A dynamical analysis of tennis: concepts and data

Henri Cochet's theory of angles in tennis (1933) reveals a new facet of anticipation

In this study, we tested the theory of angles that was proposed almost a century ago by the tennis player Henri Cochet. This theory proposes that expert tennis players should position themselves on the bisector of the angle of the opponent's possibilities in order to optimize shot return, suggesting a geometric occupation of the court relative to the opponent's affordances; namely what he/she is capable of doing. We tested this hypothesis by analysing player and ball positioning data from professional tennis matches recorded with a Hawk-Eye system. We compared this hypothesis with two alternative computational and probabilistic hypotheses which would consist in positioning oneself on the average or the median of the shots usually played from a given location. The results show that expert tennis players apply the principles of the theory of angles and thus confirm Henri Cochet's intuition. That is, for lateral court positioning, a geometric strategy is deemed optimal by expert players. It also appears that the more experienced the players are, the more precise their application of this strategy becomes.

Badminton as a dynamic system - A new method for analyzing badminton matches based on perturbations

This study presents a method for analysing badminton matches based on the concept of perturbations. We transfer this principle to a badminton rally and describe the decisive shot, which turns a balanced situation into an advantage for one team or one player. Our paper proposes an observational system, which models the decisive shots by using four consecutive actions: impulse (the perturbation), follow-up, survival, and convert. To test the objectivity of the operationalization, independent raters analysed six matches in the singles disciplines of the 2022 World Championships. To evaluate rater agreement, Jaccard coefficient and Cohen's kappa were used. Results show an agreement in identifying impulses of J(R1, R2) = .80, while the agreement in classifying the impulse type (positive/negative) reached κ = .70. A comparison of this perturbation-based analysis and last shot analyses shows significantly different results. Direct errors usually occur in the midcourt (56.4%), whereas most negative perturbations originate from the backcourt (40.0%). In contrast to direct winners, mostly originating from a smash (45.5%), most positive perturbations are created by net shots (30.1%). We argue that our method can be complementary to common last shot analyses and provides a possibility to describe players' strengths and weaknesses in more detail.

Change-of-Direction Speed Assessments and Testing Procedures in Tennis: A Systematic Review

ABSTRACT

Schneider, C, Rothschild, J, and Uthoff, A. Change-of-direction speed assessments and testing procedures in tennis: a systematic review. J Strength Cond Res 37(9): 1888-1895, 2023-Change-of-direction speed (CODS) plays an essential role in tennis match play, and CODS performance is, therefore, commonly assessed and monitored in tennis players. Thus, the aim of this systematic review was to describe test characteristics, performance metrics, test-retest reliability, construct validity, and test outcomes of tests that are used to assess CODS in tennis players. A literature search conducted on PubMed and SPORTDiscus yielded 563 results. After applying the eligibility criteria, a total of 27 studies were included in the present review. Ten unique CODS tests were identified. 505 test variations were most frequently used across all studies, and total time required to complete the test was the predominant performance metric investigated. Intrasession test-retest reliability ranged from "moderate" to "excellent." Intersession test-retest reliability as well as the effects of tennis performance, sex, and age on CODS performance were unclear given the subject demographics and the limited number of studies that investigated these aspects. In conclusion, most studies included CODS tests that exhibit longer COD entry and total distances but similar COD angles to those seen during tennis match play. All CODS tests have at least "moderate" intrasession test-retest reliability. However, to improve CODS assessment methods and to increase our current understanding of CODS performance in tennis players, there is a need to conduct more research on the intersession test-retest reliability, construct validity, and the effects of sex, age, and tennis performance and to investigate other performance metrics that might provide additional insights into CODS (e.g., phase-specific performance variables).

Elite male table tennis matches diagnosis using SHAP and a hybrid LSTM-BPNN algorithm

This study adopts a new approach, SHapley Additive exPlanation (SHAP), to diagnose the table tennis matches based on a hybrid algorithm, namely Long Short-Term Memory-Back Propagation Neural Network (LSTM-BPNN). 100 male singles competitions (8535 rallies) from 2019 to 2022 are analyzed by a hybrid technical-tactical analysis theory, which hybridizes the double three-phase and four-phase evaluation theories. A k-means cluster analysis is conducted to classify 59 players' winning rates into three levels (high, medium, and low). The results show that LSTM-BPNN has excellent performance (MSE = 0.000355, MAE = 0.014237, RMSE = 0.018853, and [Formula: see text] = 0.988311) compared with six typical artificial intelligence algorithms. Using LSTM-BPNN to calculate the SHAP value of each feature, the global results find that the receive-attack and serve-attack phases of the ending match have essential impacts on the mutual winning probabilities. Finally, case applications show that the SHAP can directly obtain each feature importance on one or more matches, which is more objective and reliable than the traditional simulation method. This research explores an innovative way to understand and analyze matches, and these results have implications for the performance analysis of table tennis and related racket sports.

Exploring the relationship between kinematic variability and fatigue development during repetitive lifting

To investigate the variability-fatigue and repeaters-replacers hypotheses, motor variability (MV) and indicators of fatigue were assessed during repetitive lifting. Eighteen participants performed sequential repetitive bouts of lifting divided into a short bout, and three phases of a prolonged bout until volitional fatigue (or until a 1-h time limit). Whole-body kinematics were collected to calculate variability in three-dimensional joint angles and in continuous relative phase (CRP) of sagittal joint angle couplings, which were summed for the upper and lower body, and whole-body. Excellent individual consistency (ICC = 0.95-0.97) was demonstrated across lifting bouts as fatigue developed. Therefore, strong evidence was obtained for MV as an individual trait in support of the repeaters-replacers hypothesis. Associations were found for endurance and baseline effort with lower body variability, while no associations were found for rate of fatigue. Thus, some support was found for the variability-fatigue hypothesis which suggests that repeaters are less fatigue-resistant than replacers.

