 4.15  Transition matrix of a table tennis match Ma Lin vs. Wang Hao, Olympic Final, 2008; 11–9/11–9/6–11/11–7/11–9. (Reproduced with permission from the chapter “Markov Chain Modelling and Simulation in Net Games” in the book Science Meets Sports: When Statistics Are More Than Numbers edited by Christophe Ley and Yves Dominicy (2020))

point or to finish it when this is more favourable. Similar things may be found out analysing the absorption probabilities from each state. These probabilities give a more complete picture about the dominance in a certain state than the transition probabilities of this state alone, because they include delayed effects, too. Taking rally length and absorption probability for each state together, this informs about the tactical battle in a match. As we saw in the table tennis example, there are more or less advantageous states for a player. The performance indicators just mentioned show whether the players were able to conduct the rally into their advantageous states or prevent going in disadvantageous ones. For example, Ma Lin was able to finish the rally before reaching disadvantageous longer rally lengths. As already mentioned, model validation in practice consists of testing for structural validity and empirical validity. First of all, one must acknowledge that the structure of net games obviously allows for state-transition modelling. Figure 4.12 depicts states for tennis that are widely accepted in sports practice. Also, the specification of starting states, transient states, transient sets of states, and finally absorbing states reflects rallies in net games very appropriately. Nevertheless, the two basic mathematical assumptions of finite Markov chains, invariance or stationarity and the Markov property, must be discussed. There are some objections against stationarity. It is well known in practice and has been studied and demonstrated in table tennis (Fuchs et al. 2018; handball: Russomanno et al. 2021) that we find phases where players show streaks of higher and lower success in a match or we have different phases in a match even with

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changes in playing style, for example. Moreover, one might assume different transition probabilities for base-line strokes in tennis between earlier and later base-line strokes in a rally due to, for example, accumulated fatigue. One might argue against the assumption of the Markov property itself, too. For example, there is good reason to assume that transition probabilities in state Return in tennis differ to a great extent depending on whether the state before was either First service or Second service as we know different service as well as return tactics for first and second services. This would be a clear violation of the Markov property, which demands that the probability of the next state does not depend on the past (note that this specific objection could be easily circumvented by introducing a new state Return after 2nd Service). These considerations show that there are severe objections from a sports practice point of view against the assumptions of finite Markov chains. But how judging whether these objections are severe enough to prohibit finite Markov chain modelling? Here, empirical validity comes into play. There are numerous variables that may be calculated under the assumption of these properties. Typically, these variables may be obtained by game observation, too. For example, the well-known match statistics of overall point winning probability for players A and B when serving is predicted by the absorbing probability starting in state First Service A or First Service B with absorption in Point A or Point B, respectively. Both observed and calculated values may be easily compared, and when comparisons reveal good agreement, this is a good argument that the assumptions of finite Markov chains are not violated to such an extent that would prohibit good predictions. For example, the examination of predictive validity by Lames (1991) based on confidence intervals on match base resulted in very acceptable predictions. For 306 players in 153 tennis matches, the winning probabilities, rally lengths, and state frequencies of eight non-trivial frequencies (state frequencies for starting, transient and absorbing states have frequency 1, i.e. they are trivial!) were calculated with their 95% confidence interval. In only 6 out of 306 cases, the observed values were found outside. More recently, Wenninger and Lames (2016) tested the prediction for point winning probabilities for 518 players in 259 table tennis matches. They found a mean difference to the observed values of 0.003% with a standard deviation of 0.118%. In table tennis, the assumption of Markov chain properties for a rally obviously leads to even higher accurate predictions of point winning probabilities than in tennis. This is possibly due to the more complicated state structure in tennis, especially with the transient set of four states in longer rallies (see Fig. 4.12). To sum up, one must admit that there are substantial objections against the Markov property as well as stationarity in state-transition models of net games. Nevertheless, empirical validations of predictions show a high agreement so far without a reported exception. This may be considered as a valid justification to make use of finite Markov chains as models for net games. At this point, there is a validated mathematical model for net games using finite Markov chains. This allows for much more than pure descriptions of what has happened, which is often the (sometimes criticized) scope of PA. We are now able to

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simulate behaviour by manipulating parameters of the model and study the impact on important outcomes such as point winning probabilities. In sports, especially in net games, the questions one wants to answer with simulation differ between theoretical and practical performance analyses. In practical PA, one is interested in questions like what would have happened if my player would have committed 5% less service or return errors or would have played more aggressively in base-line rallies and attacked more often at the net? Theoretical PA is interested in general laws and in sensitivity analyses as follows: Which transition has most impact on point winning probability? Which ones are indifferent? If one is able to give answers to these questions, several interesting further questions may be answered: What are the most important targets for training? Which behaviours have the best cost-benefit relation for training? The perspective to get answers for these central questions of performance analysis incited already early simulations with finite Markov chain models of net games. The procedure of simulations using finite Markov chains is straightforward. To study the impact of a behaviour change, for example, 5% less service errors of player A, one may follow a three-step approach: 1. Calculate the point winning probability of player A using the observed transition matrix. 2. Simulate the behaviour under scrutiny by manipulating the transition matrix accordingly. In our example, this would mean to decrease the transition probability from state First Service A to Second Service A by 5% (Note: as the sum of all transitions of First Service A must be 100%, this decrease must be compensated by increasing other transitions, see below). 3. Now, calculate again the point winning probability of player A. The difference compared  to the initial point winning probability may be interpreted as the impact of this behavioural change on overall winning probability. There may be different strategies for compensating the changes reflecting the tactical behaviour under scrutiny. If there is a specific suggestion, for example, a practitioner may state that a decreased service error rate is compensated by an increased transition to Return B and not by an increase in Point A (aces), this may be implemented as well as more general models, for example, a compensation by increasing all the other transition probabilities in sum by 5% in proportion to their size. If we want to compare the impact of different behavioural changes on overall point winning probability, which is a typical question in PA, we need another modelling step. We need to change the initial transition probabilities to an extent that should be of comparable difficulty, that is, the difficulty of a behavioural change in a net game must be modelled. The nearby way of a constant percentage is doubtful. There is good reason to assume that it is less difficult to reduce the return error rate from 30% to 25% than to reduce the rate of double faults from 6% to 1%, not to speak about the impossibility of reducing a double fault rate of 4% by 5%.

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Lames (1991) suggested a model for comparable changes of transition probabilities as a sum of a constant change that seems realistically feasible even in extreme areas (close to or at transitions of 0% and 100%) and a relative change that is proportional to the distance to either 0% or 100%, because changing behaviour close to the boundaries may be assumed to be more difficult than far away from them. With a representative sample of net games, one is now able to simulate a number of relevant tactical behaviours (Note: it must be possible to express these behaviours with changes in transition probabilities). This gives rise to an ordering of behaviours according to their impact on winning probability (see Fig. 4.16), which is a central desiderate of theoretical PA. Also, one may study the importance of behaviours in dependence of gender of players or court surface (in tennis) or other independent variables such as performance level, handedness, or player’s nation. The dependent variable is the per cent change of the winning probability when changing transitions describing a certain behaviour to the degree modelled above and compensating this change in a documented way. It may be called the relevance of the tactical behaviour under scrutiny. Rothe (2021) studied the relevance of tactical behaviours in tennis with a sample of 14 matches of female and male players each at the Australian Open 2020 (see Fig. 4.16). He found that the base-line errors early in the rally (base-line strokes #3 and #5 of the serving player and #4 and #6 of the returning player) as well as the error rate of the return on first service were in general the most relevant transitions. On the other hand, net errors, double faults, and errors of returns on second service show the least impact on overall success rate, maybe because of being rare events. The gender comparison reveals results that might be expected: base-line game is

Fig. 4.16  Relevance of tactical behaviours in tennis. (Rothe 2021, Courtesy of Frederic Rothe)

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more important for women, whereas net game and (of course) first service errors are more important for men. Errors of the return on first service are more important for men, while returns on second service is more important for women. With the exception of net game errors, no behaviour showed significant gender differences, maybe only due to the small sample size, but may also give rise to the interpretation (with caution) that male and female playing style in tennis have converged. There have been a number of applications of finite Markov chains in the sense mentioned above (there are also some papers studying only one transition applying the Markov property, for example, in squash (McGarry and Franks 1994, 1996) or in taekwondo (Menescardi et al. 2019)) to different net games until now. The idea was introduced in tennis (Lames 1991) quite early and transferred to table tennis by Zhang (Zhang and Hohmann 2005; Zhang 2006; Pfeiffer et al. 2010). Also for the team net game volleyball, a description as transition matrix and the simulation of game behaviours including an assessment of the impact of single players using the Markov chain property were presented rather early (Lames et al. 1997). Other team sports were addressed, too. The dissertation of Pfeiffer (2005) did so for handball and Liu and Hohmann (2013) applied Markov Chains to football. One may assume that simulations using finite Markov chains could easily be extended to badminton, squash, or beach volleyball providing valuable results on the game structure for these sports as well. Compared to the valuable information obtained by simulation with finite Markov chains in sports, these are rather few applications yet. In the following, it is shown that some persisting problems and so far not addressed questions could be dealt with by using more appropriate procedures and models from the Markov chain theory. Wenninger and Lames (2016) presented a method using numerical differentiation that allows to overcome the necessity of modelling comparable changes of transition probabilities. The idea is that the simulation of the relevance of a certain match behaviour can be perceived as a function f : ℝn → ℝ with n being the number of all transition probabilities. The point winning probability may be conceived as a landscape or potential over an n-dimensional parameter space. The relevance of a certain behaviour then may be expressed by the gradient of its directional derivative: How steep is the rise of my point winning probability when I “go” in the direction of reduced service errors? This may be of course compared to the gradient when moving into other directions, that is, tactical behaviours. The holy grail of PA, determining the individual contribution of a player to team success, may also be addressed with simulation. If we eliminate all transitions caused by a certain player from the transition matrix of a team game, the point winning probability of the remaining transition matrix should show the impact of this player on overall success. A first investigation of this method of Lames et al. (1997) in volleyball demonstrated in principle the feasibility of this approach, but it became also obvious that a more appropriate modelling of a player’s impact on team behaviour is required. In football, there is so far only one application (Liu and Hohmann 2013) using transitions of the ball between different areas in the field. It is quite likely that more meaningful analyses could be done if one could model different states in ball

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possessions of a team (episodes). The problem with the conventional method here is that it is hard to deal with different durations of team and/or individual ball possessions. A possible remedy for this problem are continuous Markov chains that replace the discrete time function with a continuous one thus being much more flexible and more adapt to “continuous” sports such as football, field and ice hockey, or basketball. The only application of continuous Markov chains so far in sports is from Meyer et al. (2006) in Australian Football. Some of the objections mentioned above against the Markov property could be removed when using higher-order Markov chains. These processes modify the Markov property in the sense that the actual state does not only depend on the transitions of the last state but on the last 2, 3, ... states. This would perfectly fit to the problem of the return transitions depending on the stroke before. Second-order Markov chains would, on the one hand, provide a universal solution to the problem but on the other hand do this at the cost of introducing many more new states. In the very small state spaces we have in modelling net or invasion games, this could be accomplished also by introducing additional states such as Return after first Service and Return after second Service instead of just Return. Nevertheless, it would be interesting to see how a higher-order Markov chain would perform and maybe create even more sophisticated applications in sport. A first approach by Wang et al. (2020) gave insights in feasibility and persisting problems, for example, the empirical footage of the many transitions and the requirement for three consecutive strokes (s − 1, s, s + 1) excluding transitions from starting states and to absorbing states. Stationarity constitutes a hard demand for net and invasion game models as we know that there is much fluctuation of performance within matches. For example, in table tennis, Liu (Fuchs et al. 2018) analyses the momentary point probability of a player by using a moving average (double moving average of length 4) of the outcomes of points played (1 = won, 0 = lost). Results show considerable fluctuations within table tennis matches of elite players typically going through almost perfect but also quite disastrous phases within one match. This finding contradicts the chain property that demands a certain invariance of the performance level all over a match. In the stochastic analysis of DNA sequences, a method was developed to get along with non-stationary processes (Vergne 2008). Drifting Markov chains estimate a polynomial drift (e.g. fourth degree polynomial) and adapt the transition probabilities using this general trend. It would be very interesting to apply the concept of drifting Markov chains to net or invasion games and see the differences to conventional findings. A final objection against the presented simulations comes from sports practice. If one devotes effort in training to improve a certain capability, for example, explosive strength, this will not only improve service speed (and ace rate as transition) but also the quality of (m)any other stroke(s). In the transition matrix, training of explosive strength might positively influence the probabilities of hitting a winner in each stroke class. The traditional method of simulation presented in this section assumes that a change in transition probability leaves the other transitions unchanged. The method with numerical differentiation introduced above may not be so much

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affected by interactions between transitions, because of using the derivation. Nevertheless it would be very interesting to find a rubber-cloth-like model for the change of transition probabilities when a change in one transition elicits changes in many (all) the other transitions, too. Having such a tool at hand, we could expect to simulate much better the impact of an improvement in a certain aspect of performance to the overall match performance. Although there is obviously room for improvement, finite Markov chain modelling and simulation have found interesting applications in PA and promise to give even more answers to questions of PA in the future.

4.3 Dynamical Systems Theory Approaches This section treats an important and influential “school” in PA, that is, researchers who apply concepts and methods of a family of theories, dynamical systems theory (DST), to sports performance phenomena. The reason that gave rise to this school is the striking compatibility between the assumptions of DST and the nature of team and net sports. As will be explained in more detail below, DST deals with complex systems, the interactions of their sub-systems, and the dynamics and outcomes of these interactions. It is obvious that there is a high congruence of DST with the notion of team and net sports as dynamic interaction processes with emerging behavioural patterns, which is the basic concept of this book. Nevertheless, it was already mentioned that a really rewarding adoption of external theories to PA (and sports science) requires more steps than just proving the potential for new insights (see Box “Importing a theory/a methodology to PA” above). We need a profound understanding of the new approach, it must be successfully applied, maybe even modified to describe sports phenomena, and it should result in new answers to questions of PA. These steps will be addressed in this section. It starts with a description of the most relevant members of the DST family. After this, the history and impact of DST approaches in PA are traced discussing critically some representative examples. The outlook tries to give an appreciation of DST with respect to future research in PA. It may be expected that approaches from DST, which were until now hardly recognized in PA, will continue to be imported. As an example, recurrence theory is introduced in the final section.

4.3.1 Dynamical Systems Theories DST is a family of theories that share the commonality of analysing the behaviour of complex systems over time. The family and its paradigmatically new point of view may be characterized best by listing some common features found in most approaches. This is done in the following to give an idea of the alternative way of “thinking in complexity” (Mainzer 2007), although risking unjustifiable simplification, especially when applying the listed features to sports.

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• The system approach implies that the objects of these theories are generally entities comprising (many) sub-systems, and there exists a relation that denotes whether something is part of the system or not. This relation creates a border between system and environment. This border may be assumed permeable or not, thus giving rise to open or closed systems. The system approach pursues a holistic view as opposed to the traditional reductionist view. A football match is a system with defined temporal and spatial borders, which may be perceived as consisting of the players as sub-systems. As weather, coaches and spectators and the other “myriads of factors” may have an impact on the match, it is an open system. • Complexity means that the objects of system theory usually consist of many sub-­ systems. The particular thing about complexity is that interactions between these many sub-systems may give rise to new properties that may not be inferred from the properties of the sub-systems alone (see bullet point “emergence” below). Although the number of players is comparatively small (only two in net games!), we may take into account that each player is a system consisting of anatomical, physiological, and psychological sub-systems giving rise to complex interactions. Some phenomena in sports, such as the failure of converting a break point or a penalty may not be inferred from properties of the sub-systems but from their specific, complex interactions. • The feature of nonlinearity characterizes the behaviour of complex systems. They do not necessarily respond to an input with a proportional output. Due to the complex interactions within a system, even the same input does not always lead to the same output (weak determinism) nor does a similar input lead to a similar output (strong determinism). A corner in football may be carried out in the same manner and with a very similar configuration of players in the box as a previous one, but its outcome (macroscopic level) may differ greatly (goal-no goal) due to the complex interactions between defenders and attackers fighting for the ball resulting in tiny decisive differences (microscopic level). • The concept of self-organization in complex systems describes the way, how order or structures on the macroscopic level emerge. The notion of an instance controlling and steering each sub-system according to a centralized plan is rejected and replaced by interactions of sub-systems on the microscopic level that give rise to the macroscopic phenomena. In cycling, the shape of the peloton can be seen as a result of self-organization. A rider tries to find a comfortable position allowing for pursuing his tactical aims. Dependent on wind direction, wind strength, velocity, race situation, and other factors, he takes his position relative to his neighbours. As each rider does so, the shape of the peloton becomes, for example, a long line, a stacked line, a drop, an inverse drop, parallel "trains"  and others. This shape is not directed or constructed but evolves from the interactions on rider level by self-organization. • Emergence is one of the most debated properties of complex systems. For example, consciousness is seen as an emergent phenomenon of the complex system

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that is made up out of the 1011 neurons of our brain, which has of course several philosophical implications not of interest here. Generally, emergence depicts a property of a system that may not be explained and not be predicted by properties of the sub-systems alone. New phenomena arise from the interplay of the sub-­ systems. This is brought about early already in the famous slogan that became programmatic for Gestalt theory (e.g. Wertheimer 1912): “The whole is more than its parts”. The observable (not the ascribed one!) playing style of a team may be seen as a case of emergence. Of course, there are some declarative common ideas and instructions, but these cannot prescribe behaviour in any situation. A player makes his individual decisions in front of his cognitive background of collective tactics as his most appropriate answer to the situation he perceives. As the other players do so also, and in addition, behavioural outputs of the other players (own team and opponent) are influencing this answer, a collective behaviour is emerging, which is in PA called playing style. The features of DST just listed demonstrate—as announced already—the potential of DST for describing central issues that were denoted as being characteristic for team and net sports at least what the conceptual foundation of the nature of these sports in this book is concerned. It is apparently easy to discover these commonalities even at this second stage, where basic concepts of DST are scrutinized in greater detail. So, at this preliminary level, there is no doubt that DST is potentially suitable as a conceptual model for game sports. At this point, it is already clear that the perspective of DST looking at game sports is not on perceiving players executing pre-determined plans or that their behaviour is explained by their levels of performance prerequisites such as fitness or skills. Explaining match outcomes by applying linear laws as it is done in statistical and most modelling approaches cited above is not the perspective of DST. Rather, DST modelling focuses on studying the interactions, describing their complex dynamics, and making aware of symmetry breaking with chance and chaos coming into play. Nevertheless, it is obvious that match plans do exist, and the level of performance prerequisites may explain behaviour in game sports as well. In the line of this book, it is of course no surprise to realize that DST is just another model with reductions like the ones just mentioned. Specifically, one may say that on one hand DST is closer to the real nature of game sports, but on the other hand, it is farther away from law-like relationships and practical impact—and that this dilemma is inevitable! The remainder of this section on DST approaches in PA will first introduce its two main (with respect to PA) approaches, the theory of complex systems, which originated in physics, and ecological psychology. The focus in presenting these approaches is of course not on a comprehensive description of the theories as such but on their relevance to sports and to PA in particular. The outlook examines new promising approaches, but problems of the application of DST to sports will be discussed also.

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4.3.2 Complex Systems, Synergetics, and Relative Phase 4.3.2.1 History The historical development of the idea of complex systems in science is the history of modern science. Our twenty-first century is sometimes called the century of complexity (Mainzer 2007). Climate change and global epidemics are only the most striking examples. At the core of this development is the transition from linear to nonlinear thinking. What does this mean? Starting with the beginning of modern science, a “linear” concept of nature was pursued and is still prevailing in several scientific areas (like statistical approaches in PA!) in the sense of Kuhn’s “normal science” (1962). The most renowned representative of this position is “Laplace’s demon”. Pierre-Simon de Laplace (1749–1827) stated that if one only knew all objects and their positions and all forces in universe, one could look back in the past and predict the future and “nothing would be uncertain”. The consequences of this position are far-reaching, not only for metaphysics (It is named “demon”, because there is no room for free decisions of human beings! And Laplace on the existence of god: “J’ai pas besoin de cette hypothèse!”). A corresponding position in philosophy of science would state that there is total determinism, past and future are governed by causal laws, and our failure to understand the past and predict the future is exclusively due to a lack of knowledge of facts and laws. The task of science then is to minimize this lack of knowledge and to approach total control and prediction on the long run. Laplace’s Demon and Football Matches

Although it might appear a little bit surprising at this point, one may nevertheless think about the consequences of Laplace’s demon for the nature of football matches and arrive at two insights. First, the discussion is relevant as it makes a difference whether we say that in principle we can predict a football match if we only knew all facts and the governing laws. (We called them already the “myriads” of influencing factors!) Or we assume that football is in principle not predictable because of emergence and chaotic laws coming into play. This would imply basic consequences for practical work (PPA): in the first case, we are in principle able to eliminate the uncertainties; in the second we are not and we have to accept this as part of the nature of game sports. Second, this example demonstrates clearly the different approaches of theory and practice to PA. For practice, the task is to do everything to achieve the aims of the team/player. This implies that a belief in determinism is appropriate to show the way to optimizing the capabilities of players with the aim of being successful. Non-controllable aspects of the match are of minor relevance. For theory though, the task is to find most appropriate models for the object even if this endeavour will uncover the non-deterministic, chaotic nature of matches suggesting even a fatalistic interpretation. Creating practical impact is of minor relevance to theory-oriented research.

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The “linear” view on nature as it is expressed in Laplace’s demon has been challenged by insights originating only in the last century. Most frequently, the name of Henri Poincaré (1854–1912) is mentioned as the founder of the mathematics we now call the “chaos theory”. Deterministic chaos expresses the idea that—although a system is governed by (known) deterministic laws—no reasonable predictions may be given. The basic reason for this is called sensitivity, which means that the future development of a system depends on its initial conditions in the sense that small or microscopic initial differences lead to large or macroscopic differences in the further development. This idea was made popular by Edward Lorenz who originally worked as a meteorologist on weather forecasts. He found out that his rather simple weather model consisting of a system of three variables (temperature, air pressure, wind direction) and three Navier-Stokes differential equations led to totally different predictions even when only one initial parameter was changed by a small, in practical terms, “meaningless” quantity. This gave rise to the famous title of his presentation “Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?” (Lorenz 1972). Further research confirmed that this behaviour is rather the rule in complex systems than the exception. Concerning practical research, there are two important aspects of sensitivity: First, as in the realm of practical measurements reputable empirical results are always given as a confidence interval, this bandwidth of a measurement may not allow arriving at a unique solution when predicting a complex system’s behaviour. This is one main reason why we cannot predict the future of complex systems. Second, only in the realm of mathematical structures, where we may assume errorless quantities, we find equation systems that converge to different attractors, no matter how close the initial states are. Famous examples are the so-called strange attractors that show some “strange” mathematical properties such as a fractal dimension which may not be expressed with an integer number. The important consequence is that chaos in a mathematical sense does only exist in mathematical structures, that is, systems of mathematical equations that show chaotic properties. “Real” systems do only approximate these properties (we only know about real systems from measurements with confidence intervals of measurement errors!) and so, the term “chaos” is most often used in a metaphorical way with respect to real-­ life systems. This means that a phenomenon may indeed exhibit aspects of sensitivity but may not be expressed in terms that are required for mathematically proving chaotic properties. Applied to football matches, sensitivity in a more or less metaphorical sense is a common phenomenon. First, there is the fact that the course of the play (the future) is hard to predict: Who may say where the ball will be in, say, 10 seconds (see also Box “Where is the ball 10 seconds after a corner?”)? The result of a single duel may have decisive consequences for a whole match, for example, a lost duel in the build­up phase due to offensive pressing may lead to a successful counter attack; if the duel would have been won (or avoided), the position attack would have been continued. The outcome of a shot on goal, especially from a larger distance, depends on very small differences in the initial impulse the player’s foot gives to the ball. The

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better “placed” a shot is, that is, the closer the ball is to bar or post, the more likely is the assumption that the shot outcome is not in control of the shooter. Also, when reflections come into play, we see sensitivity (Perl 1996), for example, goals from deflected free kicks or converting a ball that was reflected by post, goalkeeper, or other players. An empirical study on chance factors being involved in goal scoring (Lames 2018) will be presented below. Besides the study of sensitivity, there were many influential developments in science that reinforced the complex systems view: quantum mechanics is not compatible with determinism; consciousness and human thinking are interpreted as emerging from neuronal interactions; economy is seen as a complex system sometimes showing dramatic dynamics; and even politics, society, public opinion, personal biographies, and many other phenomena may be better understood when applying a complex systems view with nonlinear interactions and emergence (Mainzer 2007).

4.3.2.2 Synergetics A very influential approach for sports science introducing the notion of complexity was Haken’s synergetics. “Synergetics” is a so-called structural science that investigates self-organization in complex systems (Haken 1983). It analyses the emergence of order (patterns) on macroscopic scale based on (nonlinear) interactions on the microscopic scale. The general assumption is that order parameters on a low-­ dimensional level exist that “dictate” the behaviour of the whole system (“enslavement” principle). The system is driven through the space of possible states (phase space) by external control parameters that are unspecific in nature (e.g. temperature, energy, movement speed). Synergetics provides a general framework for analysing the system dynamics, for example, how the control parameters drive the system through phase space and how stable states, that is, attractors in phase space, emerge. At this point, it is important to note that this framework has to be filled in with details (data and relations) by the respective science that investigates the system under scrutiny. Figure 4.17 illustrates some of these basic concepts. It shows the phase space of a pendulum that may be expressed in two dimensions: speed (v) and vertical angle (φ)  both seen, for the sake of simplicity, in pendulum plane. The trajectory over time, the system dynamics, in this phase space is in Fig. 4.17 given for a damped and a driven pendulum. A damped pendulum, that is, a “normal” pendulum, is damped by friction (air resistance and friction in the suspension). It starts with an impulse giving it a certain initial speed, but the dampening makes the trajectory spiral back to the point attractor of zero speed and zero angle. A pendulum in a pendulum clock is a driven pendulum. A mechanical device compensates per cycle the energy lost by friction. This leads to a cycle attractor where certain combinations of speed and angle will be run through (theoretically) for ever. There are many well-documented and well-investigated system dynamics in synergetics (Haken 1983, 1993). Haken himself worked on lasers, where the unspecific excitement of atoms/molecules in a laser device makes them emit coherent light as a consequence of a self-organization process with coherent light as attractor. In chemistry, the Belousov-Zhabotinsky reaction is known, where the interaction of

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Fig. 4.17  System dynamics of a damped (left) and a driven (right) pendulum

Fig. 4.18  A tennis rally of Justine Henin (left) and Serena Williams (right) with phase space trajectories of each player (black marks, player’s hitting positions, and white marks, position when opponent hits). (With permission of ÖSG from Lames and Walter (2006))

certain molecules provokes a cyclic colour pattern that may be described with the formalisms of synergetics. Finally, the Rayleigh-Bénard experiment, where a fluid is slowly heated and forms a pattern of convection rolls, has become a showcase for synergetics, because it describes how an unspecific control parameter (heating) leads via self-organization to the emergence of a macroscopic pattern (convection rolls) with an unforeseeable impact of small differences in initial conditions (sensitivity) to macroscopic structures (spinning direction and geometry of convection rolls). Figure 4.18 shows the system dynamics of two tennis players in a tennis rally (Lames and Walter 2006). The phase space is given here as the speed of a player and his distance from the mid-line of the court. The nature of tennis imposes circular structures to the players’ trajectory in phase space due to the fact that typically the ball is hit either to the forehand or backhand side of the opponent, forcing him to move to the hitting point. After the shot, the player returns to a neutral position mid-­ court, where he has the best position for reaching the next ball. Ideally, but only achievable in training exercises, the two players could show a trajectory in phase

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space that would be quite similar to a cycle attractor. They only would need to play a series of (almost) identical shots, for example, forehand crosses. As this “friendly” or cooperative behaviour is not the nature of tennis, perturbations of this regular pattern are of bigger interest, because they finally lead to a point in tennis (Jörg and Lames 2009). Hysteresis, Critical Fluctuations, and Critical Slowing Down

For the system dynamics of complex systems, three properties are predicted when moving between attractors (Haken 1983, 1993): • Hysteresis: The transition from attractor A to attractor B occurs at a different threshold value of the control parameter than the transition from B to A does. • Critical fluctuations: The local fluctuations in the order parameter (typically expressed as moving standard deviation if appropriate) are larger in a transition region than in the vicinity of an attractor. • Critical slowing down: Returning to the initial state after a perturbation takes the system longer in a transition region than in the vicinity of an attractor. These three properties may be tested empirically and thus serve as a confirmation of the notion of a complex dynamic system for the system under scrutiny.