Integrating physical and tactical factors in football using positional data: a systematic review

Background

Positional data have been used to capture physical and tactical factors in football, however current research is now looking to apply spatiotemporal parameters from an integrative perspective. Thus, the aim of this article was to systematically review the published articles that integrate physical and tactical variables in football using positional data.

Methods and Materials

Following the Preferred Reporting Item for Systematic Reviews and Meta-analyses (PRISMA), a systematic search of relevant English-language articles was performed from earliest record to August 2021. The methodological quality of the studies was evaluated using the modified Downs and Black Quality Index (observational and cross-sectional studies) and the Physiotherapy Evidence Database (PEDro) scale (intervention studies).

Results

The literature search returned 982 articles (WoS = 495; PubMed = 232 and SportDiscus = 255). After screening, 26 full-text articles met the inclusion criteria and data extraction was conducted. All studies considered the integration of physical and tactical variables in football using positional data (n = 26). Other dimensions were also reported, such as psychophysiological and technical factors, however the results of these approaches were not the focus of the analysis (n = 5). Quasi-experimental approaches considered training sets (n = 20) and match contexts (n = 6). One study analysed both training and play insights. Small sided-games (SSG) were the most common training task formats in the reviewed studies, with only three articles addressing medium-sided (MSG) (n = 1) and large-sided games (LSG) (n = 2), respectively.

Conclusions

Among the current systematic review, the physical data can be integrated by player's movement speed. Positional datasets can be computed by spatial movement, complex indexes, playing areas, intra-team and inter-team dyads. Futures researches should consider applying positional data in women's football environments and explore the representativeness of the MSG and LSG.

Football Match Dynamics Explored by Recurrence Analysis

A widely accepted notion of football matches in performance analysis (PA) is to consider them as dynamic interaction processes with emerging behaviors. The description and analysis of these processes requires specific methods. Recurrence analysis is a technique for analyzing complex systems in many domains like astrophysics, earth sciences, engineering, biology, cardiology, and neuroscience. Its general concept is to examine the recurrence behavior of a system, as in when, how often and how close its trajectory in a phase space returns to a previous state. The aim of the study is to apply recurrence analysis to football matches. Positional data from 21 football matches of a German Bundesliga team were examined. The phase space was made up of the field players' x,y-positions at each second of the match. For each pair of seconds, the average distance of all the players between their positions at these two time points was calculated. Recurrence plots (RPs) were obtained by color-coding these distances. With a recurrence threshold of rt = 9 m and a minimum line length of lmin = 3 s, general recurrence parameters were calculated to characterize the individual recurrence behaviors of each match. Three football-specific recurrence parameters were defined to represent recurrence properties of open play. RPs showed commonalities (typical features indicating set plays and continuous gameplay) as well as unique structures during each match (number, distribution, and sequence of typical features). The recurrence parameters showed several significant correlations with traditional performance indicators like number of goals and passes completed, e.g., the correlation between number of goals and recurrence rate is r = -0.622 (p = 0.003). By extending the sample and design of recurrence studies, there is great potential for recurrence analysis to improve both the practical and theoretical potential of performance analysis.

The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind

This article presents a brief retrospective on the Haken-Kelso-Bunz (HKB) model of certain dynamical properties of human movement. Though unanticipated, HKB introduced, and demonstrated the power of, a new vocabulary for understanding behavior, cognition and the brain, revealed through a visually compelling mathematical picture that accommodated highly reproducible experimental facts and predicted new ones. HKB stands as a harbinger of paradigm change in several scientific fields, the effects of which are still being felt. In particular, HKB constitutes the foundation of a mechanistic science of coordination called Coordination Dynamics that extends from matter to movement to mind, and beyond.

Identification, Computational Examination, Critical Assessment and Future Considerations of Spatial Tactical Variables to Assess the Use of Space in Team Sports by Positional Data: A Systematic Review

The aim of the review was to identify the spatial tactical variables used to assess the use of space in team sports using positional data. In addition, we examined computational methods, performed a critical assessment and suggested future considerations. We considered four electronic databases. A total of 3973 documents were initially retrieved and only 15 articles suggested original spatial variables or different computation methods. Spatial team sport tactical variables can be classified into 3 principal types: occupied space, total field coverage by several players; exploration space, the mean location (±standard deviations in X- and Y-directions) of the player/team during the entire game; and dominant/influence space, the region the players can reach before any other players. Most of the studies, i.e., 55%, did not include goalkeepers (GKs) and total playing space to assess occupied space, however, several proposed new variables that considered that all playing space could be “played” (i.e. effective free-space, normalized surface area). Only a collective exploration space variable has been suggested: the major range of the geometrical centre (GC). This suggestion could be applied to assess collective exploration space variables at a sub-system level. The measurement of the dominant/influence space has been based on the Voronoi region (i.e. distance d criteria), but several studies also based their computation on the time (t). In addition, several weighted dominant areas have been suggested. In conclusion, the use of spatial collective tactical variables considering the principal structural traits of each team sport (e.g. players of both teams, the location of the space with respect to the goal, and the total playing space) is recommended.

Analysis of serve and serve return on different surfaces in elite tennis players

Abstract The aim of the current study was to analyze players’ interactions in serve and serve return situations and examine the way points were decided due to players’ positions and surfaces. Fourteen ATP 1000 tournament matches were analyzed (7 on hard surface; 7 on clay surface). The type of surface did not affect the way points ended (χ²=9.26; p > 0.05) but did influence serve return vertical positioning (χ²=270.86; p < 0.001). The return positioning, both lateral (χ²=92.68; p < 0.001 on deuce side - χ² = 78.98; p < 0.001 on advantage side) and vertical (χ²=33.59; p < 0.001), and the type of serve (χ²=45.13; p < 0.001) affected the way points were decided. The results from the present study suggest that tennis players should use, or at least seek, strategies based on aggressiveness and consistency of the 1st serve and also indicate that in the 2nd serve return, players are more offensive, and that on hard surfaces, players stand a few steps inside the court to return the serve, differently from clay surfaces. It recommended that serve returns should combine aggression, by inside the court positioning, and accuracy.

The tactics of successful attacks in professional association football: large-scale spatiotemporal analysis of dynamic subgroups using position tracking data

Association football teams can be considered complex dynamical systems of individuals grouped in subgroups (defenders, midfielders and attackers), coordinating their behaviour to achieve a shared goal. As research often focusses on collective behaviour, or on static subgroups, the current study aims to analyse spatiotemporal behaviour of dynamic subgroups in relation to successful attacks. We collected position tracking data of 118 Dutch Eredivisie matches, containing 12424 attacks. Attacks were classified as successful (N = 1237) or non-successful (N = 11187) based on the potential of creating a scoring opportunity. Using unsupervised machine learning, we automatically identified dynamic formations based on position tracking data, and identified dynamic subgroups for every timeframe in a match. We then compared the subgroup centroids to assess the intra- and inter-team spatiotemporal synchronisation during successful and non-successful attacks, using circular statistics. Our results indicated subgroup-level variables provided more information, and were more sensitive to disruption, in comparison to team-level variables. When comparing successful and non-successful attacks, we found decreases (p < .01) in longitudinal inter- and intra-team synchrony of interactions involving the defenders of the attacking team during successful attacks. This study provides the first large-scale dynamic subgroup analysis and reveals additional insights to team-level analyses.

Collective Variables and Task Constraints in Movement Coordination, Control and Skill

In this paper we review studies that have identified collective variables (order parameters) in movement coordination, control and skill with emphasis on whole-body multiple joint degree of freedom (DF) tasks. Collective variables of a dynamical system have been proposed formally and informally from a diverse set of perceptual-motor tasks, from which we emphasize: bimanual coordination, locomotion (pedalo, walking, running, bicycle riding), roller ball task, static (quiet standing) and dynamic (moving on a ski-simulator) balance, grasping, and juggling. Several types of candidate collective variables have been identified, including: relative phase, frequency ratio, number of hands active in grasping, synchrony, learning rate and relative timing. There is a strong influence of the task goal in determining the collective variable that can be body or environment relative. The emergence of the task relevant collective variable is typically in the early stage of skill learning where subjects through practice adapt movement organization to realize a never previously produced movement coordination pattern. Throughout, the paper elaborates on open theoretical, experimental and analysis issues for collective variables in the context of task constraints and Bernstein's (1967) view of skill acquisition as learning to master redundant DF.

The Winning Probability of a Game and the Importance of Points in Tennis Matches

Purpose: This study builds a stochastic model of a discrete-time Markov chain (DTMC) that fits well with a dataset of professional playing records. Methods: The point-by-point dataset of Men's single matches played in the Association of Tennis Professionals (ATP) tour from 2011 to 2015 is analyzed. A long-debated assumption on the iid-ness in the point winning probability of the server is statistically tested. A DTMC model is then developed to analyze the dataset further. Results: The statistical test results indicate that the identicality of point winning probabilities is not a valid assumption. For example, the server's point winning probability from scores 40:0, 30:15, 15:30, and 0:40 are significantly different. On the other hand, the independence is a generally valid assumption except for 40:15 where who won the previous point influences the point winning probability. Game winning probabilities and the importance of each point in winning a game are analyzed using the DTMC model by court surfaces and player groups of the different levels of serve effectiveness. Conclusion: Extensive empirical validation concludes unsealed debates over the stochastic models for tennis. The presented results reveal interesting properties in professional tennis matches.

A systematic review of collective tactical behaviour in futsal using positional data

Although many studies on collective tactical behaviour have been published in the last decade, no study has revised and summarized the findings provided for futsal. The main aim of this systematic review was to identify and discuss the geometrical centre (GC), distance and area tactical variables used to assess team behaviour in futsal. In addition, it summarizes the findings on the tactical response during futsal competition and training. A systematic review of the relevant articles provided on futsal was carried out using seven electronic databases (SPORTDiscus, ProQuest, Cochrane Plus, Scopus, Google Scholar, PubMed and Web of Science) until September 25, 2019. From a total of 1,209 studies initially found, 12 were included in the qualitative synthesis. There were some trends in the analysis of positional data in futsal with the most relevant situations analysed being 1 vs 1 and 5 vs 4+Goalkeeper. The distances and angles between two points were the most assessed tactical variables. Five types of distance variables were used to assess collective tactical behaviour in futsal: GC-GC, GC-player, player-player, player-ball and player-space. Pressure (GC-GC) was greater in shots on goal than in tackles during professional futsal matches. Area variables were reduced to occupied space, exploration space and dominant area. Occupied space was measured only during competition while the dominant area was measured only during training sessions. The surface area and dominant regions were greater when players were attacking in comparison to when they were defending. In addition, two non-linear techniques (i.e. relative phase and entropy) were applied to analyse synchronisation and complexity and regularity or predictability. Defenders were highly synchronous, while attackers tried to break this coordination to achieve possibilities for action. Task constraints are suitable to induce different regularity patterns. This review is an opportunity to develop studies aimed at bridging the gap in collective tactical behaviour in futsal.