4.3.2.3 Relative Phase Relative phase is an important construct in complex systems analysis and synergetics. It serves as an order parameter in complex systems, when spatio-temporal coordination of sub-systems is investigated like in the coordination of different body parts in movements such as walking or rope skipping but also in the coordinated movements of players on the pitch. The classical calculation of relative phase requires two objects A and B who perform cyclic movements in time. If this is the case, we can specify for each object its position in the cycle expressed as angle: αA resp. αB. This angle is obtained by setting the full cycle as 360° and determining the fraction α of the completed cycle by an object for a given point in time as is illustrated in Fig. 4.19. The difference between the two angles, ω = αA − αB, is the definition of relative phase ω. In doing so over time, we obtain relative phase as a function over time: ω(t). In movement coordination, a stable ω(t) between two limbs, for example, indicates a stable coordination pattern that is in a synergetic view interpreted as an attractor of the phase space of a movement. Frequent attractors are a relative phase of ω = 0°, the so-called in-phase coordination, and a relative phase of ω = 180°, which is called anti-phase coordination. The two arms in crawl swimming exhibit (roughly) an anti-phase pattern, whereas in breaststroke, we have an in-phase coordination of the two arms and the two legs (not between arms and legs!).

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Fig. 4.19  Illustration of relative phase for in-phase, anti-­phase, and the general phase relation between two objects

There are alternative methods for the calculation of relative phase not all requiring definable cycles like in the classical definition above. Also, the classical, very intuitive method—it basically consists of wrapping the trajectory around a unit cycle—is quite tedious especially for longer processes (Pikovsky et al. 2001). An easier way to arrive at an equivalent to relative phase is the correlation between the time series x(t) and y(t): Corr(x,y). The correlation may be computed for the whole process, providing something like the average coupling of x and y, or as a moving correlation (Lames 2006) resulting in time-dependent values. Using correlations, values close to −1 stand for anti-phase coupling and close to 1 for in-­ phase coupling. The problem with using moving correlations (besides all the other problems when using correlations) is the length of the data window. Its length has to be chosen in a way that it contains relevant episodes where coupling may be observed, that is, it must not be too narrow, but on the other side, it must not be too wide to be sensitive for changes in coupling. A more demanding method for obtaining relative phase is to calculate Hilbert transform. This is an option provided in advanced statistical packages such as Matlab, R, or Python. A so-called analytical signal sA(t) may be calculated for each signal s(t) by using Hilbert transform H(t):

sA (t ) = s (t ) + i ⋅ H (t )

As the analytic signal is complex valued, it may be expressed with exponential notation:

s A ( t ) = A ( t ) ⋅ e − iω (t ) This term directly contains the relative phase ω(t).

4.3.2.4 Applications of Synergetics in Sports Science In the middle of the last century’s 1980s, there was a fruitful encounter between synergetics (Hermann Haken) and movement science (Scott Kelso). Kelso had discovered earlier the spontaneous change in coordination pattern in his famous

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Fig. 4.20  Coordination patterns in finger-waggling (upper left); positions of the two fingertips over time in Kelso’s finger-waggling experiment (upper right); potential landscapes for coupled oscillators with increasing dominance of the in-phase oscillator from left to right (below). (Based on Haken et al. (1985))

finger-­waggling experiment (Kelso 1981). Since then, one may assume that this experiment has been demonstrated in each undergraduate course in movement science; nevertheless it is described here in a little greater detail to illustrate the synergetic method. When a person is asked to move his index fingers in a parallel mode (see Fig. 4.20, upper left) and increase the frequency of this movement (waggling), the parallel mode will spontaneously change to the antiparallel mode beyond a certain threshold frequency. When reducing movement frequency again though, the antiparallel mode will prevail. Figure 4.20 (upper right) shows a typical evaluation of a finger-waggling experiment. The blue curve is the position of one fingertip; the red curve is the one of the other, each one taken relative to a reference system that is the same per hand. With increasing time, the frequency is increased which can be seen in the horizontal compression of each fingertip curve (one may even see that this person is not able to maintain the initial amplitude of the fingertips when the frequency increases, but this is not of importance here). The two curves stay remarkably symmetric, but after second 6, this coordination pattern breaks down, and after a short transition phase, a different coordination pattern has taken over with the red curve overlaying the blue one, because movements now are identical with respect to the reference. This experiment in movement science was successfully modelled with the instruments of synergetics (Haken et al. 1985). Cycling frequency was taken as unspecific control parameter. Relative phase between fingertips served as order parameter. In the case of parallel waggling at each time, the antagonists (finger adductors-finger abductors) are activated in the other hand; thus this is an anti-phase pattern; anti-­ parallel coordination is described as in-phase pattern, because corresponding (homologous) muscle groups are producing the finger movements at each time. In using a model of two coupled oscillators, later known as the Haken-Kelso-Bunz model (HKB-model), the authors were able to describe a potential landscape that “explained” the stability of the coordination patterns with the relative impact of these oscillators shifting from a bi-stable potential landscape (see Fig. 4.20, lower

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row, left) being characteristic for low cycling frequencies to a landscape with only one attractor, the in-phase mode (see Fig. 4.20, lower row, right), which is found for high cycling frequencies. The relatively simple formula for this potential landscape V is

V ( ? ) = ? a ? cos ?? b ? cos 2 ?

The HKB model from 1985 was the starting point of a series of extensions all dealing with coordinated movements until today (Birklbauer 2006). In 1988, Schöner added a random term to simulate the influence of fluctuations (Schöner and Kelso 1988) thus getting closer to coupling in biological structures that is more flexible than physical phase-locked coupling. Important for PA is the extension of the HKB model to social coordination. Schmidt et al. (1990) report the same unconscious phase transition to in-phase driven by cycling frequency when two persons move their legs, but only in the presence of informational coupling, that is, seeing each other. Motor learning was conceptualized by Zanone as a potential landscape where troughs form over time leading to the final skill (Zanone and Kelso 1992; Kelso and Zanone 2002). A very similar approach was taken in theoretical concepts of motor development as well (Thelen 1995). A theoretical development is brought about the construct of “meta-stability” for the description of brain activity and behavioural coordination (Kelso 2012). Meta-­ stability overcomes the idea of rigid phase locking with huge energy costs to arrive at a different attractor state. It rather prefers a more ephemeral view with the system permanently “browsing” through all possible states and never getting stuck/fixed/ trapped. Below, it will be shown that there is evidence for applying the concept of meta-stability to football matches (recurrence analysis). A recent review from Tognoli et al. (2020) demonstrates that the HKB paradigm is still undergoing innovations with a present focus on modelling social interactions. A Synergetic Experiment in Golf

Lames (1992) designed an experiment consisting of a series of golf shots that allowed studying some principles of synergetics. A golf flag was carried from 100 m to 5 m in 5 m steps and then back from 5 m to 100 m. The golfer had the task to play the ball “carry” (landing, not stopping) to the flag. The different techniques (drive, pitch, chip) of each shot were identified from the relation of the duration of sub-phases of the swing, for example, time for upswing and time for downswing. It could be shown that the unspecific control variable (flag distance) drives the system through a phase space consisting of these three techniques or coordinative patterns. Hysteresis and critical fluctuations could be detected. This experiment showed the direct applicability of synergetics to macroscopic sports phenomena and that it is not restricted to inter-limb coordination. As mentioned in the Sect. 4.2.3, it is desirable that results relevant to PA are obtained, and in this respect, a transfer to more macroscopic sports movements such as a golf swing is to be appreciated as finger waggling is not quite an Olympic discipline (golf has become one again in 2016)!

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4.3.3 Ecological Psychology As mentioned above, ecological psychology is presented here under the roof of dynamical systems theories. This is unusual on the first glance as the classical complex systems theories such as synergetics stem from physics and here the root is psychology. There are two reasons justifying to do so: first, it will be shown that all the properties (interaction, dynamics, emergence) that are characteristic for team and net sports and make them attractive for DST modelling are typical for ecological approaches as well, and second, modelling approaches referring to either of the two roots are very similar in their methods applied, for example, relative phase is a tool used in both approaches.

4.3.3.1 History In the second half of the last century, a Kuhnian analysis of psychology (similar to the one above for linear science) would have identified cognitive psychology and computational neuroscience as “normal science” both focusing on information processing in the brain. As to be expected, “revolutionary” science has evolved in contrast which is one of the roots of ecological psychology (Glazier 2017). An overview on schools in ecological psychology is given in the special issue “Ecological approaches to cognition in sport and exercise science” in the International Journal of Sports Psychology (Araújo 2009). One outstanding school relevant to PA was established by Gibson (1986), who proposed a theory of perception and action coupling without relying on a central representation of information. He examined optical flow fields and stated that information about external objects and their positions and movements as well as about position and displacement of the observer is contained in these flow fields. Gibson postulated the perception of these flow fields as “direct”, that is, not mediated by internal representations, and also a direct coupling of perception and action. These assumptions were extended to experimental programs, for example, on estimating time to contact (Lee 1976; Savelsbergh et al. 1991; Hecht and Savelsbergh 2004), catching (Peper et al. 1994), or interceptive actions (Davids et al. 2002). At this point, it is obvious already that this position seems to be very applicable to many situations in sports. It is characteristic for many sports that movements have to be carried out as fast as possible. Either top speed is a task requirement, for example, the approach in long jump under the side condition of hitting the takeoff board exactly, or opponents try their best to reduce one’s time for actions and decisions. The latter is typical for team and net sports, where, for example, defenders cover attackers tightly or the opponent in tennis creates pressure with fast, well-­ placed shots. In all these situations, the resulting actions may be interpreted as “answers” to a rapidly changing environment. Giving these answers, especially when there is not much time for movement coordination nor for drawing tactical decisions, the assumption is very reasonable from a sports practical perspective that something in the environment tells us what to do rather than actions being the result of sophisticated mental processes.

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The second great achievement of Gibson was to identify and specify the nature of what he called “affordances” (1977). Affordances are options for actions and we perceive the environment in terms of options for actions. For example, a specifically dimensioned open space and the movements of own and opponent players “tell” me, which actions are possible, for example, to which player a pass is possible and desirable. Some more formal aspects of affordances (Fajen et  al. 2009) are the following: • Affordances are real: They are properties of the environment-actor relation. This is prerequisite for direct perception of affordances. Moreover, this notion creates an interesting philosophical case (realism vs. idealism), but this is not the place for an in-depth discussion of this issue. • Affordances are subjective: They are defined relative to the action capabilities of a given individual, for example, whether a dunk in basketball is perceived as an option for action in a specific situation depends on the prerequisites of the player. Thus, affordances are a relational property. • Affordances allow for prospective control: Only by accurate perception of affordances it is possible to create reliable expectations on the outcome of a situation. This, in turn, is a central aspect of playing ability in game sports that heavily relies on prospective control rather than only reacting to the environment. • Affordances are meaningful: This on the first glance trivial property points out the difference between ecological and “scientific” approaches to perception. Where affordances being options for action bear sense for the actor, this may be doubted in other concepts of perception that focus on constructs such as space and time and have to be transferred to action only by sophisticated operations of a central intelligence. • Affordances are dynamic: They arise and dissolve, for example, with a changing position of a player on the field as well as with a changing configuration of the other players. In most situations, we have both, making affordances in a football match highly dynamic. Adding Turvey’s (1992) notion of the interactional properties of affordances and above all Stoffregen’s (2002) interpretation of affordances as emergent properties of the environment-actor interaction, it becomes clear that the theory of affordances is very close to the concept of game sports as dynamic interaction processes with emergent behaviour which is the basic assumption of PA in this book. Extensions of the concept of affordances are constraint-led approaches and embodiment approaches. Constraints may be conceived as the negation of affordances: constraints are limitations that prohibit an action rather than affordances that are options for actions. Positively spoken, constraints are boundaries or limitations of the degrees on freedom of a movement system. A systematics of constraints originally proposed by Newell (1986) has become very popular and given rise to the so-called “constraint-led approach” in movement science. The following definitions of the different constraints are extracted from Glazier (2017, p. 142f):

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• Organismic constraints: Constraints that reside within the boundaries of individual movement systems. –– Structural organismic constraints: Relatively stable physical or morphological properties of the athlete, for example, genetics, body proportions, and level of skills and capabilities. – – Functional organismic constraints: Relatively faster changing properties of the athlete accounting for much of the variation in sports performance over the duration of an event such as fatigue, emotions, or heart rate. • Environmental constraints: Constraints that are external to the movement system, typically non-specific constraints imposed by the spatial and temporal layout of the surrounding world such as ambient light and temperature and properties of surfaces but also social expectations and psychological attitudes of the human environment. The classic environmental constraint in PA is playing at home or away. • Task constraints: Constraints that are specific to the task being performed and are related to the goal of the task and the rules governing the task. For example, shooting distance in football or basketball is a task constraint and the game-­ specific rules on correct ball handling as well. A practically very important group of task constraints are instructional or informational constraints, with which a coach or physical education teacher directs the athlete or pupil towards the desired execution of an exercise, for example, instructions given for the next trial in a feedback-driven motor learning process.  Finally, it should be mentioned that a recent step in the development of ecological psychology is its impact on the understanding of cognition. The notion of embodied cognition becomes more and more acknowledged pointing out that perceptual and motor systems are not just peripheral input and output devices for the central brain. Rather, mind must be understood in the context of its relationship to a physical body that interacts with the world (Wilson 2002). One important line of argument in favour of this position is evolutionary: originally, brain was meant for deriving meaningful recommendations for action from the environment (hide or run away from the sabre-tooth tiger). In the focus were immediate, on-line interactions with the environment, which sheds a new light to practising sports, where these requirements still prevail (Stay on first plate or go for second!). The idea that game sports behaviour preserves evolutionary deep-rooted behavioural situations with adequate decisions as most valuable outcome emphasizes the pedagogical qualities of game sports. Beilock (2008) shows that an adequate perception of affordances is dependent on the level of expertise in the domain. It is well known that high-skilled athletes understand better the actions of other players and develop more adequate action plans. The consequences from the contributions of embodiment, for example, on sports training, giving instructions in sports and developing, communicating and pursuing tactical plans, remain to be systematically explored.

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4.3.3.2 Applications in Sport Science Ecological psychology found several applications in sport science, mostly in movement science. Below, some examples are given and their relevance to behaviour in sports competitions is underlined. The sophisticated refinements existing in almost each case are not of interest here: • The school of “Gibsonians” examined tau and other optical variables with respect to their relevance to sports actions such as catching and hitting (Lee 1976; Savelsbergh et al. 1991; Hecht and Savelsbergh 2004) typically in lab settings. • The perception of affordances also turned into an experimental topic in movement science. Especially the early experiments of Warren (1984) became famous discovering the perception of affordances to be body-scaled. Whether the height of a high step (“riser”) is perceived as “climbable” depends on a person’s leg length: if the height is less or equal to 0.88 the leg length, the person judges it as climbable. • Another experimental line is the study of action-scaled affordances. This first means that actions such as self-positioning require that affordances are perceived correctly. Oudejans et al. (1996) demonstrated this for the perception of a fly ball as catchable. The correctness of this perception is improved when athletes are allowed to move before giving their judgement. Even more important for sports than this nice demonstration of the relevance of perception-action coupling is the finding that knowledge of one’s physical limits impacts perception, too, as, for example, Fajen (2007) demonstrated with his model including “action boundaries”. • As one might expect, there are also studies showing that the perception of affordances depends on body-scaled and action-scaled perceptions. Pepping and Li (1997) showed that the perception of “blockability” of a volleyball spike is influenced by the own body height and the jumping abilities of the blocker. • Other relevant results on the nature of affordances are insights that the perception of affordances is dynamic, that is, it is permanently calibrated. This may be due to perceived changes of environmental constraints, such as more or less slippery surfaces (lawn, snow), or to changes of functional organismic constraints such as fatigue (Fajen et al. 2009). • This takes over to affordances in social contexts, which are especially relevant to team and net sports, where one must be able to perceive the affordances of either own or opponent players. Baron and Misovich (1993) distinguish different types of “social affordances”: affordances for the other person (What can the other person do?), joint affordances (What can we/they do together?), and affordances of the other person (What does the other person allow me to do?). All these examples show the relevance of ecological psychology for PA. In PA merely descriptions of observable behaviour are given. If one wants to know why players behaved the way they did and what to do to improve their performance, it is especially in team and net sports a good idea to adopt the ecological perspective: first, because the perception of constraints and affordances is in many respects relevant to guiding behaviour in team and net sports, and second, if we knew what were the constraints and affordances a player perceived, we could design training exercises to improve these capabilities. Thus, this approach could help to improve

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training based on PA findings. This is the purpose of practical performance analysis (PPA) that will be dealt with in detail in the next chapter. In sum, ecological psychology is a very valuable contribution to PA from the conceptual standpoint. Whether this is the case for guiding practical studies in PA will be discussed below.

4.3.4 Applications of DST in PA As mentioned at the beginning of this section, there are numerous references to DST from researchers in PA. There is no doubt that the structure of team and net sports makes them eligible for a DST modelling. On the other hand, it has to be demonstrated that the application of DST does make sense in terms of the aims of PA, that is, either to get new insights in the nature of sports or to deliver practically relevant information for the improvement of players. In the box below, four steps for a comprehensive DST modelling are given. It becomes obvious that this is a demanding task. Especially the last step, explaining the system dynamics by understanding the details of the underlying self-organization processes is most demanding. At this point, it may critically be noted that even the widely acknowledged modelling of the coordination dynamics of Kelso’s finger-waggling experiment by Haken et  al. (1985) is not very satisfactory with respect to the explanation of the underlying self-­ organization. What are the “real” corresponding anatomical and physiological structures that correspond to the two coupled oscillators that are used to describe the system dynamics? The Agenda of DST Modelling in Sports

One may criticize that many applications of DST in sports just apply tools from DST and present the outcomes without really doing DST-based modelling. This may only be achieved by working on the full agenda, which is given below in terms of synergetic modelling: 1. Demonstration of the appropriateness of DST modelling for the examined sports or the aspect under consideration. This is an analytical, not an empirical, task, where assumptions about the nature of the sport under scrutiny must be disclosed. 2. Outlining a hypothetical phase space with control and order variables (attractors) with their operational definitions. These are necessary assumptions on the internal working of the system. 3. Description of the system dynamics: This is a functional relationship between control and order parameters, which describes how the control parameters “drive” the system through phase space including attractors. 4. Explanation of the system dynamics: In addition to merely describing the system dynamics, a real understanding of the underlying self-organizing processes must be achieved for a full understanding. This is requisite when, for example, interventions are to be designed intending to impact on the system dynamics studied, like we want to do in designing training exercises.

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In this vein, a review of selected applications is given in the following, starting with the reception of the concepts of DST, treating the central tools of relative phase and perturbations, and ending up with the reception of ecological psychology in PA.

4.3.4.1 Concepts There is widespread agreement that team and net sports may be treated as complex systems (Davids et al. 2014). Nevertheless, empirically founded models corresponding to this concept, that is, formulating the phase space, describing trajectories in it, and identifying attractors, are hardly to be found. The underlying problem was already mentioned: advancing to the mathematical structures of a dynamical system is much more difficult than just giving metaphorical descriptions. Hristovsky et al. (2006, 2009), for example, gave a convincing example in boxing how the control parameter distance to the opponent (in terms of arm length) leads to the selection of a specific boxing stroke, but things are obviously much more complicated in team and net sports. Phase space: Accordingly, a suggestion for a phase space in football (Lames and McGarry 2007; Lames 1998) remains highly abstract. In Fig. 4.21, some features of a potential phase space are depicted: the attractors, in the sense of a state the teams want to achieve, are for each team to score a goal and to prevent the opponent from scoring. The teams enter an interaction process in time, which is one dimension of the suggested phase space. The other dimension is the closeness to either of the attractors. This contains for sure spatial information, as the aim is to bring the ball into the goal, but must take into account also other variables indicating the threat to the goal by the tactical configuration at each point in time. An interesting suggestion is the modelling of dangerousity with spatial and configurational parameters by Link et  al. (2016), although not giving a continuous variable applicable to both teams at the same time. Fig. 4.21 Conceptual model of a phase space in football. (English: with permission of Taylor and Francis from Lames and McGarry (2007); German: with permission of Hofmann Verlag from Lames (1998))

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Another idea expressed in Fig. 4.21 is the nature of approaching the attractors. It may be assumed that far from the attractors, the match is more or less stable, but to score goals instability must be created. Teams have to overcome the resistance of the opponent becoming the stronger the closer the match approaches the attractors (scoring a goal!). It is only typical for complex systems when in these regions of instability chaotic features such as sensitivity decide whether the attractor is reached or not. As already mentioned, the phase space in Fig. 4.21 can serve only as an idea how the system dynamics of a football match could be imagined. The next steps in a DST way to model football would be to look for an adequate model for the trajectory of a match in phase space, which requires in addition to time and space contextual and configurational variables expressing the actual coordinates of a match in phase space. This could, for example, be a complex function (the “football formula”!) with a one-dimensional outcome (as shown in Fig. 4.21) or a higher-dimensional approach in a higher-dimensional phase space. Emergence: A central characteristic of dynamical systems is that the interactions between sub-systems are based on self-organization mechanisms with an emergent outcome, that is, what will happen at the macroscopic level may at best be described on a statistical level (goal rate of penalties, 75%; corners, 3%; direct free kicks, 7.5%) but are totally unpredictable prior to a single event. A good exercise to demonstrate emergence is to reason about answers to the question: Where will the ball be in 10 (or so) seconds? This is illustrated in the box below listing some possibilities of where the ball might be 10 seconds after a corner kick. There is not only a great variety in the outcome, but the essential message is that these outcomes depend on microscopic differences in the determinants of the outcome of—typically—a header duel in front of the goal. Where Is the Ball 10 Seconds After a Corner?

To illustrate that a football match is a dynamic interaction process with emergent outcomes based on self-organized interactions between the two teams, it is an interesting exercise to ask where the ball will be 10 s after a corner. Some options are the following: • The ball is on its way to a kickoff, because the corner was converted with a header of the attackers. • The ball is lying again for a corner, because the goalkeeper saved the header of the attackers clearing it over the bar. • The attacking team continues its position attack because the clearing header of the defence was brought under control by the attacking team. • The ball is lying for a goal kick of the defence, because the header of the attacker missed the goal. • The defence is in ball possession and tries to build up a position attack against the offensive pressing of the attackers, because the defence cleared the corner and brought the ball under control.

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• A fast break is threatening the goal of the attackers, because the corner was cleared and a counter attack could be initialized by the defenders. Of course, all these events after a corner happen with a certain probability, but in or before a concrete case, the outcome is not known. The outcome depends on the result of interactions, which in turn depend on microscopic differences in position, physical dynamics, and also uncontrollable aspects, that is, the outcome emerges from self-organizing interactions between attackers, defenders, and ball! Nonlinearity in state transitions: As has been mentioned above, a typical feature of DST is to assume nonlinear state transitions. Again, it is easy to assume nonlinearity on a metaphorical level but hard to deliver a concrete empirical proof. Note that nonlinearity in the sense the word is used here does not mean that a functional relationship other than a linear one (e.g. a quadratic or cubic or any other functional relation) governs the system. Instead, we are speaking of sensitivity as a property of dynamic systems, that is, very similar conditions lead to a totally different outcome. This is mathematically hard to grasp and may so far only be illustrated and underlined instead of proven by empirical findings from PA. A second remark must be made on the relatively few studies aiming to demonstrate nonlinear patterns in the structure of team and net sports. The “normal” scientist is trained to search for (mostly) linear relationships best  with significant result  and not  to prove non-­ linearity and non-predictability. Significant p-values are the holy grail of this widespread attitude (Palesch 2014). This might explain why in PA even some researchers acknowledging very much the emergent pattern and nonlinearity in sports still stick to linearity. Figure 4.22 falls back to the entirely metaphorical level and describes nonlinearities with which we may express basic concepts of PA in team and net sports, especially in football. The first general nonlinearity we typically find in team and net sports is between performance and success. The attractiveness of this group of sports lies in the fact that the outcome is not necessarily proportional to the overall performance in a match but may rather depend on a mishit in the tie-break of the fifth set in tennis or on the outcome of a single situation in a 1–0 victory. The second Fig. 4.22  Left: Basic nonlinearities in team and net sports. Right: Nonlinearities in football matches

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Fig. 4.23  Left: Goals shot in Bundesliga season 2019/2020 plotted against shots at goal; right: plotted against goal attempts (shots at goal without goals)

nonlinearity holding true generally for team and net sports is the relationship between the performance prerequisites, that is, skills and abilities as stable properties of the players, and the actual performance on the pitch. As the performance on the pitch has to be regarded as the emergent outcome of the interaction between the two parties, this outcome is of course associated with the respective strength of the parties but typically in a nonlinear way. In the right side of Fig. 4.22, nonlinearities that are typical for football matches are depicted. It may be assumed that the relation between ball possession and scoring opportunities as well as the relation between chances and goals exhibit a nonlinear structure. Whereas the former assumption is supported, for example, by the results of Collet (2013) examining the determinants and consequences of ball possession, empirical support for the latter one is given in the following.