Combat as an Interpersonal Synergy: An Ecological Dynamics Approach to Combat Sports

In combat sports, athletes continuously co-adapt their behavior to that of the opponent. We consider this interactive aspect of combat to be at the heart of skilled performance, yet combat sports research often neglects or limits interaction between combatants. To promote a more interactive approach, the aim of this paper is to understand combat sports from the combined perspective of ecological psychology and dynamic systems. Accordingly, combat athletes are driven by perception of affordances to attack and defend. Two combatants in a fight self-organize into one interpersonal synergy, where the perceptions and actions of both athletes are coupled. To be successful in combat, performers need to manipulate and take advantage of the (in)stability of the system. Skilled performance in combat sports therefore requires brinkmanship: combatants need to be aware of their action boundaries and purposefully act in meta-stable regions on the limits of their capabilities. We review the experimental literature to provide initial support for a synergetic approach to combat sports. Expert combatants seem able to accurately perceive action boundaries for themselves and their opponent. Local-level behavior of individual combatants has been found to lead to spatiotemporal synchronization at the global level of a fight. Yet, a formal understanding of combat as a dynamic system starting with the identification of order and control parameters is still lacking. We conclude that the ecological dynamics perspective offers a promising approach to further our understanding of skilled performance in combat sports, as well as to assist coaches and athletes to promote optimal training and learning.

Unlocking the potential of big data to support tactical performance analysis in professional soccer: A systematic review

In professional soccer, increasing amounts of data are collected that harness great potential when it comes to analysing tactical behaviour. Unlocking this potential is difficult as big data challenges the data management and analytics methods commonly employed in sports. By joining forces with computer science, solutions to these challenges could be achieved, helping sports science to find new insights, as is happening in other scientific domains. We aim to bring multiple domains together in the context of analysing tactical behaviour in soccer using position tracking data. A systematic literature search for studies employing position tracking data to study tactical behaviour in soccer was conducted in seven electronic databases, resulting in 2338 identified studies and finally the inclusion of 73 papers. Each domain clearly contributes to the analysis of tactical behaviour, albeit in - sometimes radically - different ways. Accordingly, we present a multidisciplinary framework where each domain's contributions to feature construction, modelling and interpretation can be situated. We discuss a set of key challenges concerning the data analytics process, specifically feature construction, spatial and temporal aggregation. Moreover, we discuss how these challenges could be resolved through multidisciplinary collaboration, which is pivotal in unlocking the potential of position tracking data in sports analytics.

Identification, Computational Examination, Critical Assessment and Future Considerations of Distance Variables to Assess Collective Tactical Behaviour in Team Invasion Sports by Positional Data: A Systematic Review

The aim of the study was the identification, computational examination, critical assessment and future considerations of distance variables to assess collective tactical behaviour in team invasion sports by positional data. A total of 3973 documents were initially retrieved. Finally, 72 articles met the inclusion criteria, but only 26 suggested original tactical variables based on the distance variables. The distance variables can be classified into player–player, player–space, player–ball, and Geometrical Centre (GC)–GC /player/space/goal. In addition, several nonlinear techniques have been used to analyse the synchronisation and predictability of the distance variables in team invasion sports. Player–opponent distance is of special interest in those sports in which man-marking is commonly used, and in the micro-structure close to scoring situations in all sports. In addition, player–player distances are used to measure the length and the width of the team and player–GC distance to assess the dispersion of the team. Player–space distances have been measured to assess the distance of the player/team-line to relevant areas of the playing space. Several techniques have been applied to analyse the synchronisation (i.e., Hilbert transformation and cluster analyses) and the complexity and regularity or predictability (i.e., approximate entropies, sample entropy, cross-sample entropy and average mutual information) of the distance variables in team invasion sports, revealing the lack of consensus. Although the distance variables may be interesting tactical variables when considered in isolation, it would be enriching to analyse the relationship among these variables.

Different Marks in the Pitch Constraint Youth Players' Performances During Football Small-sided Games

Purpose: This study aimed to compare players' performances when manipulating the external markings of the pitch during football small-sided games. Methods: Ten under-15 players performed a 5-a-side (plus goalkeepers) under three conditions: (i) Lines, the game was played in a pitch in which the external boundaries were painted with full lines; (ii) Dashed, the game was played in a pitch in which the external boundaries were painted with dashed lines; (iii) Corners, the game was played in a pitch were the external boundaries were delimited by one marker at each pitch corner. Players' positional data was used to compute tactical and time-motion variables. Also, technical analysis was comprised using video footage. Results: Results showed similar tactical, physical and technical performances between the Lines and Dashed conditions. In contrast, the Lines condition showed small higher effects than Corners scenario in the time spent synchronized in longitudinal and lateral displacements, game pace, total distance covered, distance covered while jogging, number successful dribbles and shots on target. The Lines scenario has also revealed a lower effective playing space, distance covered at walking and running and a lower number of passes (small effects) compared to Corners. Conclusions: These results highlight that these changes in informational perception constraints modify players movement behavior. Accordingly, pitches with more visible boundaries were likely to decrease team dispersion, which may optimize team synchrony and technical performances, while decreasing the distance covered at higher speeds. Coaches may use this information to modify the types of pitch external boundaries markings, exposing the players to different environmental information.

A Systematic Review of Collective Tactical Behaviours in Football Using Positional Data

BACKGROUND

Performance analysis research in association football has recently cusped a paradigmatic shift in the way tactical behaviours are studied. Based on insights from system complexity research, a growing number of studies now analyse tactical behaviours in football based on the collective movements of team players.

OBJECTIVE

The aim of this systematic review is to provide a summary of empirical research on collective tactical behaviours in football, with a particular focus on organising the methods used and their key findings.