4.3.4.2 Goal Scoring and Chance in Football If one depicts goals and shots at goal for each team in each match in a season (here Bundesliga 2019/20), a typical result will look like the left part of Fig. 4.23. We find a Spearman rank correlation of ρ = 0.266, which is significant (p fifth goal (30.4%). Especially the latter finding sheds a light on the nature of chance goals. In the beginning of a match, at 0–0, it seems to be “harder” to score a goal without the “help” of chance, whereas a higher number of goals already scored seems to facilitate scoring without chance support. Tactically, this corresponds to a stable organization in the beginning that may only be overcome with relatively many chance goals. This organization must be given up after one team has scored, the trailing team must try harder, and the leading team may go for counter attacks where scoring in a controlled way is assumingly more likely. It is interesting to study how single teams are affected by chance goals. This may happen in two ways, examining the chance goal rate of the scored goals and of the goals conceded, that is, the goals of the opponents. Descriptive statistics given in Table 4.2 express the large variation of the proportion of chance goals between the

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Table 4.2  Descriptive statistics for the percentage of chance goals per team in Bundesliga and Premier League 2011–2012 (Note that statistics are given per team which is different from overall values in Fig. 4.24)

Mean Standard deviation Coefficient of variance Maximum Minimum

Bundesliga (n = 18) Scored Conceded 47.7 48.2 6.7 9.8 14.0 20.3 62.5 70.8 34.7 30.4

Premier League (n = 20) Scored Conceded 47.9 47.5 8.7 6.6 18.1 14.0 67.5 60.5 27.8 39.0

18 teams of Bundesliga and the 20 teams of Premier League 2011–2012. For example, the coefficients of variation, ranging from 14.0% to 20.3%, indicate that chance rates are highly variable between teams. Minima and maxima differ between 21.5% and 40.8%, so that in this season in Bundesliga, one team (Mönchengladbach) had to concede 70.8% of their goals with a chance variable involved, whereas the luckiest team (Stuttgart) was overcome only in 30.4% of all goals with the help of a chance variable. In Premier League, for example, the opponents of champion Manchester City “needed” a high chance rate of 55.7% to score and the runner-up Liverpool scored their goals with a low chance rate of only 37.1%. As these figures indicate, it is interesting to examine chance involvement of more or less successful teams expressed in the final ranking that may be taken as an indicator of the skill level of the teams. The hypotheses would be that better teams score more goals based on their superior skills, that is, with a lower chance rate, while lower-ranked teams need more often support of chance for scoring. For conceding goals, the opposite should hold true: better teams may only be overcome with substantial support of chance, while lower ranked teams with inferior skills concede relatively more skill-based goals and less chance goals. Figure 4.25 shows that this seems to be the case at least on a descriptive base. The first team in Bundesliga in this season (Dortmund) had a much lower chance goal rate for scored goals (48.7%) than the team finishing last (Kaiserslautern, 62.5%). The opposite is true for conceded goals where a very high chance rate applies to the champion Dortmund (64.0%) and a lower one to relegated Kaiserslautern (46.3). These descriptive results for the first and the last can be confirmed taking the first and last four teams together (see Fig. 4.25). Except for the comparison of first and last four teams’ conceded goals (Chi2 = 4.95; p = 0.026; V = 0.116), no other comparison showed significant results. Lames (2018) reports Spearman correlations between final rank and chance rate for conceded and scored goals for all teams in the league that show the same trends as mentioned here but not becoming significant. It must be said that the study was criticized quite heavily, especially the chance variables distance (“When Ronaldo shoots from 18 metres it is a goal for sure!”) and defence, referring, for example, to the tactics of giving up control (crosses or corners in crowded areas in front of the goal) but planning to get the “second ball” after

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Fig. 4.25  The rate of chance goals in scored and conceded goals by the first and last team and the four first and last teams of Bundesliga 2011–2012

a contact of the opponent. Thus, a goal would result from planned behaviour even if the ball was touched by the defence before. This may (partly) be acknowledged, but even with dropping these variables completely (which is not justified), the rate of chance goals would be 39.7% (dropping distance) and 30.0% (dropping defence), which are still very respectable quantities. These results have been confirmed among other studies in a Bachelor thesis applying the same observational system for chance variables, based on the goals of season 2017/2018. Niehaus (2019) found 42.9% of the 855 Bundesliga goals showing at least one chance variable and 41.5% of the 1011 goals (6 goals missing) in PL.  A recent replication of the origial  study was published by Wunderlich et  al. (2021). They basically confirmed the empirical findings for seven Premier League seasons. In his study, Niehaus (2019) examined also tactical aspects of goal scoring and found some indicators of a not planned way of scoring like the failure to identify a tactical action leading to the goal, for example, pass, dribbling, or cross, in 25% of all goals. Wright et al. (2011) could not identify the tactical means leading to the ball possession prior to a goal in 39% of their goal sample. Another consistent finding typically not perceived in the light of chance involvement is the small number of players involved before scoring. Wright et al. (2011) do regrettably not differentiate the wide category of 0–4 players scoring 85% of the goals (Niehaus: 91.9%), but Niehaus found 3.6% involving no player of the scoring team (own goals), 20.5% involving 1 player, and 31.5% involving only 2 players. The fact that 55.6% of all goals are scored with only two players or less of the attacking team being involved indicates that something not explained by intentional,

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planned scoring is very influential! It will be interesting to note whether the impact of chance will become a regular object of study of PA in the future. At the end of this paragraph on goal scoring and chance in football, a very simple consideration will be presented demonstrating that the outcome of a football match is almost unpredictable because of a wide dispersion of probable results. Since Reep and Benjamin (1968), it is a well-established fact that the number of goals scored in a football match obeys a Poisson distribution (for small adjustments, Heuer et al. (2010)) and the number of goals scored from a certain number of chances obey a negative binomial distribution. Assuming (for the sake of simplicity) two independent goal scoring processes, one may easily simulate the distribution of possible results in football given the number of chances and the converting probability. In Fig. 4.26, an exemplary distribution is shown graphically. The empirical parameters used are from Bundesliga season 2019/2020 and simulate an average match. The home team has 14 shots at goal and the away team has 12; both values are the rounded means for that season. The conversion probability of 0.121 was obtained from the averages of 1.60 goals per match from 13.19 shots at goal found in that season. Using one efficiency rate for both teams is not really necessary for the simulation but acknowledges the results of Heuer and Rubner (2014) quoted above. Given these parameters, the most likely result is 1–1 (11.1%), followed by 2–1 (10.0%) and 1–2 (8.4%). Striking features of the distribution of the possible results are its flatness (peak of 11.1%) and large dispersion: eight results have a higher probability than 5%; another seven results come in when the threshold is lowered to

Fig. 4.26  Distribution of results in a football match assuming two independent negative binomial distributions with empirical data from Bundesliga season 2019/2020 averages: 14 shots at goal of home team, 12 shots at goal of away team, and 0.121 shot efficiency

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2%. Outcomes such as 0–3 (2.0%), 4–1 (2.1%), and 3–3 (1.9%) show that even rather extreme results have around 20% of the probability of the most likely ones. In other words, practically any result is possible in a balanced match like this. Simulating more unbalanced matches results (of course) in a higher winning probability for the dominant team, but still everything is possible—like in reality. The extreme dispersion of results in football may be illustrated by asking for the requirements of winning with statistical confidence. To achieve a victory with a chance of 95%, the average of 26 shots at goal per match must be exclusively be delivered by the dominant team and no shot at goal by the inferior one, but even in this extremely one-sided match a 0–0 has a probability of 3.5%!

4.3.4.3 Relative Phase, Synchrony, and Entropy in Sports The DST framework and the concepts of relative phase and perturbations within it were introduced in PA with the seminal paper of McGarry et al. (2002). There, it was suggested to use order and control parameters for better understanding the structure of net and team sports. As appropriate control parameter, relative phase is outlined, and some hypotheses are developed on characteristics of relative phase in net and in team sports. These predictions later turned out to be very accurate. The problem at that time was basically that position data was scarce, because it had to be collected by manual tracking of videos on an electronic board sensing the contacts of a magnetic pen. This technology was introduced in the mid-1980s already, for example, by Franks and Miller (1986) as digital keyboard and by the “Tessy” project group of Jürgen Perl for recording pitch positions, for example, for tennis serve placements (Lames et al. 1990). Also, deficiencies in PA for actually calculating RP persisted quite long, so that in the first papers on relative phase in PA, there are only qualitative assessments (McGarry et al. 1999, 2002). At the 2004 ECSS conference in Clermont-Ferrand, where Lames (2004) presented the relative phase for a tennis rally obtained by the rather cumbersome method suggested by Pikovsky et al. (2001), Palut presented a study investigating the relative phase in tennis rallies calculating RP for the first time in PA with Hilbert transform. The full paper was published in 2005 (Palut and Zanone 2004, 2005). An early study of relative phase in football between team centroids is from Lames et al. (2010) using positional data of the 2006 World Championship final between Italy and France (see Fig.  4.27). Also very early, in basketball, RP was calculated by Bourbousson et al. (2010a, b). After positional data becoming more widespread and the corresponding programming skills more common among performance analysts, a breakthrough for applying tools from DST to positional data in sports took place. A recent review (Low et al. 2020) comprehends 151 references to the topic for football alone. Very soon, RP assessed via Hilbert transform was applied in football to all possible dyads such as intra-team dyads, attacker-defender dyads, and ball-player dyads (Siegle and Lames 2013). Then, for team-team and group-group dyads, new variables analysing different aspects of team/group geometry were introduced;

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Fig. 4.27  Team centroids of Italy and France in the World Championship Final 2006 with relative phase. (Reproduced with permission of Edizioni Luigi Pozzi from Lames et al. (2010))

besides team-centroids in x- and y-direction, this was longitudinal and lateral stretch, convex hull, team spread, spatial exploration index, and others (Folgado et al. 2014a, b; Low et al. 2020). Conceptual problems with RP in net and team sports lie in the fact that the phase relationship is basically dictated by the nature of the game or its task and environmental constraints. In team sports, both teams are moving forward and backward on the pitch resulting in a strong in-phase relationship. In net games, the series of strokes forces the players in a cyclic behaviour (go for the stroke, return to neutral position, go for the next stroke, etc.), which imposes an anti-phase relation because of the alternating sequence of strokes. Although these are interesting findings from a DST perspective (the game enslaves the players to move in a tightly coupled way expressed in the phase relation), one might dare to state that this is not very informative from a PA perspective. One could even say that net games would look very strange if players would not exhibit anti-phase behaviour, and team games maybe even more so (not to say they would look funny!) if defenders would not be in-phase coupled with the attackers but pursue their trajectories independently or even in the opposite direction (anti-phase). The conceptual problems become even more relevant as there is no convincing study yet demonstrating that the degree of coupling may serve as a performance indicator, that is, that better teams show a stronger coupling or that successful attacks are distinguished from non-successful ones. Occasionally there are some results going in this direction (Folgado et al. 2014a, b), but the mere fact that no RP-based PI is at present in practical use talks a different story.

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A recent and methodologically very advanced study investigating player coupling in football is from Goes et  al. (2020). Based on a large dataset of attacks (n = 12,424), relative phase was calculated for dynamically detected subgroups of players (attackers, midfielders, and defenders). Whereas almost all examined subgroups and team variables showed significant differences in mean RP between successful and non-successful attacks (sample size?), effect sizes remained with few exceptions low. Together with the study’s definition of success by advancing in a controlled attack from either last or middle third of the pitch to the attacking 30 m and also given the restriction to ball possessions lasting longer than 5 s, the practical conclusions of the authors must remain preliminary. From a PA perspective, it is worth noting that not the general phase relation is of paramount interest but deviations from this standard behaviour are most interesting. In team games such as football (small), deviations from in-phase would describe interesting behaviours such as escaping the defender, going for a fast break, and creating a gap for a shot at goal. In net games, these deviations from anti-phase would stand for creating pressure for the opponent, making him being late at hitting or even outplaying the opponent. Lames and Walter (2006) examined the phase relationship between two tennis players in a single rally together with the tactical situation in this rally (Serena Williams outplayed Justine Henin). Changes in tactics could be synchronized to transitions of RP between rather stable states. Due to the very demanding position tracking at that time, the idea was not pursued further. Disappointingly, empirical findings in team sports show that these deviations of interest from the overall in-phase coupling are obviously way too small compared to the overall movements on the pitch to have an impact on RP. Moreover, the common practice to treat phases in the game where the dyads show a phase relation of RP 100% because more than one perturbation per CGS). Black framed bars are aggregated single perturbations following on the right

position detection technologies will allow analysing more “microscopic” phase relationships between players in decisive situations. A final remark addresses a potential reason for the obvious decline in interest in perturbations, which for sure may not be found in their relevance. Maybe the tendency to work with commercially available data in PA is to be blamed for this, because for assessing perturbations that must be identified by qualitative judgements, the current routine data processing methods do not apply.

4.3.4.5 Ecological Psychology as Framework for PA Vilar et al. (2014) put it very clear: “Ecological dynamics as an alternative framework to notational performance analysis” is the title of their chapter and the conceptual aim they want to achieve for PA. As starting point, they blame traditional PA for being merely descriptive thus lacking explanative power for what is going on in the field. One might add that the desire of PA for delivering useful information for training is hampered as well by a merely descriptive approach as will be discussed more deeply in Chap. 5 on PPA. Conceptual adequacy is easy to acknowledge for the constraint-led approach: ecological dynamics explains the interaction between players and information from the environment and how this leads to the emergence of stability, variability, or symmetry breaking, what is assumed to be “precisely what sport scientists and coaches need to understand in analyses of team game performances” (p. 232). It would be interesting to hear grass-rooted coaches’ opinions about their perceived  needs!

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Examples given in the remainder of the Vilar et al. (2014) chapter are relative phase relationships between players in futsal from studies of Vilar et al. (2012) assessing the interpersonal coordination of the players. At this point, one must state that it is debatable whether the term “explaining” is apt, when an ecological approach is empirically restricted to the calculation of spatio-­temporal coupling between players. One point is that relative phase may obviously be seen also as an order parameter in a synergetics approach which is originally from physics and may operate without information processing and human perception at all. Another point is that when working strictly with an ecological paradigm, one should aim to understand how players perceive affordances and constraints and above all in the relevant setting, that is, the pitch. This (until now) poses almost insurmountable obstacles for analysing match behaviour from a strictly ecological perspective. It would require analysing the player perceptions with all the many properties of body-scaled, action-scaled, and dynamic affordances and constraints in their social context during the match. This is still beyond present research methodology, although there is much progress in this area, for example, virtual reality, eye tracking, or multi-object pose estimation. But at least for the near future, the capabilities required to do “real” ecological dynamics studies in matches will remain limited. This view is confirmed by several opinion papers pleading for the use of ecological approaches in PA (Glazier 2017; Duarte et al. 2013a, b; Balagué et al. 2019) compared to the few studies actually doing so. The best we can hope for at the moment is to establish lawful relationships between some properties of organism, environment, and task and some aspects of behaviour in sports. In this sense, many of the PA studies investigating contextual parameters that were listed above in the section of statistical approaches already practise a constraint-led approach, for example, when Link and Weber (2017) examine the influence of ambient temperature on running performance in football. While there are persisting problems for conducting truly ecological studies in real matches, that is, studies investigating the perception-action coupling, there is one special area, where the ecological approach turned out to be a useful framework for experimental studies: investigations on the design of small sided games (SSGs). In sports practice, these are well-established exercises in training. The idea of manipulating environmental and task constraints of SSGs to achieve the desired training impact either on physical load or on tactical behaviour is well known in sports practice. As these constraints may be quite easily varied experimentally (pitch area, goal size, goalkeepers, rules), very many studies have been conducted in this area in the past; some of them making explicitly use of the ecological framework and methodology (Silva et al. 2014a; Torrents et al. 2016). Finally, Glazier’s (2017) suggestion to take the constraint-led approach as the GUT (Grand Unified Theory) for sports science must also be seen in this perspective. The conceptual advantages are very obvious: the constraint-led approach is a comprehensive framework for topics to be addressed in PA and other disciplines of sports science. On the other hand, assessing the core of constraints in their ecological meaning, the perception-action coupling in a sports context, poses and will pose

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insurmountable problems. The two consequences are, first, that Glazier’s suggestion for a GUT is either rejected or broken down to a very abstract, conceptual level, and second, that PA has to look for specific methods for reconstructing the constraints players perceive in a match, which is doubtlessly necessary for explaining player behaviour. This will be dealt with in the next chapter on practical PA.

4.3.5 Outlook DST in PA In the previous section, the application of concepts and methods originating in dynamical systems theory to problems and questions of PA was discussed. A very brief summary must mention the conceptual advantages but also the pertaining difficulties in solving problems and questions of PA.  As pointed out already, the research strategy to borrow methods and concepts from other fields is a rewarding strategy and deserves to be pursued further. Either researchers look for modifications of already existing adoptions, such as finding ways to detect perturbations by micro-shifts in relative phase, or new members from the large family of DST are examined for their PA potential. An example of the former strategy is the introduction of new tools or developments in the imported theory, such as, for example, multi-level approaches in social networks (Ramos et al. 2018), and for the latter strategy, the reception of swarm theory (animal collective motion) including the method of identifying highly correlated segments of trajectories (Marcelino et al. 2020) may serve as an example. Another example of a still highly unexploited theory from the field of DST for applications in PA is recurrence analysis that will be presented in detail now as the end of this chapter.

4.3.5.1 Recurrence Analysis2 Recurrence analysis or recurrence quantification analysis (RQA) is a technique for analysing complex systems in many domains such as astrophysics, earth sciences, engineering, biology, cardiology, and neuroscience (Marwan et al. 2007). In sports science, it was introduced by Kuznetsov et al. (2014) in their chapter on nonlinear time series methods with the potential to analyse complex systems in sport. The general concept of RQA is to identify repeating patterns in the phase space trajectory of a complex system, for example, when the trajectory returns to the present state at a later point in time. A phase space is typically a high-dimensional space that contains all possible states of a complex system. The central tool for examining the recurrence behaviour of a time series is the recurrence plot (RP, example see Fig. 4.32). An RP is an nxn-pixel matrix with n representing the length of the time series being investigated. Each pixel has a colour value that corresponds to the distance between the positions in phase space for each pair of time points tx and ty. A dichotomous RP has a black pixel at point (tx,ty)  Parts of  this section are reproduced from  Lames, M., Hermann, S., Prüßner, R. and  Meth, H. (2021). Football Match Dynamics Explored by Recurrence Analysis. Frontiers in Psychology, 12, 747058, under the terms of the Creative Commons Attribution License (CC BY). 2

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Fig. 4.32  Colour-coded recurrence plot for a football match (Lames et al. 2021)

whenever the distance between the positions in phase space is smaller than a certain recurrence threshold. This procedure creates a pixel pattern that is distinctive of the examined time series. Thus, in RQA, the dynamics of the underlying complex system is expressed in a two-dimensional RP with typical patterns formed by these “recurrence points” characterizing the complex dynamics of the original system. This gives RQA a conceptual advantage compared to other nonlinear time series methods such as relative phase, approximate entropy, or sample entropy that only express the current state in a single figure. A convenient and appropriate phase space for football is the x,y-coordinates of all the players over time, containing a complete spatio-temporal representation of the match. It is very likely that tactical patterns such as position attack or fast attack are repeated in a similar manner over the duration of a match, leading to corresponding patterns in the RP.  Moreover, set plays such as corners and free kicks, which typically show a unique and similar positioning of the two teams, are expected to appear in RPs as well.

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RQA, although acknowledged as a tool for nonlinear time series analysis (Kuznetsov et al. 2014), has only found very few applications in PA so far. Cotuk and Yavuz (2007) investigated the time series made up by the number of contacts in ball possessions in football with a RP. Carvalho et al. (2013) examined the recurrence rate and maxline (longest parallel trajectory of consecutive recurrent points) in tennis, where they found significant differences in recurrence parameters before and after a break shot (meaning here a perturbation shot in tennis rallies). Stöckl et al. (2017) gave the so far most comprehensive methodological introduction of RQA in sports presenting two applications. First, sequences of shots by 74 golfers were analysed over four rounds in a golf tournament. For each shot, its quality was assessed by the Shots Saved statistic (Stöckl et al. 2012). It could be demonstrated with RQA that even top-class golfers showed unpredictable or chaotic behaviour regarding the quality in a series of shots. In their football study, they analysed 12 matches from the 2009–2010 Bundesliga season with RPs and RQA. A qualitative identification of match events was done, and these events were correlated with the number of recurrence points at the time of the event; this is known as the pointwise recurrence rate. Results show that the highest number of recurrence points occurs during open play, whereas special and rare situations such as corners and free kicks, as well as shots on goal, show a lower number of recurrence points. This observation is ascribed to the fact that, on the one hand, in open play situations, typical defensive and offensive configurations are found and occur repeatedly throughout a match, with the exception of shots on goal, which are only delivered on rare, singular occasions. On the other hand, set plays are rare events, which explains the lower recurrence rates for set plays compared to open play. Within set plays, one may find a high recurrence, because the positions of players before a set play, that is, waiting for a corner, are quite static and, as such, are locally recurrent. Moreover, the configurations between two similar set plays, for example, corner from the left side for team A, should also be quite similar leading to high recurrence rates between similar set plays. Stöckl et al. (2017) identified “blocks” in the RP, that is, rectangular areas with a higher density of recurrence points and clearly defined boundaries marked by broader (blue and green) bands (see Fig. 4.32). These football-specific recurrence structures may be associated with open play phases without long interruptions. Internally, these blocks consist of alternating sub-phases with highly repetitive (red) structures and medium (orange) to low (green) repetitive structures. Sub-phases of open play consist of controlled ball possessions with a higher degree of order and recurrence. These sub-phases typically only last a relatively short amount of time and a perturbation is likely to happen. After a perturbation, there is a less-controlled and less-structured sub-phase with lower recurrence values, but after some time, when one of the teams establishes stable ball possession, there will be higher recurrence again. This pattern corresponds to the phenomenon of “metastability” (Kelso 2012) that has been previously discussed in dynamical systems theory. Metastability expresses the idea that the system is not characterized by a few stable states with very energy-­ demanding transitions between them but by many stable states with easier and more frequent transitions. Originally, metastability was introduced as an extension of bior multi-stable systems, for example, in coordination dynamics (Kelso 1995). Later,

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Fig. 4.33  Recurrence plots of nine randomly selected football matches (Lames et al. 2021)

it was discovered that metastability is the rule rather than the exception in complex systems because, in biological systems like the brain, it provides evolutionary advantages (Kelso 2012). Recently, the concept of metastability was also successfully applied to describe self-organization processes leading to collective behaviour (Tognoli et al. 2020). In football, metastability is an interesting concept for describing the distinctive back-and-forth movement or the “to-and-fro behaviour” as football-specific collective behaviour was described already by McGarry et al. (2002). Thus, metastability in football may be represented in an RP of a football match. In Fig. 4.33, RPs of nine football matches are shown. It is obvious that there are some common features such as the red diagonal indicating the trivial fact that the distance between the player positions at the same second on the x- and y-axis is 0 and thus below any recurrence threshold. Here it may be interesting to study the

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“thickness” of the diagonal, that is, how long the match stays in a similar spatial configuration. Besides that, we find blue stripes indicating events with a low recurrence rate, for example, set plays with a specific lineup of the players such as corners or free kicks near to the goal. Between these blue lines, the rectangles of open play with their characteristic alternating pattern of orange and green spots are embedded. Visualizing nine matches at a time gives a good impression of the dynamic interaction processes with emerging behaviour in football. The ingredients (stripes and rectangles) are the same for all matches, but what seems to be randomly dispersed is their number, volume, and sequencing. In addition to the qualitative patterns in an RP, RQA also allows for the measurement of objective features of the RP by so-called recurrence parameters. Most of them deal with diagonal and vertical “lines” in the RP meaning consecutive recurrent time points either in diagonal (dynamic recurrence) or vertical (static recurrence) direction. In football, diagonal lines represent dynamically recurrent sequences, for example, when both teams move across the pitch in a repeating sequence, whereas vertical lines could mark static events where a configuration is maintained for a longer period of time, for example, when teams are waiting for a corner. Marwan et al. (2007) suggested the following general recurrence parameters to quantify certain aspects of recurrence: Recurrence rate (RR): This is the most well-known recurrence parameter and the only one that is not associated with lines in the RP. It simply counts the recurrence points in the whole RP and provides the rate of these points compared to all points in the RP. Essentially, RR quantifies the general degree of recurrence in the examined process. In football, we might expect to see a range of RR values that are typical for the sport with some variance due to very chaotic, unstructured matches (low RR) and very structured repetitive matches (high RR), for example, when a team exhibits a possession-oriented playing style. Determinism (DET): DET is the ratio between the recurrence points that lie on a diagonal line equal or longer than a minimum length lmin (≥lmin) and the total number of recurrence points. DET signifies the fraction of longer instances of recurrence compared to all recurring instances. In football, we might expect higher values of DET because football tactics are known to have certain preferred spatial configurations and pre-planned processes in both defence and offence. Laminarity (LAM): LAM means very much the same as DET but for vertical lines ≥ lmin instead of diagonal ones. The semantic difference in football is that diagonal lines represent periods where the game unfolds in a similar manner, whereas vertical lines represent periods where the initial configuration stays similar for a period of time. In football, DET could be more characteristic of open play, whereas LAM is high when there are many set plays. Average diagonal line length (LL): LL is defined as the average line length of all diagonal lines ≥ lmin. LL is also called “mean prediction time”, indicating that the process, on average, will unfold for this duration of time once it is in a recurrent state.

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Trapping time (TT): TT is analogous to LL but is the average vertical line length of all lines ≥lmin. TT is the average time a match configuration remains close to an initial configuration. Entropy of diagonal line lengths (ENTR): ENTR is the Shannon entropy of the different diagonal line lengths ≥ lmin. Frequently occurring line lengths contribute largely to ENTR, while rarer line lengths contribute less to ENTR. This results in low ENTR values that represent chaotic systems with few perceivable and mostly short patterns, whereas high ENTR values are characteristic of predictable, highly structured behaviour. This means that more organized play in football should lead to higher ENTR values and vice versa. Entropy of vertical line lengths (ENTR-V): ENTR-V is the entropy of the vertical lines. Although not explicitly suggested by Marwan et al. (2007), ENTR-V is an interesting parameter in addition to ENTR, because diagonal and vertical lines each represent different aspects of a football match as mentioned above. In addition to these general recurrence parameters, Lames et al. (2021) suggest three football-specific recurrence parameters. They identified the meta-stable areas (“blocks”) in the RP indicating open play with a pattern detection algorithm and defined some of their properties as football-specific recurrence parameters (FRP): Prevalence of open play (FRP-1): This is the overall area of the metastable regions in the RP, expressed as a percentage of the area of the whole RP.  This parameter assesses the degree of open play in a match. Recurrence rate of open play (FRP-2): This is the recurrence rate within the areas of open play. FRP-2 assesses whether open play is characterized more by stable periods of position attacks or more by “chaotic” transition phases between stable ball possessions. Recurrence shares of open play (FRP-3): This parameter is the fraction of recurrence points occurring in open play relative to all recurrence points. Aside from open play, recurrence points can also be found in recurrent set plays. If FRP-3 is relatively high, this indicates a more organized playing style with more structured attacks like FRP-1, though not compared to non-open play phases in the match but to other highly recurring points in the match. Table 4.3 shows the descriptive statistics of the recurrence parameters including the coefficient of variation (CoV). In general, football RPs show rather low recurrence rates when compared to other RPs, for example, RPs of periodical processes. The mean of RR is 0.015 with a span of 0.02. This means that, on average, 1.5% of the points in a football RP are recurrence points (range: 0.8–2.8%) with a relatively high coefficient of variation (34%), indicating that there are considerable differences between football matches with respect to recurrent events. Determinism and laminarity show values around 90% indicating that the length distribution of diagonal and vertical lines is shifted away from values below of lmin. This suggests that there are longer recurrent periods caused by intentionally repeated behaviour rather than chaotic or random recurrence. Also, relatively high values of determinism and laminarity at the same time produce a patch-like pattern made up of longer diagonal and vertical structures as shown in the RPs in Figs.  4.32 and 4.33. This pattern reflects the mechanical nature of movement on the pitch including a certain latency

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Table 4.3  Descriptive statistics of the recurrence parameters of 21 football matches (Lames et al. 2021) Parameter RR DET LAM LL TT ENTR ENTR-V FRP-1 FRP-2 FRP-3

Mean 0.015 0.867 0.933 7.475 8.468 2.423 3.171 0.622 0.319 0.828

STD 0.005 0.017 0.009 0.797 0.693 0.150 0.141 0.118 0.032 0.092

Min 0.008 0.837 0.917 6.404 7.605 2.158 2.924 0.341 0.280 0.577

Max 0.028 0.904 0.951 9.589 10.360 2.747 3.504 0.829 0.403 0.956

CoV 34.09 2.01 0.96 10.67 8.18 6.21 4.43 18.92 10.05 11.06

imposed by the energy costs of changing positions very rapidly. It is interesting to note that for each football match, LAM was higher than DET, which suggests a higher prevalence of static phases compared to dynamic recurrent episodes. The results for the average line length (LL) and trapping time (TT) show the same relationship as DET and LAM, that is, the persistence of an initial state lasts longer than two match phases following the same track. Moreover, the average duration of episodes that unfold in a recurrent manner during a football match is around 7.5 s, but there were between-match variations of more than 3 s and high CoVs around 10%. Entropy values show a higher entropy for the distribution of vertical lines, whereas diagonal lines tend to display a more regular distribution, both with only small variations between matches. The rate of open play (FRP-1), that is, the detected patterns, makes up 62.2% of the RPs on average with high match-specific variation (range, 34.1–82.9%; CoV, 18.92%). This means that FRP-1 addresses specific properties of a football match. Open play is made up of more stable situations as well as more “chaotic” ones. This specific combination is expressed in FRP-2 with a mean of 31.9% and a range from 28.0% to 40.3%. It is interesting to note that less than half of open play periods are highly recurrent, and again, there is considerable variation between matches. The recurrence share of open play at all recurrence points during a match is on average quite high (82.8%), but it also varies considerably between matches (range: 57.7–95.6%). In Table 4.4, the intercorrelations between all of the recurrence parameters and selected PIs are provided. At first glance, there are several significant and even highly significant correlations with medium to large effect sizes suggesting that the recurrence parameters truly describe relevant aspects of the game. There are examples where the frequency of events is correlated with the recurrence parameters. For example, the number of goals has a highly negative correlation with the recurrence rate (r = −0.622**) and the number of corners is significantly related to entropy; this indicates that there is more ordered behaviour surrounding this event. All passing PIs (the number of passes, completed passes, and pass percentage) show significant correlations with the football-specific parameters FRP-1 and FRP-3, both

Recurrence parameter RR DET LAM LL TT ENTR ENTR-V FRP-1 FRP-2 FRP-3

Goals −0.622** −0.209 −0.283 0.082 −0.008 −0.210 −0.144 −0.166 −0.293 −0.166

Goal difference −0.417 −0.175 −0.171 −0.015 −0.074 −0.218 −0.054 0.035 −0.051 0.110

Shots on goal −0.334 0.263 0.203 0.472* 0.309 0.331 0.305 −0.444* −0.244 −0.569**

Dist. Cov. M 0.274 −0.382 −0.383 −0.429 −0.403 −0.295 −0.452* 0.367 −0.048 0.265

Dist. Cov. Diff 0.032 0.015 −0.059 0.034 0.111 0.016 0.004 0.203 0.282 0.193 Passes 0.194 −0.375 −0.326 −0.525* −0.404 −0.454* −0.446* 0.543* 0.264 0.611**

Passes compl 0.180 −0.358 −0.326 −0.514* −0.406 −0.418 −0.412 0.572** 0.321 0.644**

Pass% M 0.099 −0.242 −0.259 −0.360 −0.318 −0.252 −0.249 0.519* 0.371 0.581**

Poss. Diff 0.444* −0.085 0.036 −0.312 −0.340 −0.045 −0.090 0.382 0.338 0.369

Duels won Diff 0.180 −0.391 −0.357 −0.425 −0.393 −0.321 −0.348 0.515* 0.250 0.455*

Corners 0.191 0.312 0.292 0.264 0.218 0.474* 0.386 −0.283 −0.179 −0.385

Stoppages −0.138 0.245 0.189 0.422 0.276 0.309 0.248 −0.346 −0.250 −0.470*

Table 4.4  Inter-correlations between recurrence parameters and traditional PIs for n = 21 matches (* = significant correlations; ** = highly significant correlations) (Lames et al. 2021)

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suggesting the prevalence of open play, which might be expected. This does not hold true for FRP-2, the recurrence rate of open play, as it seems to be an independent variable. There is also a significant negative correlation between the mean distance covered and the entropy of the vertical lines, the latter representing a more static match. Compared to the frequency of events, the differences in performance indicators between the two teams have a lower impact on the recurrence parameters, for example, the goal difference and the difference in distance covered by the two teams. The difference in possession is significantly correlated with the recurrence rate suggesting that when a game is dominated by one team, the match shows more recurrent patterns. The difference in the percentage of duels won, also representative of one team being dominant, is significantly associated with the two football-specific recurrence parameters (prevalence of open play and the share of recurrence points of open play). This finding is plausible as the more dominant team has the ability to continue the game by winning more duels than their opponent. There are contradictory findings in the correlations of the number of shots on goal. They are associated with a lower share of open play, although we observed a higher average line length, which is representative of more open play. In sum, Table 4.4 provides interesting insights into the relationships between the recurrence parameters and the traditional PIs. However, these relationships are not yet fully understood and need further research and validation. Summing up this section on recurrence analysis for PA, it may be mentioned that RPs give a good visualization of the dynamics and emergence in a football match. Standard recurrence parameters are innovative PIs characterizing specific aspects of football matches that have not been scrutinized in detail before. In the section on modelling approaches in TPA above, the research strategy in PA to adopt new tools or methods from established theories in other scientific areas was critically acknowledged, and four steps were distinguished (see Box “Importing a theory/a methodology to PA”). Lames et al. (2021) make suggestions for footballspecific recurrence parameters presented here, which would meet the demands of step 3, introducing domain-specific amendments to the theory. It may be hoped for that findings from PA will re-enter the theory of recurrence analysis, which would give an example for step 4. There is much potential in football recurrence analysis such as RP plots and parameters for single teams only. Cross recurrence plots with different entities (teams, players) on x- and y-axis of RP may constitute a visualization for coupling which is not the strength of known coupling parameters (relative phase, approximate entropy, sample entropy). It will be interesting to see the new PIs applied in typical PI analyses such as profiles or performance level and sports comparisons.

5

Practical Performance Analysis

5.1 Introduction One basic message of this book is the distinction between theoretical performance analysis (TPA) and practical performance analysis (PPA), which are the two sub-­ disciplines of performance analysis (PA). The reason for this distinction is the different scientific approaches applied within each of the two sub-disciplines, as listed there in Table 1.1. This distinction was introduced at the beginning of the book in Chap. 1. In the present chapter, dedicated exclusively to PPA, concepts and methods of PPA will be covered in more detail. The chapter starts with conceptual issues of PPA. The general contributions of sports science for supporting practice are presented in a systematic manner, where the research approaches relevant to PPA are evidenced and the importance of evaluation research as most appropriate research strategy for PPA is underlined. The general task of PPA is seen in establishing an informational coupling between competition and training, that is, that information obtained from analyses of behaviour in competition is transformed into information that informs practical action in training and coaching. The informational coupling of competition and training is described in large detail with a comprehensive approach to PPA as a natural consequence. In the second part, the basic methods of PPA are examined. One main message here is that PPA makes either implicitly or explicitly use of qualitative methods. As this message may be controversial among traditional, “stats”-moulded performance analysts, a short explanation of qualitative research methodology is provided. Besides qualitative game analysis, there are two other central activities of PPA. The first is deriving a match plan, that is, developing a tactical strategy for the next match against a specific opponent. The second activity is facilitating the transfer of the results of game analyses to the athletes, which has given rise to a unique training method used in PPA called video-based tactics training. The chapter concludes with practical aspects of PPA in professional training systems. Recently, the analysis of the professional role of match analysts in © Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5_5

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professional soccer has become a topic of interest in PA (e.g. Martin et al. (2021)). The professional role will be analysed here as well, but with a focus on aspects being specific to PPA such as technical support, communication strategies, and the role of PA in a comprehensive club information system.

5.2 Concepts of PPA 5.2.1 Definition, Aims, and Research Strategies The view taken at PPA in this book is somewhat different from traditional perspectives, especially those brought forward in notational analysis, the precursor of performance analysis (Hughes and Franks 1997, 2004). There, the aim was merely to objectively and systematically record what was happening on the pitch. This data was seen as feedback for coaches and athletes, but it remained their responsibility to draw practical conclusions. Here, instead, the notion of PPA is more comprehensive and includes conclusions that are drawn from the data. As stated already in the initial chapter, we define PPA as follows:

Practical Performance Analysis

PPA comprehends all performance analysis activities conducted in sports practice, for example, the analysis of own performances in competition to identify targets of training or of the next opponent’s matches to develop a match strategy but also the analysis of training exercises and athletes’ abilities. The general aim is to generate useful recommendations for practical action (practical impact). Conducting research in PPA aims to provide a scientific foundation for concepts and methods applied in PPA, typically using a spectrum of research strategies. There are good reasons for this more comprehensive view. PPA is organized, financed, and implemented in practice for its expected benefits, that is, for having a practical impact such as improving training and being more successful in the long run. Thus, drawing practical conclusions should also be part of PPA. In practice, specific methods of PPA, such as deriving a match strategy or applying video-based tactics training have evolved, that go beyond the mere description of matches. It is worth noting that the above definition of PPA does not imply that all activities are carried out by performance analysts in a sports club. Instead, PPA is performed by a team of actors in the sports club, mostly of course the game analysts, but also the head coach and other coaching staff. The aim of PPA as a scientific activity is to provide a scientific foundation for the application of PPA in practice, for example, how do we arrive at good match analyses, what has to be considered in developing a match strategy, and what are effective methods for transferring the results of analyses to the athletes?

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To achieve this aim, a spectrum of scientific activities is required (Hohmann et al. 2020). A short overview contains three broad research strategies: • Basic research: Research that aims to establish general laws, for example, to clarify the structure of a sport’s performance (TPA), but also to study the mechanisms of adaptation and other relevant questions. Some of these types of investigations overlap with basic research from other disciplines such as physiology or psychology, while others—such as modelling the complex structure of sports performances—are of no interest to other disciplines. This type of research provides background knowledge for practical action, for example, why to train in a certain way or what are the key game elements that predict success. • Intervention studies: Experimental research, ideally conducted in field settings, that compares the effectiveness of different or additional interventions for training and coaching. The aim here is to establish “technological rules”, that is, scientifically approved ways to solve a certain problem in practice, which provides operational knowledge for how to proceed in certain situations. • Evaluation research: Systematic analyses of practical measures and their impact and appropriateness in practice using scientific methods. This strategy provides knowledge for best practices that may serve as a model for practical action (summative evaluation). An appropriate method for evaluating one’s own training processes or match preparations is formative evaluation. The involvement required by PPA researchers, as well as the practical impact of these three research strategies, differs largely. Typically, basic research is not conducted in a practical setting; rather, results are taken from the research literature and reviewed to determine its relevance to the own application case. Similarly, intervention studies, especially when a highly controlled experimental design is required, can be impractical for PPA purposes. Nevertheless, intervention studies can still serve as a valuable PPA research strategy. Comparing different treatments for their effectiveness under typical field conditions could be part of PPA activities. The research strategy that requires the most involvement by the local performance analysts is evaluation research. Summative evaluations of one’s own interventions such as end-of-season reports of match performance, and formative evaluations, such as the permanent monitoring and control of training processes and playing performance are core activities. Basic research can inform practical action, predominantly by providing background knowledge, for example, the statistical relevance of a certain skill, a certain tactics, or the level of an athletic property for overall performance. Intervention studies can also contribute to decision-making; however, the cursory interpretation of existing intervention studies may lead to naïve practical conclusions. For example, a coach may be tempted to implement the most successful intervention based on a previously published experiment. Unfortunately, the success of this specific intervention may be specific to the sample and the circumstances set out in the experiment. Before adopting any intervention, it is prudent to determine whether the conditions of the existing study align with one’s own situation or desired outcome. Thus, the most appropriate approach for a performance analyst working in practice

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is responsive evaluation (Stake 1980), where everything is devoted to make the intervention a success. Evaluation research is the most important source for the following sections. Insights into appropriate concepts and appropriate methodological steps were obtained during several interventions in sports practice that are listed in the box below. Only exceptionally one may run controlled field experiments such as the one described at the end of the section on video-based tactics training. The majority of concepts and practical recommendations was derived as a generalization of practical experiences.

Practical Experiences

Concepts and methods for PPA presented here are on the one hand based on theoretical concepts of relevance and on the other hand and most important on practical experiences of members of the Chair for Performance Analysis and Sport Informatics at TU Munich. These members were typically doctoral students and domain experts in their respective sports, and they engaged in projects developing match analysis software and conducting qualitative game analysis (QGA) and video-based tactics training (VTT) to support the cooperating federations and clubs. The foundational research concept of these interventions was evaluation research, where these practical experiences were collected and aggregated to form general concepts and methods of PPA. Beach volleyball (Gunnar Hansen, Steffen Lang,  Daniel Link, Sebastian Wenninger) • QGA and VTT: 2000 Olympics • Match analysis software: 2012, 2016, and 2021 Olympics Handball (Karsten Görsdorf, Christoph Moeller) • QGA and VTT: German National U17 EC 2008 and WC 2009 • QGA and VTT: German National U19 WC 2007 • QGA and VTT: German National Women’s Team WC 2009 Soccer (Ole Cordes, Christoph Moeller, Karsten Görsdorf, Thomas Blobel) • QGA and VTT: Clubs in first and second German League • Player VTT: Players from German first and second league • QGA and VTT: women, champions-league winner 2010 Paralympic Goalball (Christoph Weber) • Match analysis software • QGA and VTT: German National Team 2016 Olympics Paralympic Table Tennis (Michael Fuchs, Sebastian Wenninger) • Match analysis software • QGA and VTT: German National teams 2021 Paralympics

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5.2.2 Informational Coupling of Competition and Training It was already mentioned that PPA giving only objective feedback about what happens in a match fails to meet the full demands of sports practice. Arguments against this attitude are given in the box below. The analysis of performance data and the development of recommendations for practical action in training are both part of PPA. This applies, no matter who is actually executing these tasks, whether it be the head coach, assistant coaches, or performance analysts. Is Giving Feedback the Central Task of PPA?

Historically, in the very first publications on PA, then known as “notational analysis”, it was commonly believed that the main purpose of PPA was to provide feedback. In the 1997 textbook of Notational Analysis, the chapter by Franks and Hodges explicitly underlined the necessity of feedback in PA. This belief may have originated from the fact that some major protagonists of this view (Nicola Hodges, Ian Franks, Tim McGarry) have roots in movement science rather than only in performance analysis. In motor learning, there is no doubt that giving feedback on one’s actual performance is crucial and contributes directly to improvement. The reason for this is that feedback combined with memory traces of the last realization of a skill helps learners to create an adequate internal representation of the movement (Salmoni et al. 1984). The aims and contexts in PPA are quite different. In PPA, the aim is to evaluate the appropriateness of tactical decisions and behaviours in a certain game situation, that is, cognitive structures such as action plans. Unlike in motor learning, there is no need to present information in short time to make a connection to the vanishing memory traces of a movement. Even after several days, the memory of player actions can be easily recalled, especially with the help of video playback. Thus, the central task of PPA involves more than simply providing feedback and extends to cover a broader scope of match analyses for tactics training. There are several different models that have been published on how to integrate PA into the coaching process. The early model by Franks and more recent models by Carling et al. (2005) and O’Donoghue and Mayes (2013) contain a box labelled “analysis”, but it is not clear what actually goes on in this box. This ambiguity was pointed out by Martin et al. (2021, p. 2), who said that “there is a somewhat ‘magical’ quality to the analysis process, in which information appears in a box within the models”. It is then important to understand what goes on in the magical box of analysis, what the general concepts are behind its meaning, and which methodological measures are appropriate to “demystify” this analysis process? There are several purposes of match analysis in PPA, many of which will be discussed in the following section. In general, analyses in PPA serve supporting

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practical decision-making within sports organizations (clubs, federations). In practice, analyses of one’s own team, the upcoming opponent, and players of interest for potential transfers are most important. In professional football, elite clubs have separate departments for each of these three purposes. Informational coupling of competition and training will be discussed in detail, as it is regarded as the most complex task in PPA, but also the one with the most potential for performance improvements. Then, there will also be discussions about the analyses of opponents and transfer candidates in later sections. To establish informational coupling of competition and training means to discover what can be learned from the analysis of competitions to later apply in the optimization of training in a short-, middle-, and long-term perspective. Through the analysis of competition-based information, performance analysts and coaching staff alike can facilitate better data collection, analysis, and information transfer to inform practical action. There are, however, other sources of information that also have an impact on what is done during training. Routine aspects of training: Some parts of training, such as the warm-up, flexibility, and trunk strengthening exercises, are focused on specific aims such as injury prevention. There are other routine aspects of training, such as coordination and speed and agility exercises, because these skills must be trained in a consistent manner to maintain fitness. Activities for achieving and maintaining specific levels of performance prerequisites: There are performance prerequisites for which a certain level must be achieved to be competitive. For example, for football players, it is essential to achieve and maintain a certain endurance level, which is characteristic for their performance level. In practice, this means that these required levels of performance prerequisites constitute targets that are permanently pursued in training. Conceptually, this poses the question of the origin of norms for the level of required performance prerequisites. Norms for the Required Level of Performance Prerequisites

When developing a training plan, it is important to specify the training targets, that is, which level of a certain performance prerequisite (endurance, strength, speed, flexibility, coordination, technics, and tactics; Hohmann et al. 2020) needs to be achieved to meet the demands in competition at the respective performance level. The levels to be attained are conceptually given by norms. There are three important types of norms to be distinguished, and each of them focus on a different aspect: 1. Ideal norms: What is the highest level achieved in a particular performance prerequisite among the world’s bests athletes? What is the endurance ability of players in the elite clubs and top national selections? 2. Functional norms: What level of performance prerequisites is sufficient to meet the demands of a certain competition level? Frequently, functional norms in PA are not based on empirical studies but on the gut feelings of the coaching staff.

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3. Statistical norms: Performance prerequisites within certain settings are sometimes reported in empirical studies, for example, VO2 max averages, percentiles, and confidence intervals among players in a national football first league are known. The type of norm which applies best to a training concept depends on the specific context: ideal norms may be more appropriate for teams and athletes striving to be the best at international level, whereas functional or statistical norms (if available) may be more relevant at lower performance levels. Why is it a good idea to derive targets for training—besides the two routine targets just mentioned—by analysing actual competitions? There is a very convincing reason to do so. If a team or athlete is able to develop targets for training from their performances in past matches, these targets can address the issues that contributed to the success or failure in these matches. Furthermore, if appropriate measures are implemented in training to improve the weaknesses and stabilize the strengths observed in previous performances, then this will most likely and much more than pursuing targets from other sources lead to improved performance and success in future matches, which is the ultimate goal in professional sports. Having so far only explained the importance of informational coupling between competition and training, we will now discuss the concept and the sequence of sub-­ tasks to be accomplished. This sequence is based on the conceptual assumptions explained in Chap. 1, especially the relationship between a team’s performance during a competition, performance prerequisites, and training (see Fig. 1.1). Even if all the different steps of the sequence in Fig. 5.1 are not yet universally agreed upon, it should nevertheless demonstrate that PPA consists of more than merely recording what happens during a match and has the potential to inform impactful recommendations in practice. A model for the informational coupling of competition and training was proposed already quite early by Lames (1994). It consists of three steps as shown in Fig. 5.1. Fig. 5.1 The informational coupling between competition and training. (With permission of Philippka-Verlag from Lames (1994))

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5.2.2.1 Step 1: Description The first step is to identify relevant match information from competitions. In modern PPA, match descriptions are generated from three sources: an observational system, position tracking, and video recordings. The appropriate type of an observational system for PPA is a category system, since the analysts do not know in advance which phase of the game may become relevant. The alternative, an event system, cannot capture anything outside of the predetermined events; thus only a category system can provide a comprehensive description of the match. As mentioned in Chap. 2, “action feeds” have recently come into  use in elite sports events and in top leagues in professional sports. Although event systems by nature, they may be  considered as  category systems, because they provide a fine-grained sequence of all relevant events. The data from position tracking allows for the analysis of kinematic variables and aspects of tactical behaviour, which contribute to the match description. Recent studies have reported valuable tactical descriptions derived from positional data by directly modelling constructs with practical relevance such as ball possession, availability, dangerousity, and the value of player actions that were presented in detail in Chap. 4 on TPA. Video recordings are an indispensable source of data on the performance of athletes and teams and allow for in-depth analyses of playing behaviour. It is crucial to have an efficient computer-video coupling, that is, the event and position data is stored with the corresponding scenes in the match video. This ensures that on the one hand, figures in match reports that attract attention may be quickly examined in depth by scrutinizing the video scenes showing the corresponding situations or events, and on the other hand, noticeable scenes in a match can quickly be checked for generalizability by examining statistics about it. Some principles of the design of match analysis software are mentioned in the Sect. 5.4.3. Finally, it is important to note the distinction between description (step 1) and analysis (step 2) in the conceptual model of informational coupling between competition and training (Fig. 5.1). This distinction is borrowed from empirical research methodology, where it is common to present the results and to discuss and interpret the results in two different steps. The reason for this is that there are different aims of the two steps, resulting in different demands (e.g. demands for description: accuracy and reliability; demands for analysis: trustworthiness and stakeholder agreement) and methods (methods for description: quantitative methods; methods for analysis: quantitative and qualitative methods). Overlap between the description and interpretation steps may lead to subjective judgements, where, in the worst case, analysts and coaches simply reproduce their prior opinions. 5.2.2.2 Step 2: Analysis This is a central step in the practical work of performance analysts. It can be further sub-divided into two steps: first, the identification of players’ strengths and weaknesses, and second, the identification of the players’ properties that give rise to these strengths and weaknesses. This sub-division is required because of the basic assumption explained in the first chapter, which is that training can only impact on

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stable properties of players, that is, their skills and capabilities. The metaphor of sharpening one’s weapons was used to illustrate what can be done in training. The battle has its own rules (dynamic interaction process with emergent behaviour) and may only indirectly (via the stable properties) be influenced by training. This makes the identification of the properties of the players that contribute to strengths and weaknesses in the match a crucial part of match analysis, thus generating potential targets for training. Step 2.1: Identification of Strengths and Weaknesses It is common to start this step by scrutinizing the reports of a match based on action and position data. As recommended by Carling et al. (2014), performance analysts typically refer to an individual set of performance indicators and compare the performances of their own team with the opponents in a match. However, it would be naïve to assume that players’ strengths and weaknesses can be easily determined through simple evaluation of PIs. Upon closer inspection of the statistical norms available for game behaviour, we find large variations in behaviour, for example, the error rate of first serves in tennis may range from 0% to 70%. Furthermore, when we have PIs that are not directly connected to the success of a match, it is difficult to specify the optimal level of a PI. What is a “good” first service error rate? Is it a very low one, implying the first service does not create much of an impact? Or is it a very high one, with a high scoring probability when the ball lands in, but resulting in a higher frequency of second serves with a lower scoring probability? The answer is explained by the nature of game sports: the optimal error rate is dependent on the interaction between the players, meaning servers should adapt the riskiness of their serve based on the opponent’s ability to return and their confidence in their second serve. This optimal error rate may even change throughout a match, for example, when a server goes through a phase with problems in serving. The same principle applies for the optimal level of kinematic parameters such as distance covered. As shown in Chap. 4 on TPA, match intensities may be considered as the result of a negotiation between two teams during a match, rather than representing either teams’ performance and by no means the endurance abilities of a team or specific players. Then, how can we actually identify a strong or weak performance? We will need additional information to arrive at an appropriate judgement. First, we need background knowledge on the individual of a player. We need to know his typical performance level, his actual preparation level (fitness, injuries), and also the tactical instructions he received. For example, the running performance of a wing defender is dependent on the match strategy; the coach may instruct him to play exclusively defensivly or to support the offence as often as possible. Second, we need to study the context of each action or decision. An example of this is the PI “duels won”. There are situations, where there is a good chance of winning a duel, for example, when several defenders put pressure on an attacker moving at low speed and situations with a low chance of winning a duel, for example, when an attacker approaches at high speed against a single defender. To

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appropriately evaluate the rate of duels won, performance analysts must examine each and every duel in a match. Third, an assumption must be made regarding the stability of the findings. Will the player consistently show this behaviour in other matches against different opponents or is this behaviour an exception? Understanding the stability of the findings is particularly when developing recommendations for training. Summarizing Step 2.1, it becomes obvious that only with detailed background knowledge of the single case investigated and with a detailed video-based reconstruction of the performance beyond summative statistics, strengths and weaknesses may be assessed. The nature of this step is a reconstruction and interpretation of facts by experts being part of the training system. Step 2.2: Identification of Performance Prerequisites As already explained in the introduction of this section, the identification of the causes of strengths and weaknesses in playing behaviour at the level of performance prerequisites, which are schematically depicted in Fig. 1.5 in Chap. 1., is required in PPA. The main challenge we face in this step is ambiguity; a specific weakness may be caused by many properties of the player. For example a low success rate of serve-and-volley attacks in tennis may be due to several specific problems: • Tactics: The decision about where to place the serve prior to starting the net attack as well as where to place the first and subsequent volleys, depending on the opponent’s strokes. • Technique: The quality of the single strokes (service and volleys) and the timing of when to approach the net after serving. • Athletics: The athletic prerequisites such as explosive strength, agility, movement coordination, and reaction time. • Anthropometry: Certain statures and body proportions can be advantageous, for example, tall players with a large arm span have an easier time reaching to hit a volley. • Psychology: Playing serve-and-volley requires determination and courage. Maybe even anxiety plays a role when expecting a fierceful return after a bad preparation. Summarizing Step 2.2, it becomes obvious that there will be persistent uncertainty in the identification of performance prerequisites responsible for strengths and weaknesses. There will never be an if-then-rule to solve the problem via some algorithm, for example, if there is a weakness in the serve-and-volley, then the reason is tactics. Similar to Step 2.1, this step requires a detailed reconstruction and interpretation of match behaviour to identify the potential reasons for the strengths and weaknesses in the system of performance prerequisites.