METHODS

A systematic search of relevant English-language articles was performed on one database (Web of Science Core Collection) and one search engine (PubMed), based on PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-analyses) guidelines. The keywords 'football' and 'soccer' were each paired with all possible combinations of the following keywords: 'collective movement behaviour', 'collective behaviour', 'tactical behaviour', 'interpersonal coordination', 'space', 'Voronoi', 'synchronisation', 'tactical analysis', 'constraints', 'ecological dynamics', and 'dynamic positioning'. Empirical studies that were related to tactical analyses of footballers' positional data were sought for inclusion and analysis.

RESULTS

Full-text articles of 77 studies were reviewed. A total of 27 tactical variables were identified, which were subsequently organised into 6 categories. In addition to conventional methods of linear analysis, 11 methods of nonlinear analysis were also used, which can be organised into measures of predictability (4 methods) and synchronisation (7 methods). The key findings of the reviewed studies were organised into two themes: levels of analysis, and levels of expertise.

CONCLUSIONS

Some trends in key findings revealed the following collective behaviours as possible indicators of better tactical expertise: higher movement regularity; wider dispersion in youth players and shorter readjustment delay between teammates and opponents. Characteristic behaviours were also observed as an effect of playing position, numerical inequality, and task constraints. Future research should focus on contextualising positional data, incorporating the needs of coaching staff, to better bridge the research-practice gap.

Effects of the pitch configuration design on players' physical performance and movement behaviour during soccer small-sided games

This study aimed to identify the effects of different pitch configurations on youth players positional and physical performances. Forty players participated in a Gk + 5vs5 + Gk small-sided game under four conditions: regular condition (regular), pitch with the direction of competitive matches; sided condition (sided), goals were changed to width; different pitch orientation (≠orientation), performed in side-to-side line compared to competitive matches; dynamic pitch (dynamic), boundaries were randomly changed every minute by: regular pitch; decrease 6 m width; diamond shape. The following variables were considered: players' effective playing space, distance between teammates' dyads time spent synchronized, average speed and a ratio between the distance covered at different intensities and distance covered while recovering. Overall, players exhibited better performances in pitches that are more representative of the environmental information seen during competitive matches (regular and ≠orientation). However, coaches may also use different boundary conditions to promote the players' ability to adapt to different context information.

Effects of pitch spatial references on players' positioning and physical performances during football small-sided games

The aim of this study was to identify the effects of adding spatial references during football small-sided games in youth players' tactical and physical performance. Twelve under-15 players performed a Gk+ 6v6+ Gk game under two playing conditions: (i) without spatial references (CONTROL condition); (ii) with spatial references, by dividing equally the pitch into three corridors and three sectors (experimental situation, LINES). Players' positional data was used to compute time-motion and tactical-related variables. The results revealed that performance under LINES situation increased the regularity in the zones occupied (~14%, Cohen's d: 0.5; ±0.3; p = 0.003) and in the distance between teammates' dyads (~19%, 0.9; ±0.2; p < 0.001). Oppositely, LINES condition decreased the longitudinal synchronization of players' displacements (0.4; ±0.2; p = 0.002), players' average speed (0.5; ±0.3; p = 0.002) and distance covered at lower (0.9; ±0.3; p < 0.001) and moderate speed (0.5; ±0.3; p < 0.001). Adding spatial references seems to promote a more structured pattern of play and increase positional regularity. However, coaches should be aware that this constraint may decrease the synchronization between players. Overall, these findings may be generalized to most invasion team sports.

Speed synchronization, physical workload and match-to-match performance variation of elite football players

This study aimed to: (i) examine whether the speed synchronization and physical performance of an elite football team changed between the first and the second half, using match time blocks of 15-min, and (ii) explore the match-to-match variation of players' speed synchronization performance. Twenty-eight outfield elite footballers participated in 51 official matches. Positional data were gathered and used to calculate the total distance covered as a physical workload indicator. For all the outfield teammate dyad combinations (45 pairs), it was processed the percentage of time that players' speed was synchronized during walking, jogging and running using relative phase (Hilbert Transform). Also, the match-to-match variation of the players' speed synchronization, expressed in coefficient of variation was computed. The differences in the total distance covered from all players within the different match's time block periods revealed a moderate decrease in the distance covered in the last 15-min of the match compared to the first 15-min (-6.5; ±1.07%, most likely: change in means with 95% confidence limits). However, when compared the last minutes from both halves a small increase was observed (2.7; ±1.2%, likely) from first to second half. The synchronization of the players' speed displacements revealed small to moderate decreases in the % of synchronization in the second half periods for the jogging and running speed, while the opposite was found for the walking speed (~13 to 24% more, most likely). The playing position analysis for the walking zone showed similar trends between the groups, with small to moderate higher values in the second half, with the exception of [30'-45'] vs [75'-90'] in the midfielder's dyads and in [15'-30'] vs [60'-75'] match periods for forwards. Similar trend was found during the running speed, in which small to moderate higher synchronization was found during the first half periods, with the exception of [15'-30'] vs [60'-75'] and [30'-45'] vs [75'-90'] in midfielder's dyads. Regarding to the match-to-match variation of the players' speed synchronization, overall results showed small to moderate increases in coefficient of variation during jogging and running displacements from the beginning to the end of the match (32.1; ±13.2% increase in jogging and 26.2; ±10.5% in running, both comparisons most likely). The higher distance covered during most of the first half periods and the higher dyadic synchronization at high speeds might have limited players' performance in the second half. In addition, the decrease trend in speed synchronization during the second half periods might have resulted from accumulated muscular and mental fatigue towards the match. Within, the match-to-match variation in tactical-related variables increased across the match duration, with especial focus in the midfielder dyads. Dyadic speed synchronization might provide relevant information concerning the individual and collective performance.