5.2.2.3 Step 3: Transfer to Training After Step 2, we now have a list of the players’ strengths and weaknesses as well as the responsible performance prerequisites analysts and coaches have agreed upon. The performance prerequisites on this list are potential targets for training. The question

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that has to be answered in Step 3 is whether and how this list of potential targets will be transferred to actual actions in training that aim to improve these prerequisites. A first consideration is a question of the coach’s philosophy: one could either try to reduce weaknesses or to reinforce strengths. The choice depends on the level of the players, that is, reducing weaknesses is a priority when educating players in youth academies, whereas reinforcing strengths is more appropriate at elite level, since these athletes will not have severe weaknesses anymore. For example, in a youth academy, it is not acceptable for a player to have a preferred leg for shooting and ball handling, especially with a large difference in performance between the two legs. Conversely, some top-level football players are known to prefer their dominant leg, for example, the left leg of Arjen Robben, the Dutch national player, and very successful Bayern Munich forward from 2009 to 2019. Besides this consideration on whether to compensate for weaknesses or to emphasize strengths, a successful transfer of the analyses from Step 2 to training again requires two steps to be accomplished. Step 3.1: Assessment of Effective Trainability While performance prerequisites can be used as potential targets for training, their potential for improvement through training (“trainability”) can differ. We can distinguish between general trainability, which is not given for anthropometric prerequisites  for example, and effective trainability, which, instead, considers the cost-effectiveness of the training. Moreover, the cost-benefit relationship should be explored for each and every potential target of training, where the costs are given by the resources that have to be invested and the benefit is the impact of improving a particular strength or weakness on overall performance. In other words, the list of potential targets for training has to be transformed into practical training recommendations. Ideally, this list also contains priorities regarding which targets are expected to impact overall performance to the greatest extent. Step 3.2: Integration into Training Process A challenge when introducing a new training target is sometimes called the “heterosynchrony” of adaptation. This refers to the different time frames that may be required for different targets before improvements may occur. There are short-term adaptations, for example, in cognitive structures like tactical plans or in psychological states like an athlete’s motivation facing a specific match, and long-term adaptations that may take weeks or months. Typically we find long-term adaptations in improving basic capabilities such as endurance or strength and skill improvement on a high performance level and in psychological traits such as general achievement motivation. New training targets also have to be compatible with the periodization of training, that is, the temporal structuring of training, typically over one season with different periods, each with different targets and corresponding training plans. Periodization aims to achieve top performance levels that align with the top relevant events during a season, for example, play-offs. This leads to the interesting effect that the same target may be addressed by different measures depending on the actual

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phase of periodization. For example, if endurance is to be improved during the preparation phase, an athlete would undergo traditional endurance training, whereas near the end of the season, this would not make sense, and instead, one would extend regeneration. Another problem might occur with two incompatible training targets, for example, hypertrophy and explosive strength or hypertrophy and endurance, being of relevance at the same time. Above all, there is a fight for resources in training not only between targets recommended by match analysis but targets obtained by other considerations like described at the beginning of this section. To successfully integrate new targets from match analysis into training, coaches and analysts must have detailed knowledge of the ongoing training process and, ideally, the individual response characteristics of each of the players. The estimation of the cost-benefit relationship is especially demanding, since the planning and development of the required training may entail an interdisciplinary effort.

5.2.2.4 Summary Informational Coupling In this section, a conceptual model for the informational coupling between competition and training was presented in three steps with sub-tasks. In elite-level sports where success in competition is paramount, past performances during competitions should be the primary source of information for training in addition to the other sources such as the norms for performance prerequisites and routine aspects of training (warm-up, injury prevention). It is this informational coupling where the largest potential lies in for performance improvement in elite-level sports. For most of the sub-tasks, there is no simple algorithmic solution. However, the steps to be taken from match analysis to training have been established. Taken together, from a methodological standpoint, these steps require detailed knowledge of context and in-depth reconstruction and interpretation with subjective interpretations involved. These are properties of qualitative research methodology that will be addressed in detail in the method section of this chapter, where qualitative game analysis is introduced as the most important method of PPA. Thus, the informational coupling between competition and training relies not only on the in-match behaviours but also the athletes’ individual performance levels and the overall training process. When all three information sources are integrated into a unified analysis approach, this is called comprehensive performance analysis.

5.2.3 Comprehensive Performance Analysis Based on the insights gained from developing the model for informational coupling in competition and training, a broader concept of PPA known as comprehensive performance analysis was established. This concept is illustrated in Fig. 5.2. Without integrating analyses of the athlete’s skills and abilities, in addition to knowledge of the training process, the practical recommendations generated to inform training would be incomplete.

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Fig. 5.2  Illustration of the concept of comprehensive performance analysis

The reasons to advocate for comprehensive performance analysis lie in the fact that there are more pieces of information needed than what is included in the model for informational coupling in competition and training (see Fig. 5.1). First, knowing the actual fitness level of the players is required for assessing strengths and weaknesses and the relevant performance prerequisites, and second, any recommendation for training can only be given knowing the training efforts in the past. Comprehensive performance analysis requires collaboration between all staff  members, including fitness coaches, performance analysts, and the overall training organization. There is a section later in this chapter that discusses the design of a club information system that can help support this collaboration. At this point, one may remember the so-called practical impact debate in PA which was outlined in Chap. 1, where the distinction between TPA and PPA was first introduced. Some researchers and practitioners criticize PA for not delivering results with sufficient practical impact. However, by the end of this section, we will have specified many solutions to overcome this supposed deficit in PA: • Acknowledgement of the distinction between TPA and PPA! • Acknowledgement of qualitative methods for PPA! • Adoption of the concept of comprehensive PA! It is also recommended as conceptional framework for PPA  to perceive game sports as dynamic interaction processes with emergent behaviours. This will prevent naïve expectations on assessing training impact, for example, it would be unreasonable expecting to observe a direct effect on match running performance solely from extended or improved endurance training. It will also prevent a certain control attitude expressed in the expectation that the result of a match is guaranteed as long as players and staff are working well and hard enough.

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5.3 Methods of PPA Having discussed the basic concepts of PPA, the informational coupling of competition and training and the concept of comprehensive performance analysis in the previous section, this section will present concrete methods applied in PPA. This includes qualitative game analysis with its adaptations of qualitative research methods like content analysis to PPA and specific methods of PPA like the development of match strategies and video-based tactics training.

5.3.1 Qualitative Game Analysis The central method for PPA is qualitative game analysis (QGA). There have been already references to qualitative methodology in the last section as well as in the first chapter when defining the characteristics of PPA. Also in PA literature, there are some indications of qualitative methods such as case studies, ethnography, interviews, and mixed methods approaches, frequently meant as add-on to quantitative methods (Mackenzie and Cushion 2013; O’Donoghue 2010). Poizat et al. (2013) mention the reconstruction of the inside view of the athlete with video-based self-­ confrontation interviews as an example of qualitative methods in PA. Sometimes the mere shifting of the focus of analyses from data to patterns is termed “qualitative” analysis (Gréhaigne et al. 2001). In agreement with Nelson and Groom (2012), this book treats the quantitative approach and the qualitative approach as two different paradigms. In contrast to Nelson and Groom (2012), they are not seen as compensatory but as sequential steps of an appropriate methodological approach, such as in the case of generating recommendations for training. To justify this rather strict methodological opinion, the following paragraph on QGA offers a short introduction in qualitative research methodology.

5.3.1.1 Qualitative Research Methodology This section is based on a number of textbooks on qualitative research methodology, for example, Denzin and Lincoln (2004), Guba and Lincoln (1989), Glaser and Strauss (1967), Strauss and Corbin (1998), Lamnek (2005), or Flick et al. (2004). In addition, there are several approaches of qualitative research methodology, each one with a specific focus, for example, grounded theory (Strauss and Corbin 1998), fourth-generation evaluation (Guba and Lincoln 1989), action research (Argyris et  al. 1985), symbolic interactionism (Goffman 1959), objective hermeneutics (Oevermann et  al. 1979), or qualitative content analysis (Mayring 1994, 2014). Nevertheless, it is possible to extract features from all these approaches relevant to PA. The following list depicts general properties of qualitative research: • The centre of qualitative research is the human being, the reconstruction of his subjective point of view, and the interpretation of the meaning of observed behaviour.

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• The intention, meaning, and success of actions are interpreted with respect to the situational context from which they originated (contextuality). • The focus is on real, everyday life and not so much on the development of theories; there is an interest in improving quality of life. • An inductive perspective is pursued, which means to draw conclusions on general properties from single findings. An important prerequisite for this perspective is the openness of researchers. • Insights are achieved by close inspection of single cases (“thick description”; Geertz 1973). There is an astonishing agreement between the aims and methods of PPA and qualitative research. Almost all of the aforementioned properties of qualitative research apply to PPA, for example, PPA supports a single case, requires the contextual interpretation of game behaviour, values openness to arrive at reliable and practical conclusions, and considers thick description as an appropriate method. Table 5.1 provides additional criteria of comparison between qualitative and quantitative research methodologies. In sum, there are paradigmatic differences between the two approaches, and it becomes clear that qualitative research methodology is perfectly suited to PPA, as it takes into account the conceptual research purpose and perspective. We cannot ignore the “scholarly bloodbaths” (Wortman 1983, p. 224; Reichardt and Cook 1979) that have occurred between qualitative and quantitative researchers. Attempts at reconciliation have been rejected from both sides. As shown in Table 5.1, it is difficult to find a common ground between the aims and properties of both paradigms, which has also given rise to the fundamental distinction between TPA and PPA presented in this book. For example, when going into details of the distinction, it becomes obvious that even the holy grail of quantitative research and the measurement criteria, that is, objectivity, reliability, and validity, need to be re-interpreted in qualitative research (Guba and Lincoln 1989): Table 5.1  Comparison of qualitative and quantitative research based on different criteria Criterion Research perspective Data Research process Theoretical work Path to knowledge Understanding things Methods

Qualitative research View of stakeholders

Quantitative research External view of researcher

“Soft”, everyday data Dynamic Discovery of hypotheses Inductive, interpretation

“Hard”, replicable data Static Proof of hypotheses fixed a priori Deductive, measurement

Understanding of stakeholders’ views

Explaining things by revealing causal relationships For example, test, experiment, and observation

For example, interview, content analysis, and observation

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• Objectivity vs. confirmability: A fundamental aspect of qualitative research is that the conclusions are interpretations made by the researcher. As such, ­objectivity, by definition, does not exist. Rather, the emphasis is on maintaining records and documentation regarding the assessment of data, the methodological decisions, and all of the subjective interpretations, so together, they can be used to determine confirmability. • Reliability vs. inter-subjective agreement: Reliability may neither be achieved in a procedural way nor assessed with statistical figures. Instead, a researcher must demonstrate the plausibility of their interpretations, or preferentially, discuss and contrast alternative interpretations. The methodological approaches to achieve inter-subjective agreement are consented or validated through communication validation, for example, a “member check” on the conclusions drawn. • External validity vs. transferability: Researchers are typically only interested in the success of their own intervention, so applying their results to different settings is not a duty of the researchers (push) but those who could benefit from their work (pull). Nevertheless, transferability should be facilitated by explicitly acknowledging the assumptions made and providing a thick description of the setting that are relevant to the research. There are some widely acknowledged application fields for qualitative research, partially most characteristic for PPA: • Settings where there is little knowledge of the research topic and a more explorative approach is appropriate • Studies which focus on the reconstruction and interpretation of human behaviour and require empathy from the researchers to reconstruct the underlying complex decision-making processes • Interventions which affect different stakeholders who should arrive at a common reconstruction of the examined behaviour and/or an agreement on practical action to be taken When applying qualitative methods, there are two common problems. First, an insufficient distinction to naïve approaches: Making subjective observations and arriving at interpretations of the perceived facts is not qualitative research per se! For example, a coach watching a match and drawing his conclusions did not necessarily apply qualitative research only because of not taking any notes and relying on gut feeling. There are strict methodological procedures to be followed to meet the standards of qualitative research; some of them are mentioned in the next paragraphs. Second, in academia and very likely in practice as well, the level of training in and the estimation of qualitative methods are frequently inadequate, especially compared to quantitative research.

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Attitudes of Qualitative Researchers

Qualitative research is a paradigm different from quantitative research. It requires people to adopt specific attitudes to adhere to its procedures (Guba and Lincoln 1989): • Holistic thinking, thinking in context and complexity • Focusing on practical problems, wanting to improve things • Proceeding in a reconstructive and interpretative manner, moving forward not with a linear approach but in hermeneutic cycles • Estimation of communication with stakeholders, trying to achieve a mutual understanding • Emancipation, trying to overcome suppression by understanding the game of power All of these attitudes are characteristic of PPA, but perhaps the last one needs further explanation. In an ideal world, players play an active role in making decisions about what should be done in the future. This results in good conditions for adherence to these decisions and creates an atmosphere of emancipation. Especially in the education and training of young academy players, it is important to convey the message that one’s capability to analyse performances is not only of help to improve performance but also to become emancipated personalities.

5.3.1.2 Qualitative Methodology in PPA Up until this point, it has been explained that reconstruction and interpretation are key activities in the informational coupling between competition and training. In the previous section, an introduction in qualitative research methodologies was given, and it was shown how it shares several properties that are important for effective PPA. Now, it is demonstrated that PPA relies on qualitative methods by showing the problems or failure of summative PIs and algorithmically derived practical recommendations. The strengths and weaknesses of a player or team cannot be derived from summative, quantitative statistics. This is evidenced by the typical PIs observed in football, such as the rate of ground challenges won in percentage, for example, 62.4%. From a PPA perspective, some of the critical questions that might arise when interpreting this PI either as strength of weakness might include the following: • • • • •

Was this rate constant within the match and/or between matches? Against whom was the challenge? Excellent players? Taller/heavier players? What were the tactical positions/tactical tasks of the player? Where/in which tactical situation was the challenge? What went actually wrong in the challenges that were lost (timing, aggressiveness, anticipation, direct body contact)? What went well in the challenges that were won?

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It becomes clear that to answer these questions, analysts would need to do an in-depth analysis of every single challenge with reconstruction and interpretation and thus use qualitative methods. Another naïve attitude may prevail towards the generation of practical recommendations for training as well. One might adhere to algorithmic recommendations given, for example, by if-then-rules like “If there is reduced performance in the end of a game due to fatigue, then more endurance training is needed”! Again, some critical questions from PPA include the following: • How dominant was the opponent? How strong was the opponent in athletics? • How was the pacing of the match? Was there a tactical decision to over-pace in the beginning of the match, knowing in advance that there might be a decrease in performance towards the end? • Which periodization phase is the player in? • Was endurance training a priority in training? Were there other, more urgent priorities? • Was it possible to reserve a slot for endurance training in the time schedule? • Do we know appropriate measures to improve endurance at the actual point in time? As opposed to if-then-rules, the solution lies in deriving recommendations based on comprehensive background knowledge of a team’s training, a detailed knowledge of the players’ situation, and an iterative approach to an agreed-upon training plan, which integrates the opinions of the experts in the staff and even players. Qualitative Game Analysis

Qualitative game analysis is the most important method for analysing sports matches in PPA. Its aim is to draw practical recommendations for training and other practical decisions. As PPA deals with the reconstruction of game behaviour and ambiguous interpretations, integration of contextual information, and opinions of training staff and players, it relies on qualitative research methods, including content analysis, a social intervention concept, hermeneutics, and stakeholder communication.

5.3.1.3 The Social Context One key element of the qualitative approach is working in real life on real-life problems. Therefore, in order to achieve the full benefit from PPA, it is prudent to go beyond just giving feedback and enter discussions with stakeholders such as coaching staff and players. This means that the interactions between analysts and staff/ athletes must be perceived as being embedded in a social context (see Fig. 5.3) that must be established. This is a consequence of two key concepts in qualitative research. The first is that the subject and the object of research are not seen as two independent, non-reactive

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Fig. 5.3  Illustration of the concept of considering interactions between match analyst and coach, staff, and athletes as being embedded in a social context

entities (subject-object dualism). Rather, the outcome of an intervention is influenced by both the subject and the object (Guba and Lincoln 1989). The second is contextual awareness, which in this case means that an intervention in the qualitative sense may never be completely understood without the social context in which it happens. The typical social context in PPA is a sports club, where there are people responsible for match analytics, and their analyses are expected to create practical impact. This requires a means for the analytics information to enter into a different social setting, from the computer lab of the analysts to the pitch with coaches and players. By acknowledging the reality of this social context, there are also some implications to consider: • The analysts must earn social recognition in the whole setting before successful interactions can take place. • The analysts must be aware of their social role, which makes them susceptible to influence by others, that is, they may be “played” by other staff or the players. • The analysts must be acknowledged as experts in the sport (and not only as technical specialists) for them to succeed in their role. These implications were also addressed by Martin et al. (2021) in their analysis of the professional practice of performance analysts. The success of a performance analyst is closely linked with their ability to build relationships with the players and other training staff. The most important relationship is the one to the coach. Max Reckers, the analyst of Louis van Gaal during his time with Bayern Munich, said that he had to learn how to see the game “through the eyes of the coach”. However, our experiences show that the relationship between analyst and players may become critical when there is tension between coach and players. The coach may “abuse” the analyst by using them to support his own opinions. Conversely, players will sometimes ask analysts for their personal opinion, which can create conflict with the coach if there is a difference in opinion. No matter how the permanent negotiations of the analysts on their roles in the complex social system of a professional sports club will turn out, if they want to work successfully, it is a good advice from qualitative methodology to study and acknowledge the specific social context in which they want to exert impact and draw the appropriate decisions.

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5.3.1.4 Qualitative Content Analysis What is the “magic” (Martin et al. 2021) that is in the analysis boxes that appear in several of the models that represent coaching process? How do analysts arrive at their conclusions when conducting match analysis? This next section on qualitative research presents the methods that are applicable to PPA. Qualitative content analysis (Mayring 1994, 2014) is described in the box below. Qualitative Content Analysis (Mayring 1994, 2014)

Qualitative content analysis is a method that was developed to analyse communication, mostly based on textual data (written or spoken). The content of these documents is analysed to infer details about the communication, such as the intention of the sender, his emotions, his historical and social backgrounds, and reactions of the receiver. The foundation of qualitative content analysis is its systematic, rule-based analytical procedure. The typical steps for reconstructing the content of a document are paraphrasing, generalization, reduction, and validation. It may be of interest to researchers in PA that there is also what is known as quantitative content analysis, which is more focused on counting and measuring aspects of the text, such as word counts and connections between words. However, this approach to content analysis does not typically explain the meanings or intentions of texts, but it has striking similarities to statistical approaches in quantitative PA. The basic idea of QGA, which was already published in 2001 (Hansen & Lames; in English: Lames and Hansen 2001), is to borrow aspects of the qualitative analysis of documents and apply them to the analysis of match videos. Instead of a written document, the video is the object of analysis, and the procedural steps of qualitative content analysis are transferred to match analysis. The analogies drawn between qualitative content analysis and qualitative game analysis are compared in Table 5.2. Figure 5.4 illustrates the analogy. The first project that explicitly applied the principles of qualitative content analysis to match analysis was conducted between 1998 and 2001: Game analysis in beach volleyball (Hansen and Lames 2001). The idea originated from a doctoral student at the time, Gunnar Hansen, who taught courses on research methods that contained methods of performance analysis and qualitative methods and he brought these methods together. He supported the German national beach volleyball team using QGA during the 2000 Sydney Olympics at Bondi Beach, which resulted in an unexpected bronze medal for Germany (Hansen and Lames 2001). It is worth mentioning that QGA was only made possible thanks to the innovation of digital video, which was based on the digital compression standard MPEG becoming available at the consumer level in the mid-1990s. When video was still stored on magnetic tapes, the database-driven retrieval of video scenes and the computer-­ based control of the video for in-depth analysis was far too time-­ consuming. This is a very apt example of innovations in PA that were made possible

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Table 5.2  The analogy between qualitative content analysis and qualitative game analysis. (With permission of Philippka-Verlag from Hansen and Lames (2001)) Qualitative content analysis Textual document Paraphrase: Structuring and shortening text Generalization: Expressing the general ideas with respect to a theoretically founded category system Reduction: Summarizing the most important messages Validation: Comparing results to previous research, communicative validation, and triangulation

Qualitative game analysis Match video Coding: Structuring and annotating video scenes, for example, rallies Exploration: Discovery of informative facts based on routine questions and spontaneous impressions based on relevant match categories Interpretation: Identification of strengths and weaknesses and suggestions for training or match plan Communicative validation: Common reconstruction of analyses with coaches and players and agreement on measures for training and/or tactics against the next opponent

Fig. 5.4  Illustration of the analogy between qualitative content analysis and qualitative game analysis

by technological innovations. The permanent stream of technological innovations with some having a potential for PA will be acknowledged in the final Chap. 6.

5.3.1.5 Communicative Validation Communicative validation is an important concept in qualitative research in general (Guba and Lincoln 1989) and specifically in QGA. The main reason is that findings of qualitative research are subjective, because they are obtained by reconstruction and interpretation, which are two inherently subjective processes. When dealing with data in a social context, communicative validation is a widely accepted method to ensure that interpretations are accurate and trustworthy. Communicative validation is achieved when the opinions of the different stakeholders are brought together (communication) and discussed to arrive at a common reconstruction (validation). In QGA, this process requires the analyst to present his findings and recommendations to the training staff (and to the players), who then have the opportunity to comment on these findings, ultimately to decide whether they agree or disagree. In

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the event of disagreement, the analyst can provide justification for his findings (e.g. based on a new analysis), which will also be subjected to another round of discussion. At the end of this hermeneutic process, a common reconstruction should be agreed upon. The following is a list of techniques that are used for communicative validation in qualitative research methodology: • Peer debriefing: an exchange of information to arrive at an agreement between all stakeholders as already mentioned. • Member checks: a presentation of the final conclusions to members of the social system, similar to peer debriefing, but the focus is on the soundness of the conclusions. Sometimes, new stakeholders, who have not been involved in the QGA process previously, are asked to join. The advantage of this is that they are less susceptible to biases such as social desirability (“We are doing a good job here, who disagrees?”) and cognitive dissonances (sticking to long-held opinions, for example, the qualities of a certain long-known player). • Ad hoc revisions: Communicative validation requires an openness to changing or adjusting one’s own opinion. The willingness to accept change is difficult for some, even when there are better arguments available. However, it can be easier to achieve when the social relationships established support emancipated communication. • Hermeneutic circle: The process of arriving at a common reconstruction and an agreement on the measures to be taken is the hermeneutic circle. This term refers to an iterative approach, in that the first round of discussion can lead to the identification of differences in opinion. In subsequent rounds, the individuals involved start the discussion with newfound knowledge gained from new analyses or peer debriefing. This procedure aligns with the definition of a hermeneutic circle (Gadamer 1975). Evidently, it is not always possible to reach an agreement, even if there was an unlimited number of discussion rounds. In most sports settings, though, the resources for a larger number of iterations are not given. Besides, there is a hierarchy within the club, where some roles have more authority than others, which enables them to dictate the decision-making process. Nevertheless, from a conceptual perspective, the  mechanisms involved with a hermeneutic cycle would ensure optimal results and may be used as orientation. • Prolonged engagement: In order for communicative validation to work, each stakeholder must be acknowledged by the others, because only emancipated ­participants are able to contribute effectively. This requires prolonged engagement, which is when a person has the opportunity to understand the relationships between all of the different stakeholders which usually takes a longer time. • Persistent observation: Whereas prolonged engagement is the technique for becoming acquainted with the social setting, persistent observation is a technique to acquire expert knowledge of the object under scrutiny, that is, players and match performances. Acknowledging the nature of game sports as singular dynamic interaction processes with emergent behaviour demands for a large knowledge base before applicable conclusions can be drawn.

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As experience shows, a sustainable realization of these principles of communicative validation in professional sports is rather the exception. On the other hand, not making use of the collective expertise of all members of staff and players is rather an unprofessional attitude.

5.3.1.6 Steps of QGA The steps involved in QGA as basic method of PPA are depicted in Fig. 5.5. Quantitative Pre-Structuring:  Match analyses typically start with a review of the existing statistical data or information sources that describe the behaviour of interest (Carling et al. 2014). The selection of PIs and number of PIs used for quantitative pre-structuring are highly individual. The extent of quantitative pre-­structuring can also vary, from a short overview just triggering the subsequent qualitative main analysis to a comprehensive examination where deep-reaching hypotheses for qualitative main analysis are generated. As previously mentioned in Table 5.2, the analyst looks for informative facts in these figures or other observations that will prompt him to pursue it more in depth. Thus, in QGA quantitative methods are by no means ignored, we rather have a sequential order of quantitative and qualitative methods. The role of quantitative methods is to give an overview on large data sets that directs the in-depth qualitative analyses to the most relevant questions. Qualitative Main Analysis and Peer Debriefing:  The relevant behaviours identified by quantitative analysis are then examined via qualitative content analysis. As mentioned in an earlier section, the aim of qualitative content analysis is to understand and interpret the behaviours of interest. These interpretations will then be discussed through peer debriefing, a means of communicative validation. The aim is to arrive at a common reconstruction between stakeholders. Typically, an agreement may not be achieved in a first round, making more rounds of analysing and inter-

Fig. 5.5  Steps of QGA. (With permission of Taylor and Francis from Lames and Hansen (2001))

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preting necessary. In PPA, peer debriefing can also include a discussion about how to transfer the analysis findings into actions for training. Transfer to Training:  This step is also part of the informational coupling between competition and training (see Fig. 5.1) and was explained there already in detail. At this point, two further methods of PPA described in sections below, video-based tactics training and match strategy development, are involved. Peer Briefing:  This step refers to discussions between analysts and staff in preparation for an upcoming match. Lessons learned from previous matches may serve as a pre-cueing for the analysts on what to focus next. This step helps to make match analysis more effective. The core step of QGA is the qualitative main analysis making use of techniques from qualitative content analysis. Mayring (1994, 2014) stresses that qualitative content analysis must obey strict methodological rules in order to be acknowledged as a scientific method. The same rules also apply to QGA. For example, the selection of video scenes to be used for the analysis is a crucial methodological step. There is, for example, an abundant number of serves in tennis or passes in football imposing the need to draw a sample for “thick description” (Geertz 1973). There are several strategies for doing so within qualitative methodology. The “Qualitative Research Guidelines Project” (Cohen and Crabtree 2006) names several strategies, each with a specific intention: • Sampling of typical cases: These include cases that are not in anyway atypical, extreme, deviant, or unusual. This type of sampling enables the analyst to identify and understand key aspects of the phenomenon under scrutiny, as they are occurring under ordinary circumstances. • Intensity sampling: These are cases that represent excellent examples of the phenomenon of interest. This enables the analyst to specific and detailed information of the phenomenon under scrutiny. • Critical case sampling: This involves selecting a small number of decisive cases. These are the cases that made a significant difference, for example, service winners in critical situations or passes that create a scoring opportunity. An understanding of these cases could explain match outcomes. • Confirming and disconfirming cases: Having come up with the initial interpretations after the first round of analysis, it is recommended to double check for confirming or disconfirming cases. There may be more cases that further support the initial findings, or there are cases that do not align, which would require alternative explanations. This step may also inform any adjustments to the scope of the analysis. • Extreme or deviant cases: This type of sampling involves selecting or searching for “outliers” that do not fit to initial analysis and interpretation. This is a valuable strategy to discover any “exceptions to the rule”.