Current Approaches to Tactical Performance Analyses in Soccer Using Position Data

Tactical match performance depends on the quality of actions of individual players or teams in space and time during match-play in order to be successful. Technological innovations have led to new possibilities to capture accurate spatio-temporal information of all players and unravel the dynamics and complexity of soccer matches. The main aim of this article is to give an overview of the current state of development of the analysis of position data in soccer. Based on the same single set of position data of a high-level 11 versus 11 match (Bayern Munich against FC Barcelona) three different promising approaches from the perspective of dynamic systems and neural networks will be presented: Tactical performance analysis revealed inter-player coordination, inter-team and inter-line coordination before critical events, as well as team-team interaction and compactness coefficients. This could lead to a multi-disciplinary discussion on match analyses in sport science and new avenues for theoretical and practical implications in soccer.

Interpersonal coordination analysis of tennis players from different levels during official matches

The purpose of this study was to assess the interpersonal coordination during official male tennis matches in players of different skill levels. Players' trajectories of three levels (Juvenile, ATP-Future, ATP-250) were obtained using video-based tracking system. A vector coding technique was applied to obtain players' interpersonal coordination in four coordination patterns: "anti-phase", "in-phase", "serving player phase" and "returning player phase". These patterns allowed identification of the nature of the coupling and lead/lag relations between players. In all categories, players presented higher degree of "anti-phase" and "serving player phase" (when only the serving player is moving on the court or his opponent is moving with a time lag) coordination. Young players spent more time in "serving player phase" during lateral displacements than professional players. On the other hand, professional players spent more time in "returning player phase" (when only the returning player is moving on the court or his opponent is moving with a time lag) during antero posterior displacements, than young players. Interpersonal coordination did not change from the first to the second set of the match, showing that tennis players maintain their displacement characteristics and strategy, independently of proficiency level. The vector coding technique allowed to identify new coordination patterns in tennis, providing additional information about tennis dynamics and how players from different categories and proficiency levels behave during the matches.

Exploring how playing football with different age groups affects tactical behaviour and physical performance

The study aimed to compare footballers’ performances when playing with teammates and opponents from the same age group with performances when playing with teammates and opponents of different age groups. Three football matches were played: i) under-15 (U15) players played with each other; ii) under-17 (U17) players played with each other; and iii) players under the age of 15 and 17 played with each other in two equivalent mixed age teams. The players’ physical performance was measured using the distances covered at different speed categories and tactical behaviour was assessed using several positioning-derived variables. The results showed that, when playing in the mixed age condition, the U15 players increased the distance covered in sprinting intensity (18.1%; ±21.1%) and the U17 players increased the distance covered in jogging zones (6.8%; ±6.5%). The intra-team movement synchronization in longitudinal and lateral displacements was higher when U15 players confronted peers of the same age, in the first half (-13.4%; ±2.0%, -20.3%; ±5.7% respectively), and when U17 players confronting the mixed group, in both halves (-16.9%; ±2.5%, 9.8%; ±4.0% and 7.9%; ±5.7%, 10.6% ±4.4%, respectively). The differences between age groups and the mixed condition may be connected with the level of players’ tactical expertise and adaptive positioning according to the dynamic environmental information. In general, these results suggest that mixing the age groups may be useful to promote a wider range of training session stimuli in these young football players.

Positional synchronization affects physical and physiological responses to preseason in professional football (soccer)

This study aimed to identify changes in tactical, physical and physiological performances in large-sided games during the preseason of elite footballers. Thirty professional football players participated in several GK+8vs.8+GK large-sided games across the first four weeks of the season. Players were monitored by GPS units and heart rate monitors to quantify physical, physiological and tactical performances. The variables were compared according to the preseason period, players' positioning and professional experience. The training situation promoted similar physiological responses during the first and the last training period. However, players were revealed to have higher levels of positional synchronization during the last preseason period, indicating an improved tactical performance. Tactical variables seem to reflect the improvement of players' performance during the preseason, measured in large-sided games situation, while affecting both physical and physiological demands. These results highlight the potential of positioning derived variables, concurrently to physical and physiological variables, for football training optimization.

Interpersonal Coordination: Methods, Achievements, and Challenges

Research regarding interpersonal coordination can be traced back to the early 1960s when video recording began to be utilized in communication studies. Since then, technological advances have extended the range of techniques that can be used to accurately study interactional phenomena. Although such a diversity of methods contributes to the improvement of knowledge concerning interpersonal coordination, it has become increasingly difficult to maintain a comprehensive view of the field. In the present article, we review the main capture methods by describing their major findings, levels of description and limitations. We group them into three categories: video analysis, motion tracking, and psychophysiological and neurophysiological techniques. Revised evidence suggests that interpersonal coordination encompasses a family of morphological and temporal synchronies at different levels and that it is closely related to the construction and maintenance of a common social and affective space. We conclude by arguing that future research should address methodological challenges to advance the understanding of coordination phenomena.