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Three aspects of QGA should be stressed from a conceptual and methodological standpoint: QGA is a dynamic process that progresses iteratively until there is a final interpretation. QGA requires a high level of expertise in the domain, here elite sports. But, most important from a research strategy point of view, QGA was developed using the same methodological principles as the ones for well-­established qualitative research. This ensures a sound foundation and also quality standards for a critical review of its procedures as well as of its results.

5.3.2 Development of Match Strategies So far, the application of QGA has been described only in the context of analysing one’s own team, but the same concept can be applied to the analysis of future opponents. The aim, then, would be to develop a specific match strategy to use in a future match. In principle, the process is similar to the analysis of the own team. For example, the general task is still to identify strengths and weaknesses, but this time of the future opponent. In this case, qualitative methods are also used, and the ultimate aim is to generate practically relevant information. The difference is the perspective of the analysis, which is to determine which measures would be most effective against a specific opponent. In Fig.  5.6, a conceptual model of this process is presented (Cordes et  al. 2012). Special attention is given to the flow of information that is necessary to build strategies, the different information sources, and the feedback-­ loop aiming to improve the staff’s capability to design match strategies. Sources of information: A major source of information for strategy development is the analysis of opponent’s past performances. Here, the focus is on analysing the

Fig. 5.6  Conceptual model of strategy development including feedback through strategy check. (With permission of Sage publishers from Cordes et al. (2012))

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opponent’s strengths and weaknesses to gain insight for the development of a specific match strategy. To say it clearly, in analysing the future opponent, one is delighted to detect weaknesses and concerned when detecting strengths, which is the opposite when analysing one’s own team. Moreover, some aspects now have an increased importance, like the stability of the findings, because the analyst needs to determine whether the findings are applicable in the match against the analysed team. In addition, the analyses of one’s own team play a big role in strategy development, too, as will be explained when we discuss the steps involved in strategy development. The coach’s philosophy is another consideration, as there is always a choice between different strategic approaches. A coach could have a preference for a more defensive or offensive playing style, or he could choose to either try to impose one’s own playing style to the opponent or adapt to them, depending on their strengths and weaknesses. Strategy building: From a conceptual perspective, developing a match strategy first requires the anticipation of the encounter of the two teams. What will happen, when one’s own team meets the opponent, how will the two expected tactical systems interact, and how will key duels between dyads or groups of players end? Will there be aspects of the game where one’s own team may be expected to perform superiorly, or are there potential threats from inferior performance to be expected in some respect? These potential outcomes must be anticipated not only based on the current level of knowledge from the analyses but also with respect to tactical changes: How will my alternative central defender perform against their centre forward compared to my usual central defender? What will happen if we change our usual tactical lineup, since it is likely to be known by the opponent? In this way, the effects of several tactical decisions are anticipated, and finally, the match strategy is chosen among all the examined alternatives. The choice of a strategy also depends on additional information, such as the fitness of one’s own players before the match, the opponent’s expected lineup, and the contextual information (e.g. is the team in a safe position or desperately needing points?). There are external influences, as well, from the audience or the club managers, preferring, for example, an offensive playing style, or even simple things such as pitch and weather conditions on the day of the match. It is even more complicated when the analyst has to consider the strategies that the opponent might use. The information that is relevant to the choice of strategy is susceptible to changes, even at the last minute (e.g. player availability, weather conditions), and thus can require quick reactions. There are also parts of the strategy that are conditional, for example, what changes would be needed if there is an early lead or lag in scoring? Which players would be suitable substitutions, given time played and score line? Match analysis: An important conceptual detail of the development of a match strategy as depicted in Figure 5.6, is the introduction of a feedback loop. From a conceptual perspective, the ability to develop match strategies must be treated like a skill that can be improved through training, similar to how players train sport-­ specific skills. The feedback provided by match analyses is essential to achieving the desired cognitive learning process. As the purpose to generate feedback on the quality of the match strategy chosen is different from other purposes (e.g. coupling between competition and training), additional types of match analyses are required after the match:

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• Analysis of opponent: Were the assumptions about the opponent’s strengths and weaknesses confirmed during the match? If not, what are some potential reasons why? • Analysis of one’s own team: Did the team show unexpected behaviour in the match? Why was this not anticipated? • Coach philosophy: To what extent did the coach’s philosophy influence the match strategy? Was it too much, too little, or adequate? • Anticipation of the encounter: Were there any misjudgements about some of the outcomes during the match? For example, were the midfielders able to exhibit control in midfield, as was expected? • Choice of strategy: Was the choice of strategy based on the anticipation of the encounter appropriate for the match? Could the strategy have been improved in any way? These analyses, as with all methods in PPA, must be conducted according to high methodological standards. To do so, analysts and staff should rely on peer debriefing and proper documentation of all analyses, including all relevant conclusions from both the analyses of one’s own team and the opponent, the anticipated outcomes, the final match strategy, and any last-minute changes. By implementing the conceptual idea of a learning cycle for improving match strategy development, an increased quality of future match plans may be expected, which may have a sustained positive impact on the performance level. In his dissertation, Ole Cordes conducted a study on a team’s perceived and observed adherence of a team to a match plan (Cordes 2013). Over an entire season (34 matches), he did pre-match interviews with the assistant coach of a German second league team and recorded the strategy to be used against the next opponent. Then, after the match was analysed, a post-match interview with the assistant coach was conducted to determine the extent to which the players had adhered to the match strategy. There were three main findings, which are published in Cordes et al. (2012): 1. The assessment of the implementation of a match strategy requires an own methodological approach. The observational items must align with the items from the match strategy, for example, the line of pressing (offensive, mid-field, defensive) is frequently a part of the match strategy  and its realization must be assessed with a specially designed observational system. 2. The interpretation of adherence must be sensitive to contextual parameters, for example, was the lack of adherence due to the strength of the opponent and therefore impossible to achieve? Similarly, the match progress can also impact adherence. For example, a bad start to the match may require deviations from the initial match plan like an early goal of one’s own team resulting in a shift towards a more defensive strategy. 3. The assistant coach who was interviewed was susceptible to bias, as the authors noticed that when the team was successful, the coach perceived positive adherence to the match plan but when the team was unsuccessful, the coach perceived negative adherence. While this may be the case sometimes, it is certainly not always correct

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as Cordes et al. (2012) showed. This bias that might typically prevail in coaches and staff must be confronted with the results of a specifically designed application of QGA. Moreover, adopting this concept of strategy development makes sure, that the development of match strategies is subject to an efficient learning process. The conceptual model depicted in Fig.  5.6 highlights the different sources of information that can be relied upon for correctly anticipating the encounter between the two teams, which is the core skill for the development of a match strategy. It also suggests that strategy development is seen as a learning process based on feedback obtained from deliberate post-match analyses. While it might be idealistic to expect coaches to explicitly undergo this learning process, later sections will discuss the role of a head coach and its expected changes in future. The coordination of and the communication with his team of experts will play an increasing role. Nevertheless, one might expect with good reason that the quality of match strategies based on specific match analyses will account for much of the differences between the efficiency of teams in the future.

5.3.3 Video-Based Tactics Training (VTT) When digital video became available in the late 1990s, it not only facilitated qualitative analyses but also gave rise also to a new method of PPA, video-based tactics training (VTT). As scenes from match videos can now be edited and presented very easily, VTT has become a very effective way to support the transfer of cognitive messages, especially tactical ones. Its outstanding effectiveness as a training tool is due to several unique properties of video that reinforce the tactical message, which will be presented in later sections. The following paragraphs will cover the conceptual foundations of VTT, which are based in communication theory, media-based learning, and self-confrontation theory. Then, the practical methodology of VTT is described in detail followed by a discussion of previous applications of VTT in PPA from the literature. Finally, the insights gathered from practical experiences are revealed at the end of this section. Video-Based Tactics Training

Video-based tactics training (VTT) is a training method aiming to the tactical improvement of players. In VTT, results of match analyses are presented to athletes with support of video technology. VTT is a very effective method of tactics training if used in a methodologically thorough way requiring a variety of didactical decisions on presentation and social setting.

5.3.3.1 Conceptual Foundation of VTT An important concept of VTT is communication theory, because VTT can be understood as the transfer of a message derived from game analysis to the athletes with

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Fig. 5.7  The trimodal communication model of Merten. (From Dreckmann and Görsdorf (2009), Courtesy of Christoph Moeller and Karsten Görsdorf)

the intention of influencing changes in future tactical behaviour. The model of Merten (1994; from Dreckmann and Görsdorf 2009) provided in Fig. 5.7 is called the “trimodal” model of communication. It illustrates that the messages transferred from a sender to a recipient are always contextualized by the recipient, that is, an “information triplet” is created and contains not only the intended message but also internal and external contexts that are associated with the message. Why is this important for VTT in PPA? It will be shown below that many of the methodological decisions for VTT must consider this context to effectively apply it in PPA. If this is not done so sufficiently, the communication may fail to achieve the intended effect. For example, failing to consider the external context of a team or player could alter their reception of feedback (positive or negative), for example, when a player is concerned with whether he will be on the starting lineup for the next match. It is also possible that information from “relevant others” (other players, staff, personal manager, parents, media, fans) may conflict with the VTT message, creating cognitive dissonance. The same holds true for internal context such as prior knowledge and psychological traits. Anecdotal evidence for this is a professional football player refusing to accept the messages from individual VTT with the words: “I earn three million a year and you want to tell me that I can’t play football!” In this case, there was a misunderstanding about the purpose of VTT, which resulted in a conflict between the message and the self-esteem of the player, making it difficult to achieve a successful communication. Besides communication theory, there is also what is called media-based learning (Giessen 2016), which is another core concept of VTT. Media richness theory (Daft and Lengel 1984) states that learners become absorbed in the learning medium to different extents, which the authors refer to as the different degrees of media

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richness. For example, match videos with scenes that show aspects of a team’s performance exhibit high media richness. It is widely accepted that a person learns best when observing processes in which they or relevant others are the participants (Bandura 1978). Mirror neurons are activated when learners can observe the efforts of other learners, but this may be even more prominent in VTT when players are confronted with their own behaviour. Although research on media-based learning has underlined the importance of different learner types (Giessen 2016), previous research on VTT has neglected to examine this phenomenon thoroughly. In psychology, there is a whole theory on behavioural change that relies entirely on self-confrontation (Lamiell 1991). Transferring these ideas to VTT, it seems plausible that the self-confrontation that a player experiences while watching and critically discussing his own behaviour from match videos could promote behavioural change effectively. Finally, there is also the cognitive load theory (Hazeltine et al. 2006), which supports the idea that players should act more autonomously in VTT based on the theoretical evidence from media-based learning. Learners under ideal and free conditions have been observed to organize their learning process in accordance with their cognitive abilities, making it comparatively more effective than externally driven instructions.

5.3.3.2 Methodology of VTT This section is devoted to the methodological aspects of VTT. It is quite common to see VTT performed without (m)any methodological considerations, because coaches and other training staff are often unaware of these approaches. This is not to say that approaches based on common sense cannot provide good results as well, but it is the task of PPA, as a sub-discipline of PA, to provide the scientific foundation for practical action. The scientific foundation of VTT is based on the theoretical concepts discussed earlier as well as the practical experiences obtained in the framework of evaluation research (see Box “Practical Experiences” at the beginning of this chapter). Aims of VTT The first consideration regarding the methodology of VTT are the two aims of VTT: 1. Improving tactical behaviour: This is the main reason for using VTT. With the help of video scenes, tactical behaviours are reconstructed to derive interpretations for practical action. The aim of VTT is to elicit cognitive processes that improve individual and collective action plans and facilitate agreement on a common action plan. 2. Improving individual ability for tactical analyses: As demonstrated by the cognitive load theory (Hazeltine et al. 2006), the use of media to understand one’s own behaviour is one of the most effective methods. Each player brings his own unique perspective. By enabling players to conduct tactical analyses on their

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own, they are more likely to understand the process of match analysis and can contribute to improving the conclusions made by members of the training staff. Furthermore, the ability of players to find creative solutions to solve tactical problems during a match will be increased. Especially in youth academies, where the education of the players’ personalities as a whole is a target, autonomously conducted VTT is very appropriate. Among other positive effects, this capability may also enable players to evaluate their own performance with better accuracy, which is a valuable skill for young players. Methodological Decisions There are a series of methodological decisions that must be made appropriately to fully benefit from the application of VTT. These methodological decisions should be made consciously, that is, being aware of the spectrum of decisions and the options in each case. 1. Didactic approach: The didactic concept of instruction can range from a fully planned presentation with content and key messages delivered by the presenters to an open classroom setting where players are asked to share their interpretations and conclusions. 2. Learning strategy: One may pursue a cognitive learning approach that is directed exclusively by the input of the presenters or an explorative learning strategy based on players searching for information in a self-organized manner. 3. Selection of media: Forms of media, either as an alternative to video or in addition to video, can be used to enhance instruction, for example, self-made drawings on flipcharts, magnetic tactic boards, or interactive electronic boards. A combination of these different types of media may be used, and the varied use of media has been shown to be very effective. 4. Selection and presentation of video clips: This is a central decision in VTT. Typically, there is an abundance of scenes that represent the tactical behaviour under consideration. The decision to include or exclude a certain scene requires a targeted selection approach that answers questions like: How many clips should be presented? What is the ideal ratio between positive and negative clips? Should an overview of the tactical issue be shown or should the desired tactical behaviour be presented? Once the selection and preparation of the video clips is complete, the next step is to decide the most appropriate way to present them. There are several options to consider, such as slow motion, freezing certain frames, and repeating scenes a certain number of times or in a continuous loop. 5. Social configuration: In each case, the social environment in which the video clips are presented may be different, and there are several options to choose from. First, the audience may be single players, small groups of players, or the whole team. Then, the presenter may be the performance analyst, head coach, other staff members, or a player/group of players. It is also possible that the social configuration is just one player analysing his own video clips in private.

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It is worth reiterating that these decisions are based on personal experiences, holding true only for specific settings, and must be adapted even within a session. In addition, there may be interplay between some of these methodological decisions, for example, a certain didactical approach can determine, to a great extent, the appropriate learning strategy and social configuration. The successful implementation of VTT in practice relies on actors consistently making informed methodological decisions. L evels of Impact of VTT A characteristic feature of video is that it creates impact on different levels. This is advantageous if properly used but can also cause problems if ignored. 1. Video creates contemporaneity: As Daft and Lengel (1984) have described, video offers high media richness. In addition, the confrontation with one’s own behaviour through video creates high vigilance, presence, and recognition of the scenes. Experiences show that players are easily able to immerse themselves in the scenes, facilitating the reconstruction of memory and the ability to recall the emotions from that scene. This suggests that each scene that is shown will create contemporaneity no matter how important the scene is for the tactical message. As a result, there is the need for and the importance of consciously selected scenes. 2. Video elicits emotions: Self-confrontation can evoke emotions in the viewer, especially if it is one’s own behaviour during critical match situations. This can either support or hinder the intended transfer of information through VTT. First, the emotions elicited may distract from or overlay the intended message. For example, if a player is too concerned about the bad impression he believes he has made in a certain scene, he may be less open to recommendations. An experienced presenter can intentionally manipulate these emotions to reinforce the desired message. Be aware that a conflict between the emotions elicited and the desired message can occur if the wrong scene is selected and presented to the player, for example, when tactical errors in a tennis rally are the issues to be addressed, but the rally ends with a point for the player (positive emotion). 3. Video transfers information: The main aim of VTT is the rational assessment of tactical behaviour to determine practical actions for improvement. In this sense, contemporaneity and emotions are side effects of the medium video that may be used to support the messages important for VTT. A prerequisite for success is that the players are acquainted with video as a training tool; otherwise these side effects could dominate the transfer of the intended message. In summary, the effectiveness of VTT will only turn out when it is regularly implemented in training to ensure that presenters understand the potential side effects and are prepared to manage them. It is equally important to select the appropriate match scenes that align with and support the transfer of the intended message. Moreover, the expertise of presenters in the use of video, the methodology of VTT, and their familiarity with the athletes enables them to fully achieve the aims of VTT.

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Virtual Reality for PPA?

The current benefit of virtual reality (VR) applications for VTT, and PPA in general, is unclear. For example, there are some applications that have tried to reconstruct match scenes from the personal visual perspective of a player. Paired with the positional data of players and the ball, this is nowadays quite simple to achieve and only requires the depiction of avatars to represent the other players (own team and opponents) as well as the first-person perspective for the target player. This kind of VR is said to allow players to immerse even deeper into the match. There are several considerations to determine whether the first-person perspective is appropriate for VTT. As perception is a psychologically mediated process, this is not reflected at all in the first-person perspective of VR. Moreover, memory and anticipation, as well as the dualism of moving to perceive and perceiving to move, are not taken into account. Similarly, the multimodal sensory input (e.g. hearing, feeling, muscular tension) cannot be incorporated in momentary VR representations. As VR applications are still relatively new, players are likely to be more accustomed to viewing traditional video than videos from the first-person perspective. Also, traditional video accounts for more context, for example, showing available players on their back that they did not perceive in this moment, which is an important information not to be found in VR. At present, traditional match videos are more than adequate for VTT. However, with significant advancements to come in VR, it is possible that future implementations of VR may be considered.

 ocial Engineering and Reinforcement Techniques S Nowadays, the term social engineering may have a negative connotation, but its historical definition refers to the design of social interventions to achieve an optimal result. In a learning process such as VTT, there are reinforcement techniques that are often used to support the intended message transfer. This concept originated from advertisement psychology but has parallels in VTT: a sender of a message (company/presenter of VTT) who wants to elicit behavioural changes (consuming goods/tactical behaviour) in their recipients (clients/athletes). The challenge of advertisement psychology is that its recipients were typically unaware they were the target of a certain message, so specific methods had to be developed to ensure the message was successfully communicated. What is the challenge with VTT communication and why is it a good idea to borrow ideas and methods from advertisement psychology? The typical setting for PPA is within a professional sports club on an ongoing basis, either with an individual athlete or a team. More specifically, one must be aware that in elite sports, there is a sophisticated sequence of load and recovery phases. This inevitably means that VTT must take place during recovery periods, because anything different from a

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load period (training or competition) is a recovery period for the players. Therefore, one has to admit that fatigue during VTT is likely and natural, which could limit the attention of players. Another consideration on the effectiveness of VTT is the ability to identify the relevant errors and demonstrate how they are negatively impacting performance. This type of feedback may not be well received by the players, even when the objective of correcting these errors is beneficial for all. For these reasons, there is a need to increase the persuasiveness of the messages conveyed through VTT. These techniques, which are borrowed from advertisement psychology, are described as follows: 1. Activation techniques: The presented video scenes may contain different types of stimuli that activate players, for example, emotional stimuli (e.g. individual close-ups, scenes from the last victory), physical stimuli (e.g. activating music at the beginning of a VTT session), or surprising scenes, for example, with the next opponent presented as a physical threat. Addressing players directly and forcing them into a dialogue can also have an activating effect. 2. Frequency techniques: Frequent and repetitive patterns of stimuli can engage players as well. For example, it may be effective to create a schedule for VTT so players can expect to attend sessions on a regular basis. And prior to each session, an agenda filling in the actual details of a fixed schedule within the VTT might also be useful. Similarly, the frequent repetition of core messages, the so-­called reminder technique, has proven to be effective. 3. Ensuring information uptake: Besides the big advantage of VTT that images are taken up better than written or oral information, there are some specific measures to ensure information uptake. A debriefing with individual players and groups, a written and signed summary on the agreements, and even written or oral retention tests after VTT sessions are appropriate measures. In general the selected approach used in VTT should be entirely dedicated to support the effective transfer of information. This does not only mean that VTT never should become boring and provide appreciated extras, for example, a ritually last scene with either funny or emotional content, but that the whole level of reasoning should be adapted to this aim. There is no need that the presenter demonstrates his capacities for sophisticated game analysis. What the players need are clear messages that are easy to remember using buzz words and frequent repetitions if necessary.  TT in Different Settings V Team VTT: Previous experiences with VTT in team settings suggest that less is more. VTT sessions should not be longer than 20 min total, and no more than 8 min of video should be prepared for presentation. The length of single video clips should be between 8 and 20 s, and clips may be separated by a black slide with a title for the next scene. The most important part of a single clip should not be shown immediately at the start of the clip but rather in the middle or near the end. Important clips should be presented at least twice: the first time completely in real time to get an overview and the second in slow motion or with freeze frames.

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It seems that team VTT is the most frequently used but also the least effective social configuration of VTT. The setting of team VTT is especially susceptible to player fatigue as explained above, because necessarily in team VTT, events are addressed that are not relevant to all players. In combination with the unusual setting (training or competition vs. listening to a presentation), team VTT requires special efforts at a high methodological standard to overcome its structural disadvantages. Group VTT: Organizing VTT in group settings allows for the analysis of one’s own behaviour and the opportunity to exchange opinions/interpretations on the tactical cooperation with the group (i.e. more than one player) that was involved. For example, the defensive line and the goalkeeper may organize a group VTT to discuss the way they played against a high pressing opponent, develop better solutions, and introduce these solutions in training and competition. Central defenders and midfielders may use group VTT to address ways to open the game and how to advance the ball. It is important to remember the principles from communication theory in group VTT, as the objective is to arrive at a common reconstruction and understanding and, most important, that the players of the group arrive at common consequences for behaviour in future matches. Methodologically, the presenter should prepare pre-selected scenes (8–10 per tactical topic) for a group VTT session. These scenes should be approved by the head coach. As for the presentation style, it is recommended to present a scene in real time and on a continuous loop while the specific scene is discussed. It is the responsibility of the presenter to engage the group members to share their interpretations of the scenes and to the expression of individual opinions without imposing their own opinions on others. They will also act as the moderator, taking care that each scene is discussed in detail and that a summary is drawn that meets the expectations of the coach as well. When successfully implemented, group VTT offers several advantages. Communication between players is very effective as they have their own “language” and have a high mutual understanding, because they share many common specific experiences. Above all, it is to be expected that agreements within a group of players on how to act together in certain match situations are most binding, because they rely on mutual support and trust in a match and there are effective sanctions when the personal obligations are not met. Overall, group VTT seems to outperform team VTT with regard to player engagement and the commitment to conclusions. Player VTT: The purpose of player VTT is to use self-confrontation methods to improve a player’s individual tactical behaviours. For this type of setting, only one player and one presenter/moderator (either a staff member from the club or an external specialist who is trusted by coach and player) are involved. Player VTT only works when the athlete exhibits a readiness for learning and changing behaviour. In other words, the willingness to reflect on one’s own behaviour and to accept feedback is a prerequisite of player VTT. This can be intellectually demanding for the players, as one’s own behaviour needs to be analysed with abstract tactical categories. Most importantly, player VTT fails if it is not perceived as personal support or an opportunity for improvement, but as personal criticism or even blaming, instead.

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Methodologically, it is recommended to address only one tactical topic per session with no more than 12 scenes. The session should start by showing all of scenes and gauging the player’s first impressions about the general tactical topic and his performance. Then, a detailed analysis of each scene may follow. The player should be encouraged to give a reconstruction and interpretation from his subjective point of view. It is also worthwhile to develop alternative behaviours, as they can be incorporated in future tactical strategies. The role of the presenter in a one-on-one setting is challenging, because he has on the one hand to be open to new individual interpretations and solutions, but on the other hand, there are expected outcomes to be achieved. Thus, the presenter should stimulate the player’s own reflections and he should not “signal” the expected answers too early. Ideally the player proposes the desired solution on his own and is only guided by the presenter (“Socratic dialogue”). Pitfalls of VTT To fully benefit from VTT, all of the actors must accept it as part of the training routine. Even then, there are some common pitfalls that can make it difficult to implement VTT successfully. The first is issues with technology. Presenters should be well versed in the use of technical equipment before attempting to adopt VTT to prevent disruptions in the process. Second, it must be acknowledged that it requires additional effort to attract the attention of players especially in team VTT, because they are physically highly loaded and VTT acts as recovery period. To do so, VTT sessions should be prepared thoughtfully as just watching a match video sequentially with spontaneous stoppages and comments by the coach is by no means effective. The presentation itself should focus only on the tactical aims. VTT is not a platform for presenters to show off their opinions or knowledge of game tactics. The biggest pitfall of VTT is when the social context creates a negative environment, for example, when the coach uses the video analysis as evidence to support his own opinions or when the players experience feelings of shame and anxiety as a result of VTT.

5.3.3.3 Scientific Evidence for VTT Methods and Effectiveness Given the aim of PPA is to provide scientific foundation for practical action, the following section will discuss the scientific evidence that has informed the methodology of VTT, making it one of the most common methods used in PPA. The first piece of evidence are the theories that were mentioned above that all address central aspects of VTT: communication theory, media-based learning, and self-confrontation theory. These theories provide valuable background and establish the theoretical framework within which the practical methods should align with. This is not sufficient, though, for becoming a scientifically founded practical recommendation. The second pieces of evidence are the practical experiences that were recorded by experts and according to the principles of evaluation research. The abovementioned recommendations for VTT were gathered from experiences using different

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interventions of the national and international levels across several sports (see Box “Practical experiences” at the beginning of this chapter). Nevertheless, as has been mentioned, the social context in which VTT is employed is case-specific, and thus, these experiences may not fully apply in a new setting. The third source of scientific evidence is the inherently logical process of developing practical recommendations for training, as depicted in Fig. 5.1. To draw conclusions for training, coaches and training staff must go through each of the sub-tasks and find solutions for each, before moving to the next sub-task. This structural sequence is so integral to PPA that even the actors themselves may not recognize each individual step in the process. One may say that at each occasion where match analysis has led to practical impact, the actors in the field have found solutions for the named sub-tasks, maybe without even being aware of the single tasks. Field experiments are the fourth and most significant proof of the effectiveness of VTT as a practical tool, but there are very few field experiments on VTT and QGA in the literature. The primary reason is because controlled field experiments are among the most difficult studies to conduct in behavioural sciences. Furthermore, there is little interest in such experiments in sports practice, because head coaches and training staff are not looking for scientific evidence for the methods employed. Nevertheless, conducting controlled field experiments on the effectiveness and details of measures in PPA remains a prominent task for performance analysts interested in the scientific foundation of practical action in PPA. Raschke and Lames (2019) published an experimental study on the effectiveness of VTT in young (10–14 years), talented tennis players. The authors conducted a field experiment with a control group (n = 12) and a treatment group (n = 12), and although the groups were not randomly assigned, the groups were stratified by initial performance level, age, and gender. Stratification might be an even more effective control group strategy compared to randomization for small samples as we typically have in this type of studies, besides the practical problems of random assignments in real-life sports settings. The treatment group devoted one training unit per week to VTT for 12 weeks (see the top of Fig. 5.8 for the organizational sequence). VTT was designed according to the tactical education needs in tennis at this age. Instructional video scenes were taken from regular matches of the players that took in general place on the weekend before VTT. Then, players were asked to give a description, an evaluation (good or bad), and alternative solutions for a selected sample of match scenes, where they showed the tactical behaviour that was to be addressed. The on-court training after a VTT session referred back to the conclusions drawn in this session. A video-based tactic test was developed to analyse the capability of players to analyse tactical behaviour from match videos. The actual tactical behaviour of the player in competitive matches was analysed via observational methods. The results show that even these very young players can benefit from VTT as depicted in at the bottom of Fig. 5.8.

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Fig. 5.8  Organizational sequence and results of video-based tactic test and match behaviour of service. (With permission of Alex Raschke and Philipp Olsson)

5.4 Game Analysts in Professional Training Systems This final paragraph of chapter PPA is dedicated to the professional role of match analysts in sports settings. This topic has recently found more attention in research, mostly from a socio-economical point of view (Martin et  al. 2021). In this book though, relevant issues of the professional role of sports analysts from the view of concepts and methods of PA are presented. First, the spectrum of applications for match analysis is given, and it will turn out that many potential applications are not yet fully exploited yet and thus give rise to many job opportunities for game analysts in the future. Typically, analysts are supported by game analysis software, which shows some common design principles that have proved to be effective in the past. These concepts for game analysis software will be presented together with examples in a separate paragraph. Then, different possible roles of game analysts in a sports club are discussed. There are different degrees of participation of game analysts in the basic tasks of PPA that are to be solved in a sports club. The overview on different roles of game analysts in natural settings leads to the concept of sports information systems, which are presented from a technical point of view but also represent future organization of top-level sports units.

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5.4.1 Applications of Game Analysis The methods of game analysis and video-based tactics training were presented in the last paragraphs of this chapter with respect to their support in solving three big tasks in PPA: • Analysis of one’s own team with the aim of generating practical training measures for improving the own team • Analysis of the next opponent aiming to the development of a match plan and recommendations for optimal tactical preparation • Analysis of match strategy providing feedback in a learning cycle that aims at improving the capability for developing match plans This is by far not the complete spectrum of applications of the methods of game analysis. The principles of qualitative research and the in-depth analysis of game behaviour based on the steps of reconstruction and interpretation are and may be used for further purposes also: • Player scouting: A dominant task of any professional sports club management is to contract players that form the best available team for the given budget. In football, for example, youth and adult players almost all around the world are monitored and entered into databases that are commercially available to professional clubs. These databases provide more or less detailed information about the players, for example, standard filtering variables such as age, position, footedness, and career but also performance indicators or economical details (duration and salary of actual contract). Typically, the databases provide long lists with hits of players that meet the search criteria of a club. Nevertheless, before selecting a player for contracting negotiations, a much more detailed analysis must be conducted as only relying on performance indicators falls short of delivering the information needed. So for a given player, a whole spectrum of skills is of interest and must be evaluated using the methods of qualitative game analysis. Moreover, behavioural aspects that are not contained in match reports are of interest as well, for example, the communication with teammates (team leader or follower?) or the communication with the referee (susceptible to yellow and red cards?). • Analysis of training exercises: In training, either small-sided games or full matches are standard exercises. Typically—besides requirements to play with a certain intensity—specific tactical instructions are given, for example, play with as few contacts as possible and prefer deep passes or even more complicated instructions on collective tactical behaviour such as pressing and counter pressing. As is expressed in general models for training control (Hohmann et al. 2020), training control requires to check whether the aims of training were achieved and the given method to do this is qualitative game analysis. Compared to quantitative approaches using performance indicators, for most tactical behaviours, there is no “black or white” judgement for the behaviour. Rather, a detailed inspection

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of the match behaviour with in-depth reconstruction and interpretation allows for evidence-based feedback. Of course, QGA in training is very demanding in terms of resources invested, but in the same way as recording intensity levels of training has become a standard in professional football, the analysis of tactical behaviour with appropriate methods is very likely to become a standard in training of professional football clubs as well. • Personal performance analysis: As mentioned above, the analysis of one’s own team’s performance by the game analysis staff of the team is one of the most common applications of QGA. Nevertheless, it might be of interest that analyses of match performances are conducted in a different setting addressing the individual interests of a player. For example, external game analysts may be hired by the club to perform individual match analyses, because either a new angle of view is looked for or the resources of the club’s own department are not sufficient to conduct individual game analyses in each case. Also, a player may be interested in specific analyses that are not provided by the analysts of his team, for example, a candidate player of a national team wants to have an analysis of how he is performing in comparison to the demands of the national coach and also in comparison to his rivals for this position in the national team. Players’ agents could be interested in personal performance analysis in addition to the club’s analyses to give optimal support to their players for increasing player values. Finally, players might be dissatisfied with the quality of their team’s match analysis and engage independent analysts. • Analysis of referees’ performances: It is reasonable to assume that with only minor adaptions, QGA can be applied to referees’ performances as well. With almost the same methods, for example, in-depth analysis of each action or content analysis of match videos, one may arrive at an evaluation of the performance of a referee, which may be very useful for an appropriate evaluation. Delegating these analyses to a specialized department would be an important step towards justice in the area of referee evaluation that is frequently blamed for lack of transparency and subjectivity. Besides these additional applications for QGA, there are also more occasions where VTT is used in practical settings: • Motivation videos: These are videos that are used before a competition to induce a positive mood or attitude towards the upcoming event. They are most effective when tailored to the players’ interests or preferences. They use appropriate scenes from prior matches, may be accompanied with the team’s preferred music and may show creatively funny or surprising events and scenes with individualized context. Experiences show that motivation videos are extremely effective and appreciated by players. • Half-time interventions: Only recently, half-time interventions using methods of VTT were still marvelled at; at present, it must be assumed that this has become very common, for example, in professional football. Coach and video analyst agree on relevant scenes either before the match or even via in-match communi-

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cation in first half. The selected scenes are presented according to a bespoken scheme based on the numerous didactical alternatives mentioned in the paragraph on VTT above. Several aims may be pursued such as turning off undesired behaviour, reinforcing the match plan or supporting intended changes, and also creating a good motivation for the second half. Problems to be solved for half-­ time interventions with VTT are given by time restrictions and finding a good technical solution for presenting the videos as well as seizing players’ attention despite emotional and physical distraction! Tests for tactic abilities: Similar to the procedure mentioned in the VTT experiment of Raschke and Lames (2019) above, tactic tests based on VTT may be constructed for other sports and performance levels as well. The principle is that a sample of appropriate scenes is selected standing for the tactical behaviour to be tested. The player enters his reconstruction, interpretations, and tactical alternatives ideally directly into the computer, and the assessment is done automatically. Of course, these tests need prior validation according to the usual standards of empirical sciences when introducing a new test (e.g. item characteristics, Cronbach’s alpha congruence, construct and criterion validity). It is highly desirable to introduce tactics tests on overall match behaviour based on real match scenes based on the principles of qualitative game analysis, because up to now, mostly only less comprehensive tests, for example, on anticipation and decision-­ making, are known. These tests could be used to assess the achievement of goals in tactics training at each performance level, especially in the tactical education of young athletes. Intranet platforms: VTT can be implemented on an intranet platform allowing players to analyse scenes asynchronously, that is, to a point in time when it fits best for them. This compensates for some of the problems of VTT such as fatigue and negative interpersonal interactions. It (theoretically) allows the players to permanently think about their performance and how to improve it. Moreover, there is a wealth of interactions made possible using VTT on intranet platforms together with social media. For example, one could imagine intra-team discussion groups on tactical details. Although this seems to be a promising perspective, practical experiences so far show that players are rather lazy (still) in making use of intranet platforms. Education of referees: VTT modified to the needs of referee education may be assumed as being well-established. Very similar to player training, where a combination of QGA and VTT is most effective, the analyses of referees’ performance can be ideally presented according to the principles of VTT mentioned above to achieve optimal results. Education of coaches: Compared to referee education, it is a rather new idea for coach education to use the principles of VTT to teach tactical analyses or the method of QGA. The skill of tactical analyses was treated for a long time as an “innate” property of coaches or future coaches. Now, when seen as a “normal” method for investigations, it may become an item in the curricula of coach education courses, which should be highly appreciated, because it is at the core of a coach’s activities.

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The purpose of enumerating the most important established and expected application fields of QGA and VTT is among others to make aware that PPA is a growing job market. One may for sure expect a growing number of positions not only in the analysis departments of professional clubs but also in federations, for example, with respect to their duties of coach and referee education. PPA has become a business as well, for example, when providing services for clubs, working with individual players and for players’ agents. Quantitatively, we see an expansion as well. For example, in top football clubs, we already have more or less independent departments for analysing their own team, for analysing the next opponent, and for identifying potential transfers. These departments are installed for the first team as well as for the youth academy. An important consequence for universities is that installing and/ or maintaining academic research and education in PA is very much justified in the perspectives of a job market for their graduates (employability).

5.4.2 The Role of Game Analysts As was already stated in the paragraph on QGA, the informational coupling of competition and training, but also other applications of QGA require an ideally seamless communication between analysts and staff, especially with tactics coach and head coach. In practice, detailed specifications of the roles of different members of the social system “elite sports club” emerge through interaction. As result we find a number of possible role characteristics for game analysts in a sports club as depicted in Fig. 5.9. First of all, the basic work of match analysis has to be done, that is, tagging and cutting match videos, writing match reports by using PIs either commercially provided or obtained by a self-developed observational system. This is more or less mechanical and does neither require too much expertise in the sports examined nor too much confidence from the other members of staff. Therefore, this role may be called the “working horse” role as there is much work to be done but without requiring high expertise. A next level is the one of analysts with a certain expertise in data processing. They may create new analyses based on event or position data either demanded for by staff members or brought about by their own ideas. The capability to meet these demands requires a good understanding of the nature of the underlying data but also a good proficiency in data processing when, for example, machine learning applications are run or mathematical models of football constructs are to be realized. With regard to the famous book Money Ball, where this role appears is described (Lewis 2003), it is named here a little bit short cutted “nerd”. Finally, we have analysts who are acknowledged experts by the staff. These analysts are accepted by the staff to give support in finding conclusions on strengths and weaknesses of their own team or the next opponent. Typically, this requires practical experiences in the sport either as a former player and/or long years of practice with match analyses. Besides these different levels of expertise of game analysts, we may find roles of game analysts exceeding their core competence of game analysis. This is the case

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Fig. 5.9  Different roles of match analysts in a sports club

when they are capable to provide recommendations on the different application fields of game analysis, for example, for training, match strategy development, or transfer decisions of the club. In these cases, their additional qualification makes game analysts an even more valuable part in the support team. It is worth mentioning that the impact of analysts has increased proportionally to the power of their analyses which in turn depends on the quality and quantity of available data. In earlier times, observation, analysis, and interpretation were seen dominantly as tasks of the coach, eventually supported by objective data provided by the analysts (Carling et al. 2005, p. 10f). In rare occasions, renowned sports scientists work in practical settings of PA as well, for example, Christopher Carling worked for OSG Lille and Martin Buchheit for Paris St. Germain. Publications of these authors are a valuable source of knowledge of how PPA is conducted in practice. Besides the very relevant contributions of Carling (2013) that were referred to at several occasions already, Buchheit (2017) gives some quite instructive practical recommendations for game analysts working in a professional sports club. He mentions three steps for an effective sports science support in practice: 1. Appropriate understanding and analysis of data: A match analyst should understand questions beyond the mere figures, for example, validity and reliability of the data and also the priority of effect size compared to significance for practical conclusions.

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2. Presenting the data: Reports should be designed as simple and powerful as possible. The format of reports depends to a large extent to the expectations of the staff, especially the ones of the head coach. 3. Delivery of data: Buchheit makes aware of the fact that professional clubs constitute a collaborative environment with specific codes, which must be understood correctly by the game analyst before intervening effectively. Taken together, the experiences of widely acknowledged scientists when working in practice make clear that sports analysts need to be proficient on a dimension of their capabilities that is usually neglected or at least not stressed enough in their professional education: the capability of finding out ways to act successfully in the social environment of a professional staff working for a professional sports club. This does not only hold true for “star” performance analysts but also for each analyst working in this complicated setting.

5.4.3 Game Analysis Software This paragraph is devoted to some common design characteristics and user considerations concerning game analysis software. First of all, the need for software support in PA will be shortly pointed out, although this has been under debate only until some decades ago. In our days, it has become unanimous consent that matches are to be analysed at least partly based on objective data and that appropriate tools for doing so are computer-based game analyses driven by game analysis software. The two main reasons are, first, that we typically have many events that have to be recorded for game analysis, for example, 1,500 strokes in a long tennis match and approximately 1,600 events recorded in a modern football action feed each provided with around 10 attributes. This sheer mass of information cannot be handled without IT support. Second, game analysis software provides indispensable functions for PA such as computer-video coupling that allows for in-depth analysis of retrieved match scenes or detailed and comprehensive reports as well as flexible browsing options. In other words, in the present and future, it is and will be unimaginable that match analysis is done without game analysis software, but it may be mentioned that this was not the case until about two decades ago and is still not the case in many settings of game sports other than the big professional ones. Is Game Analysis “Big Data”?

In the second decade of our century, the term “big data” became a buzz-word. Originating from worldwide leading IT companies such as IBM, Oracle, SAP, Microsoft, or Apple, this meant data processing within technological achievements such as parallel computing and real time data processing. For several sciences, big data opens new perspectives, for example, for psychology, where Woo et al. (2020) identified five relevant sources of big data, that is, social media, wearable sensors, internet activities, public network cameras, and smartphones.

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In a quick reaction in sports science, the term “big data in game analysis” was coined as a hallmark for the future of performance analysis (Rein and Memmert 2016; Memmert et al. 2016; Memmert and Rein 2018). Only in the latter publication, the authors discussed whether sports analytics meets the definition of big data. IBM initially defined big data with the big “Vs”: volume, velocity, and variety and later added veracity (validity) and value (Ward and Barker 2013; Gandomi and Haider 2015). Thus it seems to be nearby to take the data volume of positional, video, and event data of a football match or a football season, the desire for fast results, and the several sources of data in professional football clubs (see section on “Sports Information Systems” below) to speak of big data in sports analytics (Goes et al. 2020). Nevertheless, it is questionable whether sports analytics will ever reach a dimension generally required for big data as Intel mentions for their average customers already in 2013 (Ward and Barker 2013): 300  TB new data per week with 500  TB per week added by data analytics. Compared to other applications of big data, in sports science, we have only very modest approaches. Consequently, the term “so-called big data” is used (www.dshs-­ koeln.de), and Goes et al. (2020) demand only for a productive collaboration between sports science and informatics and not for big data research.

Designing match analysis software is not an issue in the big professional sports as here we have the so-called data providers that care on a commercial base for action and position data. Nevertheless, we have several less or semi-professional sports as well as amateur sports, some nevertheless competing at Olympic level, where this is not the case and the clubs or federations have to care for data acquisition at their own. Moreover, it might be the case that data providers, being frequently financed by media, do not supply the information needed by the coaching staff in the sense of PPA or access is a problem. In introducing match analysis software, there are basically two alternatives: one may rely on customized standard software or the software is exclusively designed for an application case. Standard software for match analysis such as Dartfish, SIMI Scout or Sportscode may be adapted to a certain sport or to a coach’s preferred categories of analysis. On the other hand, software exclusively designed for analyses in a particular sport requires more programming and financial effort, but the whole design may be chosen according to the tasks to be solved and special gadgets, for example, video-based speed measurements or graphically supported annotations, may be more easily integrated. No matter how this decision is taken, there are general requirements to be met by game analysis software. Data collection and analysis have to work as fast as possible in order to use results between matches of a tournament (some sports even know more than one match per day in a tournament) or between match and next training. It has to provide meaningful reports that are easily comprehensible for coaches and athletes. And finally, qualitative game analysis requires options for in-depth

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analysis of phases in a match (ball possessions, rallies) that are selected according to the demands of the users, that is, filtering options and video player functionality. A principle that was applied in each match analysis software that was realized at our chair was to provide a two-step solution. The first step is meant for live recording and giving immediate feedback after matches or even in half times (“live scouter” in Fig. 5.10). It must be easy to use, with simple consistency checks and very easy ways of live corrections. Of course, only a limited number of variables may be collected online per observational unit (e.g. rally in beach volleyball and table tennis or throw in goalball). This stage serves also to pre-tagging the match video for further analyses. The second step is meant for detailed offline data recording (“remote scouter” in Fig. 5.10). Here, the full observational system for a sport is implemented with many variables, with levels that are sometimes hard to detect even for experts, for example, a differentiated category system on service techniques in table tennis, and require repeated video inspection. Moreover, specific gadgets may be implemented serving for an easy assessment of more complicated variables. In Fig. 5.10 bottom left, we see the user interface for the remote scouter with a table tennis table where the landing points of strokes may be recorded for stroke placement analysis and a ball where the impact of the racket may be recorded to analyse the type of spin. In other applications, other specific gadgets may be realized, for example, a video-­ based assessment of ball speed in goalball. There are multiple requirements for a match analysis software coming from ergonomics, that is, making the use of the software as convenient as possible in the setting of data acquisition. First, all specifications of the system (hard- and software) must be adapted to the use cases. Typically, it is possible to obtain an

Fig. 5.10  Design and user interfaces of a table tennis match analysis software. Upper left, design; upper right, user interface live data capturing (live scouter); lower left, user interface remote data capturing (remote scouter); lower right, user interface of analysis tool with filter, playlist, and video (viewer)

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accreditation for the game analysts for using cameras at the match location. But additional limitations, for example, concerning space requirements, power supply, robustness against environmental impacts, or even internet connection, must be taken into account. User interfaces should be designed in a way that users not necessarily being acquainted too much with the software may work independently with it. This is absolutely necessary with regard to the innovation cycle (Ghorbani and Lames 2016), where the aim is to transfer the responsibility for the service from the academic developers to users in sports practice. A general ergonomic requirement is to save as much time devoted to routine input as possible. Therefore, it is necessary to use as much algorithmically defined input as possible, for example, fixing the new score-line as soon as the result of the last rally in tennis is recorded. Moreover, shortcuts or intelligent guesses as default input may help a lot in improving data recording efficiency. International competition in top-level sports, especially with regard to Olympic medal rankings, implies that there is a competition in IT support for sports as well. This means that game analysis on a higher level than the other nations results in a competitive advantage at a certain event. But all competitors should be aware of the fact that these advantages are only of temporal nature and continuous effort must be realized to preserve these competitive advantages based on match analysis software.

5.4.4 Club Information Systems As already frequently mentioned in this book, the staff of a professional team or athlete consists of many experts responsible for different areas. In

Fig. 5.11  Different roles in the staff of a professional football club. (https://www.liverpoolfc.com/ team/first-­team retrieved in 2/2020)

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Fig.  5.11, the staff of FC Liverpool is shown as it operated in 2/2020. It becomes obvious that PA is the core activity of at least two departments: match analysis and scouting. Above, a staff in professional clubs was seen as a social system, where a game analyst has to find his role and must be acknowledged before working effectively. In this section, it is seen as a communication network with different members, each producing information with potential relevance to other members. The assumption is that only the optimal use of all this existing information allows for optimal decisions in sports practice. The question now is how to support this communication network technologically at the current level of knowledge. Blobel and Lames (2020) submitted the idea to adopt design and architecture of information systems in business informatics for club information systems (CIS). In business, we have a similar situation as in sports clubs: different departments provide information, and making the best use of all relevant information is prerequisite for good management decisions. Figure  5.12 shows the three-layer architecture of a CIS containing a data layer with an interface to the different domain knowledge bases, a logic layer where relevant information is generated by merging domain knowledge, and an access layer where access is granted for the different users. The architecture expresses some basic ideas as follows: • The expert domains are not part of the CIS, because this would potentially cause problems with data integrity and privacy. Only data relevant to other users are contained in the CIS database. • At the logic layer, new demands appear: How to integrate data from different sources to provide the full information background. • The access layer has to incorporate potentially intricate questions such as data property, data sharing, and access rights. • Developing and running a CIS requires experts in computer science to organize and run the system very much like in companies with their IT departments. • On the other hand, these IT experts need to be in close contact with experts from sports science capable of bridging the gap to sports practice. The sheer size of the problem and the perception of its benefits and necessities by the responsible in professional sports clubs have led to the fact that the concept shown in Fig. 5.12 is hardly fully realized in sports practice. A market analysis on CIS (Blobel et al. 2021) showed that there are many products but hardly any providing the full spectrum of capabilities needed to serve as an optimal CIS. Nevertheless, perceiving match analysts as experts playing important roles in a support staff of professional teams and athletes together with a number of other experts is the core vision of future developments in top-level professional sports. A future head coach will have to focus more on communication supporting decision-­ making processes between the experts of his staff than pursuing the old (Carling et al. 2005) one-for-all idea.

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Fig. 5.12  Architecture of a club information system. (With permission of editor from Blobel and Lames (2020))

6

Outlook

This chapter tries to give an outlook on the future of PA. This is a daring endeavour because it requires predictions, and many aphorisms already underline the difficulty of this task. For example, one of the most famous ones is attributed to Niels Bohr (1885–1962; but also to Nostradamus (1503–1566)): “Prediction is very difficult, especially if it’s about the future”. Whereas this aphorism might be a little bit deterring, there is another one by Mark Twain (1835–1910): “The future interests me – I’m going to spend the rest of my life there”.

6.1 Outlook on the Core Topics of PA Inspired by Mark Twain but also because it is an inspiring challenge, in the following, an outlook is given on the topics of the five preceding chapters of this book. Summaries of the basic messages or references to the corresponding sections are given, and predictions of the relevance of topics from these areas for short- and middle-ranged future will be made.

6.1.1 Basic Concepts This book contains two basic messages: the first is the notion of game sports as dynamic interaction processes with emerging behaviour, and the second is the distinction between theoretical and practical performance analyses being considered as the two sub-disciplines of performance analysis. These messages are certainly analytical judgements and in this sense arbitrary. On the other hand, there is much scientific and empirical evidence speaking in favour of these concepts. Seeing game sports as dynamic interaction processes with emergent behaviour has led to many important insights throughout the chapters of this book: the relation between observable match behaviour and the underlying capabilities of players being not directly retrievable because of interaction with the opponent, the failure of © Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5_6

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our usual static, summative performance indicators to reflect the dynamics of a match, and the consequence of emergence that sometimes one may not explain why a team or a player has won. Future research in PA will remain to be challenged by this basic notion, and it will be interesting to see which new ideas and methods will “emerge” to grasp these essential aspects. The introduction of a systematic distinction between TPA and PPA will especially in PPA support new perspectives of research. The professional role of game analysts comes into focus (Martin et al. 2021) as well as the workflows that need to be established to manage the problems of PPA. In sports practice, more support by business intelligence systems such as club information systems may be expected. Management approaches, especially from innovation management, will be introduced to promote their implementation and productive use in the setting of professional sports clubs and federations or leagues. For TPA, the consequences of this distinction are not as far-reaching as for PPA. The problem so far was that TPA was taken for PPA (see Box “The Practical Impact Debate”), which is solved by introducing the two sub-disciplines. Nevertheless, the frequently naïvely drawn conclusions in TPA papers that improvements for practice are to be expected from the results of the conducted study should become less common. The practical impact of future TPA studies depending on the applied research strategy will hopefully be perceived more realistically.

6.1.2 Action Detection In the area of action detection, one might expect an increasing number of studies that try to detect actions automatically based on position data of players and ball. One might assume that with the help of supervised learning, one will arrive at a level where it is possible to generate automatically so-called action feeds, that is, fine-­ grained event systems touching the border to a category system. As there is a high commercial interest in this capability replacing the armies of human observers that need to be employed when using observational methods, progress may be expected in the near future. When automatic action detection will have been realized, observational systems, that is, systems with a human observer as measurement instrument, will only be applied for more in-depth analyses of events, for example, when technical details of the execution are of interest. In football, this might concern set plays (penalties, free-kicks, corners) as well as special topics such as action chains leading to injuries. It will be interesting to see whether future developments in informatics will lead to tools employing pose estimation that are able to provide movement analyses in necessary detail for solving the questions mentioned. A new area of relevance for observational methods may become the validation of data for AI applications, touching the aspect of “veracity” of big data (Firmani et al. 2015). Ground truth is needed here, and therefore, the methods of assessing agreement between observational ground truth and big data feeds will be of special

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interest. So, even when traditional observational data as such may become outdated, there is an ecological niche for classical game observation. In addition, it must be mentioned that the considerations on the future of action detection hold true only for professional sports where the application of advanced analytics including AI can be afforded. Other sports, youth sports or on non-professional levels of professional sports (in Germany, there are 154,887 amateur and youth football teams with 1.5 million official matches per season involving 2.3 million players (www.fussball.de)) would rely on more traditional methods of action detection. This implies also that a future problem for PA may arise when only professional sports with professional data providers will be eligible for the most up-to-date methods of PA. In sports, where these are not available, it will become more and more the task of national top-level sports support systems to provide the latest achievements to their teams to be competitive at international level. This holds true—at the time being—for all Paralympic sports, for example.

6.1.3 Position Detection Giving an outlook on the future of position detection, two present and presumably persistent problems of EPTS validation must be mentioned. First, we still do not dispose of a full pitch gold standard for evaluating position detection. As results show (see Linke and Lames 2019), we have more accuracy problems with faster movements and with higher accelerations. We also know that on small pitches, for example, the 30 × 30 m measurement volume of current gold standard studies, players do not reach by far the maximum speed and acceleration they show in full pitch matches. This is not a surprise as top-level sprinters need more than 40 m of maximum linear acceleration to reach their top speed. (The “PI” fastest player in the match denotes the player who had the opportunity for a long maximal linear acceleration which is a rare event in football, and this is usually not the fastest sprinter.) To make it even worse, these high-­intensity movements, where we cannot test the accuracy of our EPTS but must assume the biggest problems, are of paramount interest to athletic coaches. This interest is recently mirrored in the search for “worst case scenarios”, that is, the periods in a match with highest loads (e.g. Oliva-Lozano et  al. (2021)), motivated by the idea that training should be designed to prepare players for exactly these scenarios. The second persisting problem is the comparability of EPTS results. Experiences show that results from EPTS that use different technologies (VBT, GPS, LPS) or from different EPTS that use the same technology show large, frequently inacceptable differences in their results (see the introduction paragraph of Sect. 3.2 in Chap. 3). This is caused by errors originating in the technology used and different data processing procedures, especially smoothing algorithms, both inevitably leading to differing results. But as there is no universal EPTS that may be used in official matches in the stadia and at the different training sites, and the necessity of having comparable results persists, more sophisticated methods of alleviating this problem

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will be needed in the future. Only in a long-term perspective one may hope that the general trend towards reduced EPTS errors will diminish the incomparability of EPTS results to an acceptable level. A technological innovation that has recently been implemented is the use of IMUs added to position tracking sensors on the pitch. Up to now mostly used for supporting EPTS in obtaining kinematic data (see Sect. 3.2.3 in Chap. 3), IMUs will introduce new options for kinematic analyses. For example, when balls are equipped with sensors including an IMU, one is able to detect every single ball contact with the accelerometer integrated in the IMU. This is at present mostly seen as support in judging offside, but there is also much potential for other analyses such as passing speed, number of ball contacts during ball control of a player (one contact is direct play!), or maybe even indices of technical skill in ball handling. It may be expected that in the near and mid future, the options of performance analysis will be increased by biosensors that will provide a deep insight into the physiological state of the players during a match. This was already early anticipated by Baca et al. (2009) who discussed the options of ubiquitous or pervasive computing in sports. The following—incomplete—list contains variables and their relevance to performance analysis that will be or are already assessable with sensors during matches: • Heart rate: Internal load and exercise/match intensity • Body temperature: Temperature regulation under exercise, fatigue, and exhaustion • Oxygen saturation of blood and blood sugar level: Fatigue indicators accessible with near infrared spectroscopy • Saliva cortisol level: Acute stress level • Breath rate: Load of pulmonary system accessible with intelligent sports clothes The physiological monitoring of players in situ will open new options for training control but also for within-match coaching. In football, for example, decisions on substitutions could profit very much when being informed on the actual physiological status of the players. The combination of these physiological variables with kinematic and action data will extend our knowledge in many respects, but it will also require specialists with interdisciplinary expertise and a highly specific education capable to manage projects involving experts in AI especially in machine learning as well as physiologists.