Mental Fatigue and Spatial References Impair Soccer Players' Physical and Tactical Performances

This study examined the effects of mental fatigue and additional corridor and pitch sector lines on players' physical and tactical performances during soccer small-sided games. Twelve youth players performed four Gk+6vs6+Gk small-sided games. Prior to the game, one team performed a motor coordination task to induce mental fatigue, while the other one performed a control task. A repeated measures design allowed to compare players' performances across four conditions: (a) with mental fatigue against opponents without mental fatigue in a normal pitch (MEN), (b) with mental fatigue on a pitch with additional reference lines (#MEN); (c) without mental fatigue against mentally fatigued opponents on a normal pitch (CTR); and (d) without mental fatigue on a pitch with reference lines (#CTR). Player's physical performance was assessed by the distance covered per minute and the number of accelerations and decelerations (0.5–3.0 m/s²; > −3.0 m/s²). Positional data was used to determine individual (spatial exploration index, time synchronized in longitudinal and lateral directions) and team-related variables (length, width, speed of dispersion and contraction). Unclear effects were found for the physical activity measures in most of the conditions. There was a small decrease in time spent laterally synchronized and a moderate decrease in the contraction speed when MEN compared to the CTR. Also, there was a small decrease in the time spent longitudinally synchronized during the #MEN condition compared to MEN. The results showed that mental fatigue affects the ability to use environmental information and players' positioning, while the additional reference lines may have enhanced the use of less relevant information to guide their actions during the #MEN condition. Overall, coaches could manipulate the mental fatigue and reference lines to induce variability and adaptation in young soccer players' behavior.

The variable and chaotic nature of professional golf performance

In golf, unlike most other sports, individual performance is not the result of direct interactions between players. Instead decision-making and performance is influenced by numerous constraining factors affecting each shot. This study looked at the performance of PGA TOUR golfers in 2011 in terms of stability and variability on a shot-by-shot basis. Stability and variability were assessed using Recurrence Quantification Analysis (RQA) and standard deviation, respectively. About 10% of all shots comprised short stable phases of performance (3.7 ± 1.1 shots per stable phase). Stable phases tended to consist of shots of typical performance, rather than poor or exceptional shots; this finding was consistent for all shot categories. Overall, stability measures were not correlated with tournament performance. Variability across all shots was not related to tournament performance; however, variability in tee shots and short approach shots was higher than for other shot categories. Furthermore, tee shot variability was related to tournament standing: decreased variability was associated with better tournament ranking. The findings in this study showed that PGA TOUR golf performance is chaotic. Further research on amateur golf performance is required to determine whether the structure of amateur golf performance is universal.

Investigating the social behavioral dynamics and differentiation of skill in a martial arts technique

Coordinating interpersonal motor activity is crucial in martial arts, where managing spatiotemporal parameters is emphasized to produce effective techniques. Modeling arm movements in an Aikido technique as coupled oscillators, we investigated whether more-skilled participants would adapt to the perturbation of weighted arms in different and predictable ways compared to less-skilled participants. Thirty-four participants ranging from complete novice to veterans of more than twenty years were asked to perform an Aikido exercise with a repeated attack and response, resulting in a period of steady-state coordination, followed by a take down. We used mean relative phase and its variability to measure the steady-state dynamics of both the inter- and intrapersonal coordination. Our findings suggest that interpersonal coordination of less-skilled participants is disrupted in highly predictable ways based on oscillatory dynamics; however, more-skilled participants overcome these natural dynamics to maintain critical performance variables. Interestingly, the more-skilled participants exhibited more variability in their intrapersonal dynamics while meeting these interpersonal demands. This work lends insight to the development of skill in competitive social motor activities.

Temporal coordination between ground reaction forces generated by leading and trailing limbs for propulsion during double stance phase in human walking

Although it was reported that ground reaction forces (GRFs) are generated simultaneously by the leading and trailing limbs during the double stance phase, the finding was not examined by temporal analyses. Therefore, the purpose of the present study is to clarify how GRFs can act to propel the body in a forward direction during the double stance phase. GRFs were recorded during the double stance phase in eleven healthy volunteers. We calculated the instantaneous phase of the GRFs for vertical and anterior-posterior (AP) components, and then calculated the relative phase between the leading and trailing limbs for each component. The relative phase of the vertical component was approximately 180° (i.e., anti-phase), indicating that the lower limb transfers weight smoothly from the trailing limb to the leading limb. The relative phase of the AP component ranged from 40 to 55°, indicating that the AP component of the forces do not occur simultaneously, but instead has a lag. This finding suggests that the forces exerted by the leading and trailing limbs would temporally coordinate to propel the body in the forward direction.

Anisotropy and Antagonism in the Coupling of Two Oscillators: Concepts and Applications for Between-Person Coordination

Coupled oscillators provide a pertinent model approach to study between-person movement dynamics. While ample literature in this respect has considered the influence of external/environmental constraints and/or effects of a difference between the two agents' individual component dynamics (e.g., mismatch in natural frequency), recent studies also started to more directly consider the interaction per-se. The current perspective paper sets forth that while movement coordination dynamics has mainly been studied alongside a model in which the coupling is considered isotropic (i.e., symmetrical; both oscillators coupled to same degree) or strictly unidirectional (e.g., for moving to a given external rhythm), between-agent coupling involves a natural anisotropy: components influence each other bidirectionally to different degrees. Furthermore, recent research from different areas has considered so-called antagonistic or "competitive" coupling, which refers to the idea that one component is positively coupled to the other (attractive interaction), while the coupling in the other direction is negative (repulsive interaction). Although the latter would be rather tricky to address in within-person coordination, it does have strong applications and implications for between-person dynamics, for instance in the study of competitive interactions in sports situations (e.g., attacker-defender) and conflicting social (movement) interactions. The paper concludes by offering a conceptual framework and perspectives for future studies on the dynamic anisotropic nature of the interaction in between-person contexts.