6.1.4 Theoretical Performance Analysis The outlook for TPA will be given separately for the three approaches presented in Chap. 4, statistical approaches, modelling approaches, and the application of tools and concepts from dynamical systems theory. Statistical approaches show at present already a tendency towards a higher complexity, trying to incorporate many contextual variables. One may expect to see more complex methods here, very likely also methods originating from big data

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problems relying on AI and especially machine learning methods. Problems to be expected using these methods will be discussed below, but we see already in “normal” statistical approaches with large databases, for example, the problem of spurious correlations, that is, significant but meaningless correlations (for n = 1,000 a correlation of r = 0.063 is significant!). In Chap. 4, two types of modelling approaches in PA were distinguished: direct modelling, where constructs of a higher abstraction level compared to kinematic variables and with practical relevance are the target, and the application of models and tools originating from other areas to game sports like social network theory. Direct modelling approaches will address new constructs of practical relevance and existing ones with an increased validity. This is a very promising field as there is a conceptual coupling between the aims of direct modelling and their practical usefulness, because the aim is to quantify constructs that sports practice is using qualitatively for analysing performances. This has become obvious already when models for passing options, pass effectivity, ball control times, dominated space, availability, fatigue, or scoring probability were presented. On the other hand, some relevant constructs are still waiting to be modelled directly from position and action data such as perturbations or no-control phases. Nevertheless, targeting at constructs that are in practical use creates some challenges concerning validation. First, there may be ambiguities regarding the nature of the construct among practitioners, for example, in football, the term “pressing” is open to different interpretations as there are different degrees and intensities of pressing. Then, a definition of a construct based on positions and actions may fall short to grasp the relevant aspects of it. For example, analysing a tactical lineup sticking to the geometrical configuration may lead to many lineups during a match. But a certain lineup must sometimes be given up for tactical reasons, for example, a defender leaves the defending line (configuration 4-0) to attack an approaching forward (configuration 3-1). In this situation, the tactical lineup may look like a different one, but in reality, it is only an adaptation of the basic lineup to the actual situation. The deeper problem here is that the construct “tactical lineup” is an action plan, whereas direct modelling hat to work only with spatiotemporal configurations. Finally, the problem of direct modelling to rely on operational definitions based on positions and actions implies also not being able to take subjective aspects into account. For example, availability (in the sense of a passing option in football) in a geometrical sense is different from a player’s perception of availability. Representatives of constraint-led approaches or embodiment would strictly reject to define availability geometrically because affordances are body-scaled (are my capabilities sufficient to play this pass?) and action-scaled (did I take the appropriate actions to play this pass?) and depend on the social context (what are the other players’ and the coach’s expectations?) as mentioned in Sect. 4.3.3. It will be interesting to see how direct modelling approaches will get along with the mentioned problems in the future. The strategy of importing methods and theories from other scientific domains will continue to discover new exciting tools capable to enlarge knowledge in

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PA. Box: “Importing a Theory/A Methodology to PA” critically mentions four steps that must be taken to arrive at a significant enlargement of knowledge in PA.  A showcase for this approach is social network analysis that was presented in detail referring to the abovementioned steps. Other approaches such as recurrence analysis are still waiting for unfolding their potential, and there may be other approaches that are still waiting to be discovered by PA. Therefore, for this strategy of PA, it is most difficult to give a prediction of future impact. For dynamical systems theory (DST), a short outlook may be found already in the section above: “4.3.5 Outlook: DST in PA”. From a synergetic point of view, one may expect from the future that the system dynamics of game sports that is at present only given at the level of abstractions (see Fig. 4.21) will be advanced further in the direction of empirically founded models. Also, it would be desirable to explain the self-­organization processes, that is, the microscopic interactions, leading to a goal or point. There is a dominance of approaches explaining regular behaviour, but less attention is given to perturbations, and only very few studies in PA focus on chaos, unpredictability, and chance effects, although the latter are part of the toolkit of DST. Significant steps in this direction might even have a revolutionary (in the sense of Kuhn) potential for PA.

6.1.5 Practical Performance Analysis It is not far-fetched to predict a quantitative and qualitative expansion for PPA in the future. In the past, we saw already the trend that an increasing number of professional sports clubs install analytics departments or even three of them for their own team, future opponents, and potential transfers (six when installed for both senior team and youth academy, nine if there is a professional women’s team). This trend will continue and affect each club in a professional league. One may expect as well that this expansion to lower levels in professional football will even take hold of amateur clubs or more precisely clubs playing in non-­ professional leagues. Admittedly, it mustn’t be expected that there will be (six) analytic departments in amateur clubs, but one could expect full-time game analysts becoming members of the coaching staff in amateur football clubs as well. In other sports being organized far less professional than football (in Germany: any other sport), we will see this trend as well but of course in a weakened form. In the top leagues, game analysts will enter the coaching staffs in near future. As was briefly mentioned above, typically there are national top-level sports support systems that have the task to support the non- or less professional sports in developing an internationally competitive national team. It is only obvious that in future, these support systems must care for high-quality game analytics in these sports in order to maintain competitiveness, for example, in Olympic and Paralympic games. A qualitative expansion of PPA may be expected in the coaching staff. With increasing data processing capabilities, analysts will play a more important role in the staff, not only because they can present results with more impact on decision-­ making but also because they will become able to provide more and more relevant

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information to other experts in the staff, for example, the physiologists, medical staff, assistant coaches (tactics and athletics), and head coach. A prerequisite for a playing this more influential role is the implementation of a club information system. The basic design and the functioning of these systems was introduced in detail in Sect. 5.4.4 in Chap. 5 on PPA. In this conclusion chapter, it is important to stress that the extent and quality of these central information system will determine to a large part the competitiveness of professional clubs in the future. In sum, the future development of PPA will see an increased relevance of PA in professional clubs that is nourished from the expanding methodological options in PA. This increased relevance is thus based on technological innovations in PA which mostly stem from information technology. This underlines again that good future perspectives are given especially for analysts who are capable of integrating informatics and sports science.

6.2 The Future of PA 6.2.1 Artificial Intelligence and PA In this outlook, we stepped already into several examples, where AI may be expected to become a central tool for game analysis allowing to generate novel, relevant information. A recent textbook on Artificial Intelligence in Sport Performance Analysis (Araújo et al. 2020) discusses profoundly the application of AI methods to theories in sports science, in this case to ecological dynamics. The authors plead to hold on to data-informed decision-making as opposed to data-driven approaches that are typical for AI and machine learning, the latter being the most important method, better family of methods, in AI. Moreover, the authors list problems that are frequently recognized when AI comes into play, for example, no evidence for increased capability of prediction of relevant events such as winning, losing or injury, insensitivity to sub-groups, perpetuation of biases, lack of privacy and ethical problems, and finally a loss of theoretical depth as big data advocates for an “atheoretical perspective” (p. 12, see Box: “The End of Theory”). They support true interdisciplinary research where sports scientists care for a sound interpretation of the findings obtained with AI.

The End of Theory: AI from a Theory of Science Perspective

A famous position paper on the impact of AI to theory of science is a three-­ pager of Chris Anderson (2008) “The End of Theory: The Data Deluge Makes the Scientific Method Obsolete”. He states that model building and hypotheses testing, the hallmarks of traditional science, are going to be replaced by the mere detection of patterns and correlations in the data by AI. This paper has provoked an intensive discussion and is rejected by most philosophers working in the area of theory of science. A most common

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argument is as data are already “theory-laden” (Haig 2020), patterns and correlations in it are so as well. Nevertheless, one must admit that with the advent of big data, traditional scientific methods need adaptations, for example, the notions of statistical significance and hypothesis testing are challenged, and our concepts of correlation and causation need to be adjusted. There seems to be agreement that AI is not the end of theory but opens new opportunities (Mazzocchi 2015). Disciplinary reasoning, based on theories and models—or concepts and methods—of the field, will remain an essential part of future scientific activities.

The methodological potential for AI applications in PA offers great perspectives, but one must be sensitive for problems that may arise, very much like when importing any other method or theory. An interdisciplinary understanding between sports science and informatics is indispensable. The International Association for Computer Science in Sports (IACSS, www.iacss.org) supports this idea in its mission statement. Regular conferences and a scientific journal (International Journal of Computer Science in Sports (IJCSS)) are dedicated to achieve the aim of promoting true interdisciplinary research. In sum, one may state that AI will become more and more relevant to PA, and tools from AI will be an important part of the skill profile of sports analytics, but the future of PA is for sure not becoming a discipline of AI!

6.2.2 Sports Practice and PA We saw at many points in this book that technological development is an important driver of the potential of PA.  Many things have become possible in the last two decades that analysts were only dreaming of before, for example, position detection or efficient video-based tactics training. And, as denoted above, there are technological innovations just behind the door that may still significantly enlarge the potential of match analysis, for example, biosensor monitoring the physical status of players during a match. This means that technological innovations will be of paramount importance in top-level sports (Lames et al. 2016). One may assume that competitive advantages of players, teams, and national sports systems will in future result more and more from the capability of a sports training system to introduce and work with technological innovations successfully. This consideration underlines the increasing importance of introducing ideas, capabilities, and staff competent in theory and methods of innovation management to the operational teams in sports systems. In the area of sports analytics that is already today characterized by a spectrum of rather different interest groups, for example, training staff, media, and management, one may assume that the specialization will continue, and we will see only loosely connected activities in the future.

6.2  The Future of PA

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In sports training systems—the focus of this book—we will most likely see a trend towards larger staffs with more specialists from different domains, where performance analysts have good perspectives to play a central role as their expertise lies in retrieving information that is essential for the whole staff. The role of the head coach will change with more emphasis on the coordination and organization of the information flow with and between the experts in the staff. Their competence will be more than today in decision-managing instead of decision-making. The same holds true for assistant coaches in their respective area of responsibility. Last but not least, there are good perspectives for the academic future of PA as we have already today a growing job market for our students. Given the qualitative and quantitative expansion of PPA mentioned above and the continuous stream of technological innovations in PA, this market for theoretically and practically welleducated students will for sure expand in the future. What research is concerned we will face changes in future as we are used to from the past. From time to time, it will become necessary to update concepts and methods in performance analysis.

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Index

A Absorbing states, 123 Absorption probability, 127 Abundance, 26 AC1, 51 Academic standards, 70 Acceleration, 73 Action detection, 23–57 Action feeds, 31, 184 Action-scaled, 166 Action-scaled affordances, 147 Activation techniques, 210 Actual fitness level, 189 Ad hoc revisions, 198 Advertisement psychology, 209 Affordances, 3, 88, 145, 166 Affordances in social contexts, 147 Agreement, 48 Agreement coefficient 1, 51 Agreement matrix, 46 Algorithmic recommendations, 194 Algorithmic solution, 188 American football, 89 Analysis of future opponents, 201 Analysis of match strategy, 215 Analysis of one’s own team, 215 Analysis of opponent, 203 Analysis of own performances, 178 Analysis of the next opponent, 215 Anomy, 4 Anticipation, 202, 203 Approximate entropy, 168 Aristotle, 10 Assistant coaches, 233, 235 Attractors, 138, 148 Australian football, 132 Autocorrelation function (ACF), 111 Average diagonal line length (LL), 171

B Background knowledge, 179 Backward moving average, 114 Badminton, 114 Ball contacts, 97 Ball control, 97 Ball possession, 98 Baseball, 11 Base stations, 63 Basic messages, 227 Basic research, 179 Basketball, 10, 132 Beach volleyball, 180 Behavioural research, 23 BEIDOU, 60 Betweenness parameters, 119 Big data, 89, 234 Bipartite, 121 Black box models, 95 Body-scaled, 147, 166 Bohr, Niels, 227 Boxing, 149 Business analytics, 22 Business informatics, 224 C Capabilities, 8 Case-by-case analysis of judgements, 44 Category systems, 24, 27, 184 Centre of mass, 77 Chance, 135 Chance goals, 154 Chance variables, 153 Chaos, 135 Chaos theory, 137 Choice of strategy, 203 Classical performance analysis, 15 Classroom settings, 117

© Springer Nature Switzerland AG 2023 M. Lames, Performance Analysis in Game Sports: Concepts and Methods, https://doi.org/10.1007/978-3-031-07250-5

255

256 Climate change, 136 Cliques, 119, 120 Club information systems (CIS), 178, 224, 228, 233 Coaching staff, 178 Coach’s philosophy, 187, 202, 203 Cognitive dissonance, 205 Cognitive learning processes, 20 Cohen’s kappa, 47 Collective behaviour, 170 Commercial data providers, 70 Common reconstruction, 197 Communication, 193, 209, 211 Communication network, 224 Communication strategies, 178 Communication theory, 212 Communicative validation, 197 Comparability, 72 Competitive level, 88 Completeness, 35 Complexity, 92, 134 Complex systems, 133, 140 Comprehension, 41 Comprehensive performance analysis, 189 Computer-video coupling, 184 Confirmability, 192 Confirming and disconfirming cases, 200 Consciousness, 134 Consistency of instrument, 38 Constraint-led approaches, 145 Constraints, 3, 88, 145, 166 Contemporaneity, 208 Contextuality, 191 Contextual variables, 88 Continuous Markov chains, 132 Contribution of a player, 131 Control, 148 Control parameter, 138, 142 Convex hull, 159 Correlation, 18, 78, 141 Counter perturbations, 162, 164 Covariation, 18 Cricket, 11, 74 Critical case sampling, 200 Critical fluctuations, 140 Critical goal situations (CGS), 164 Critical slowing down, 140 Cross-country skiing, 17 Cross recurrence plots, 175 Curve fitting, 68 Cycle attractor, 140 Cycling, 134

Index D Data processing, 77 Deceleration, 73 Degree parameters, 119, 120 Descriptive statistics, 85 Design principles for testing observer agreement, 44 Determinism (DET), 171 Development of match strategies, 201 Didactic approach, 207 Differential GPS, 62 Direct modelling, 97 Distribution of possible results, 157 Doppler effect, 62 Drifting Markov chains, 132 Dynamical systems theory (DST), 83, 88, 133, 232 E Ecological psychology, 3, 9, 88, 144, 147 Ecological validity, 75 Education of coaches, 217 Education of referees, 217 Effective trainability, 187 Electromagnetic waves, 63 Elevation angle, 65 Emancipated personalities, 193 Emancipation, 193 Embodiment, 145 Emergence, 12, 134, 138 Emerging behaviour, 171 Emotions, 208 Empirical model validation, 94 Empirical validation, 94, 116, 120 Encounter, 202, 203 Endurance training, 194 Entropy of diagonal line lengths (ENTR), 172 Entropy of vertical line lengths (ENTR-V), 172 Environmental constraints, 146 Environmental determinants, 8 EPTS, 66 Equilibrium, 162 Equivalence classes, 28, 102, 124 Ergonomics, 222 Evaluation research, 179, 180 Event profiling, 53 Event system, 27, 184 Expected goals, 153 Expected rally length, 126 Expert domains, 224

Index Expert rating, 104 Explanation, 148 Explorative approach, 192 External context, 205 Extrapolation, 80 Extreme or deviant cases, 200 Eye tracking, 166 F Factors, 136 Fatigue, 97 Fatigue during VTT, 210 Feedback, 20, 181 Field, 132 Field setting, 74 FIFA, 66 FIFA EPTS initiative, 71 Figure skating, 86 Filtering, 67, 68 Finger-waggling experiment, 142 First-five-minutes effect, 105 Flap of a Butterfly, 137 Flow fields, 144 Focusing on practical problems, 193 Football, 10, 68, 91, 131, 132, 149 Formative evaluations, 179 Forward moving average, 114 Fourier transform, 68 Fractal dimension, 137 Frequency spectrum, 68 Frequency techniques, 210 Full pitch gold standard, 74, 229 Functional norms, 182 Functional organismic constraints, 146 G Gait analysis, 73 Galileo, 60 Game analysis software, 214 Game analysts, 178 GDR, 10 Gender comparisons, 91 General trainability, 187 Germany, 25 Gestalt theory, 135 Global epidemics, 136 Global positioning system (GPS), 60 GLONASS, 60 GNSS, 61 Goalball, 89, 180

257 Goal kick, 98 Gold standard, 72 Golf, 143, 169 Granularity, 35 Grey box models, 95 Ground truth, 72 Groups of sports, 10 Group VTT, 211 H Haken, Hermann, 138, 141 Half-time interventions, 216 Handball, 10, 114, 131, 180 Handicap class, 89 Head coach, 178, 233, 235 Hermeneutic cycles, 193, 198 Hermeneutic process, 198 Heterogeneous sub-groups, 78 Heterosynchrony, 187 Higher-order Markov chains, 132 High-pass filter, 69 Hilbert transform, 141 Holistic thinking, 193 Hysteresis, 140 I Ice hockey, 132 Ideal norms, 182 IFAB, 66 Importing a theory, 115 Improving quality of life, 191 IMUs, 230 In-depth analysis, 194 Index building, 101 Index construction, 101 Index of player performance, 103 Individual ball possession, 98 Individual response characteristics, 188 Individual speed thresholds, 88 Inferential statistics, 85 Informational constraints, 146 Informational coupling, 181–183, 188 Information systems, 224 Information uptake, 210 Infrared cameras, 73 Infrared movement analysis systems, 74 Infrared-reflecting markers, 73 Innovation cycle, 223 Innovation management, 228 Instructional constraints, 146

Index

258 Intended message, 205 Intensity sampling, 200 Internal context, 205 Internal representation, 181 Inter-observer agreement, 52 Interpretation, 192–194, 197 Inter-subjective agreement, 192 Intervention studies, 179 Intranet platforms, 217 Intra-observer agreement, 52 Item analysis, 101 J Job market, 235 Job opportunities for game analysts, 214 K Kalman filter, 67 Kant, 41, 42 Kappa paradox, 51 Kelso, J.A.S., 141 Kuhn, T.S., 93, 136, 144 L Lab setting, 73 Laminarity (LAM), 171 Laplace, Pierre-Simon, 136 Laser-based distance measurement, 73 Learning, 203 Learning strategy, 207 Levels of modelling, 94, 95 Levels of observational variables, 34 Light conditions, 65 Line of sight, 61 Local positioning systems (LPS), 63 Long-term adaptations, 187 Lorenz, Edward, 137 M Marker-based systems, 73 Marker detection, 74 Markov chain, 123 Markov chain modelling, 115 Markov process, 123 Markov property, 123, 128 Match analysis, 181 Match analysis software, 180 Match analytics, 195 Match dynamics, 92 Match half, 88

Match strategy, 5, 178, 190, 201 Match-to-match variation, 92 Media-based learning, 205, 212 Median frequency, 109 Media richness theory, 205 Medical staff, 233 Member checks, 198 Memory traces, 181 Meta-stability, 143 Metastable system, 162 Minimum spanning trees, 118 Modelling approaches, 83, 115 Modellism, 94 Model validation, 26, 94 Momentary playing strength, 114 Momentary success rate, 114 Moore’s law, 59 Motivation videos, 216 Motor learning, 20, 181 Movement science, 147, 181 Moving average, 68 Mutual understanding, 193 Myriads, 136 Myriads of factors, 134 N Natural settings, 24 Nature of models, 94 NAVSTAR/GPS, 60 NBA, 66 Negative binomial distribution, 157 Negative perturbations, 162 Negotiation of match intensities, 107 Net playing time, 108 Network analysis, 115, 117 Network graphs, 118 Networks, 121 Neutralizing perturbations, 162 No-control phases, 99, 100 Nonlinear interactions, 138 Nonlinearity, 134, 151 Nonlinear thinking, 136 Normal science, 144 Nostradamus, 227 Notational analysis, 19, 178, 181 Number of perturbations in net games, 162 Nyquist-Shannon sampling theorem, 68 O Objectivity, 45 Observability, 33, 162 Observational system, 163, 184

Index Observer, 40 Observer agreement, 24, 43 Observer training, 24, 43 Operational definitions, 35 Opposition, 13 Order parameter, 138, 140, 142 Order variables, 148 Organismic constraints, 146 P Pacing, 106 Pacing strategy, 106 Paradigm change, 93 Paralympic sports, 89, 229 Paralympic Table Tennis, 180 Para table tennis, 89 Para tennis, 89 Peer briefing, 200 Peer debriefing, 198, 199 Penalty kick, 54 Per cent (%) agreement, 46 Perception-action coupling, 166 Performance analysts, 178 Performance improvements, 182 Performance indicator profiles, 86 Performance indicators, 13, 77 Performance indices, 97 Performance prerequisites, 3 Performance profiles, 85 Periodization, 187, 194 Persistent observation, 198 Personal performance analysis, 216 Perturbations, 87, 140, 161, 162 Phase space, 148, 168 Physiologists, 233 Physiology, 109 Pitfalls of VTT, 212 Pixel pattern, 168 Pixel-to-world transformation, 65 Play-by-play networks, 122 Player coupling, 160 Player scouting, 215 Player VTT, 211 Playing positions, 89 Playing style, 97, 98, 100 Playing time, 88 Playmakers, 119 Poincaré, Henri, 137 Pointwise recurrence rate, 169 Poisson distribution, 157 Pose estimation, 166 Position detection, 229 Position tracking, 184

259 Positive perturbations, 162 Potential transfers, 182 Practical decision-making, 182 Practical experiences, 180, 212 Practical impact, 5, 195 Practical performance analysis (PPA), 177, 178 Predefined movement circuit, 73 Presenter, 212 Prevalence of open play (FRP-1), 172 Professional role, 178 Professional role of game analysts, 228 Projection, 26 Prolonged engagement, 198 Q Qualitative content analysis, 195 Qualitative game analysis (QGA), 180, 190 Qualitative main analysis, 199 Qualitative methods, 194 Quality of opposition, 88, 91 Quantitative pre-structuring, 199 Quasi-experimental, 84 R Rally, 87 Rally length, 127 Rating scales, 28 Rayleigh-Bénard experiment, 139 Readiness for learning, 211 Ready-to-use, 63 Recommendations for practical action (practical impact), 178 Reconstruction, 6, 192–194, 197 Reconstruction and interpretation, 14 Recurrence analysis, 115, 143 Recurrence parameters, 171 Recurrence rate (RR), 171 Recurrence rate of open play (FRP-2), 172 Recurrence shares of open play (FRP-3), 172 Recurrence threshold, 168 Reduction, 26 Reductionist approach, 96 Referees’ performances, 216 Reflections, 138 Regression to the mean, 113 Reinforcement techniques, 209 Relative phase, 140, 142, 168 Relevance of tactical behaviours, 130 Reliability, 38 Re-sampling, 77 Residual category, 36

Index

260 Responsive evaluation, 180 Revolutionary” science, 144 RFID (radio-frequency identification), 63 RMSE, 62 Roles of game analysts, 214 Rugby, 10 S Sabermetrics, 21 Sample entropy, 168 Samples in top-level sports, 18 Sampling of typical cases, 200 Scientific foundation, 178 Scientific foundation for practical action, 212 Score line, 88, 107 Second-order Markov chains, 132 Self-confrontation, 211, 212 Self-organization, 134, 148 Semiautomatic, 66 Sensitivity, 137 Set plays, 171 Short-term adaptations, 187 Shots saved, 169 Signal processing, 70 Simulation, 129 Simulation of game behaviours, 131 Small sided games (SSGs), 166 Smoothing, 67, 68, 77 Soccer, 10, 180 Social configuration, 207, 211 Social context, 195, 213 Social engineering, 209 Social interventions, 209 Softball, 11 Space synchronization, 77 Spain, 25 Spectral analysis, 109 Spectral fatigue index (SFI), 110 Speed, 74 Speed of light, 61 Spline regression, 68 Sports analytics, 21 Sports psychology, 70 Spurious correlations, 231 Squash, 11, 131 Stability of conditions, 39 Stability of variables, 38 Stakeholders, 192 Standard software, 221 Starting states, 123 State-transition modelling, 95 Static, summative performance indicators, 228 Stationarity, 123, 126, 132

Statistical approaches, 83, 84 Statistical norms, 183 Stochastic processes, 123 Strange attractors, 137 Strengths and weaknesses, 5 Stroke, 87 Structural model validation, 94 Structural organismic constraints, 146 Structural validation, 94, 116, 120 Structure of performances, 9 Sub-disciplines of PA, 7 Subject-object dualism, 195 Summative agreement, 44 Summative evaluations, 179 Summative match statistic, 98 Swarm theory, 115 Swimming, 19 Symmetry breaking, 135 Synergetic experiment, 143 Synergetics, 138, 142 System approach, 134 System dynamics, 138, 148 T Table tennis, 11, 114, 131 Taekwondo, 131 Targets for training, 178, 183, 184, 186 Task constraints, 146 Team spread, 159 Team VTT, 210 Technical support, 178 Technological innovations, 197 Technological progress, 59 Temperature, 166 Tennis, 11, 74, 86, 91, 131 Test prolongation, 39 Tests for tactic abilities, 217 Theoretical performance analysis (TPA), 83, 177 Thinking in complexity, 133 Threats to reliability, 38 Time-motion analysis, 59 Time-of-flight, 63 Time synchronization, 77 Timing gates, 73 Track and field, 19 Trainability, 187 Training exercises, 178, 215 Training staff, 197 Training systems, 235 Training targets, 188 Trajectory, 68 Transferability, 192

Index

261

Transfer to training, 200 Transient fatigue, 112 Transient states, 123 Transponders, 63 Trapping time (TT), 172 Triangulation, 61 Twain, Mark, 227 Type of observational systems, 27 Types of validation, 94

Values for actions, 103 Variants of observational systems, 27 Video-based tactics training (VTT), 180, 190 Video-based tracking (VBT), 64 Video clips, 207 Video recordings, 184 Virtual reality (VR), 166, 209 Visualization, 175 Volleyball, 11, 114, 131

U UK, 19 Uniqueness, 35 US, 21

W Water polo, 31, 103 Weighted kappa, 49 West Germany, 103 White box models, 96 Winner-loser paradigm, 90 Workflows, 228

V Validation, 38, 175 Validation of observational systems, 37 Validation of tracking systems, 70 Validity, 38

X Xy-position, 76