Analysis of the distances covered and technical actions performed by professional tennis players during official matches

The purpose of this study was to analyse the physical and technical performances of professional tennis players during official matches. The trajectories of eight players were obtained during matches, using an automatic tracking method. The distances covered and technical performances were analysed for the first and second sets. The athletes covered (mean ± standard deviation) a total of 1702.4 ± 448.2 m in the first set, 1457.6 ± 678.1 m in the second set and 3160.0 ± 880.1 in the entire match. No differences were found between the sets for the physical variables (lateral and forward displacements, distance covered per rally, per game and per set, and the percentage of time spent in each range of velocity). However, the distances covered by the athletes during the rallies in which they were serving (median = 5.2; interquartile range (IQR) = 6.7 m) were statistically smaller than when they were returning (median = 6.2; IQR = 7.7 m). Forehand ground stroke proficiency decreased from the first (mean ± standard deviation: 75.2 ± 4.11%) to the second set (mean ± standard deviation = 65.5 ± 14.3%). In conclusion, tennis players did not present reduced physical performance from the first to the second set.

Preparatory Body State before Reacting to an Opponent: Short-Term Joint Torque Fluctuation in Real-Time Competitive Sports

In a competitive sport, the outcome of a game is determined by an athlete’s relationship with an unpredictable and uncontrolled opponent. We have previously analyzed the preparatory state of ground reaction forces (GRFs) dividing non-weighted and weighted states (i.e., vertical GRFs below and above 120% of body weight, respectively) in a competitive ballgame task and demonstrated that the non-weighted state prevented delay of the defensive step and promoted successful guarding. However, the associated kinetics of lower extremity joints during a competitive sports task remains unknown. The present study aims to investigate the kinetic characteristics of a real-time competitive sport before movement initiation. As a first kinetic study on a competitive sport, we initially compared the successful defensive kinetics with a relatively stable preparatory state and the choice-reaction sidestep as a control movement. Then, we investigated the kinetic cause of the outcome in a 1-on-1 dribble in terms of the preparatory states according to our previous study. The results demonstrated that in successful defensive motions in the non-weighted state guarding trial, the times required for the generation of hip abduction and three extension torques for the hip, knee, and ankle joints were significantly shortened compared with the choice-reaction sidestep, and hip abduction and hip extension torques were produced almost simultaneously. The sport-specific movement kinetics emerges only in a more-realistic interactive experimental setting. A comparison of the outcomes in the 1-on-1 dribble and preparatory GRF states showed that, in the non-weighted state, the defenders guarded successfully in 68.0% of the trials, and the defender’s initiation time was earlier than that in the weighted state (39.1%). In terms of kinetics, the root mean squares of the derivative of hip abduction and three extension torques in the non-weighted state were smaller than those in the weighted state, irrespective of the outcome. These results indicate that the preparatory body state as explained by short-term joint torque fluctuations before the defensive step would help explain the performance in competitive sports, and will give insights into understanding human adaptive behavior in unpredicted and uncontrolled environments.

The preparatory state of ground reaction forces in defending against a dribbler in a basketball 1-on-1 dribble subphase

We previously demonstrated the relationship between sidestepping performance and the preparatory state of ground reaction forces (GRFs). The present study investigated the effect of the preparatory state of GRFs on defensive performance in 1-on-1 subphase of basketball. Ten basketball players participated in 1-on-1 dribble game of basketball. The outcomes (penetrating and guarding) and the preparatory state of GRFs (non-weighted and weighted states, i.e. vertical GRFs below and above 120% of body weight, respectively) were assessed by separating the phases. In the non-weighted state and the weighted state to determine the outcome, the probability of successful guarding was 78.8% and 29.6%, respectively. The non-weighted state prevented delay of the defensive step in the determination phase. Both the non-weighted and weighted states, immediately before the determination phase, were likely to change to the weighted state in the determination phase; during this time, the defender's preparatory state would be destabilised, presumably by the dribbler's movement. These results revealed that the preparatory GRFs before the defensive step help to explain the outcome of the 1-on-1 subphase, and suggest a better way to prevent delaying initiation of the defensive step and thereby to guard more effectively against a dribbler.

The effects of congested fixtures period on tactical and physical performance in elite football

The aim of this study was to examine the physical and tactical performances of a professional football team under congested and non-congested fixture periods. Six home matches of an English professional football team were analysed during competitive season (3 matches distancing three days from the previous fixture and 3 matches distancing six or more days from the previous fixture). Players' physical performances were measured by the total distance covered and distance covered at different speed categories. Tactical performances were measured by the percentage of time of players' movement synchronisation of lateral and longitudinal displacements. This variable was calculated considering all the possible pairs of outfield players, for the overall match and at different speed categories. Results showed no differences in the physical performance, although players' spent more time synchronised during the non-congested fixtures compared to congested fixtures, both for lateral (41.26% to 38.51%, ES: -0.3, P < 0.001) and longitudinal displacements (77.22% to 74.48%, ES: -0.5, P < 0.001). These coordination differences were particularly evident at the lower speed categories and in dyads composed by positions that tend to be further apart during the match, typically central and wing positioned players. Tactical performance seems to be affected by fixtures distribution, with players' spending more time synchronised during the non-congested fixtures. As players' cover the same amount of distance at similar intensities in both fixtures distribution, this reduction of synchronisation may be associated with an increased perception of fatigue and consequent adaptation strategies.

The relevance of the cross-wavelet transform in the analysis of human interaction - a tutorial

This article sheds light on a quantitative method allowing psychologists and behavioral scientists to take into account the specific characteristics emerging from the interaction between two sets of data in general and two individuals in particular. The current article outlines the practical elements of the cross-wavelet transform (CWT) method, highlighting WHY such a method is important in the analysis of time-series in psychology. The idea is (1) to bridge the gap between physical measurements classically used in physiology - neuroscience and psychology; (2) and demonstrates how the CWT method can be applied in psychology. One of the aims is to answer three important questions WHO could use this method in psychology, WHEN it is appropriate to use it (suitable type of time-series) and HOW to use it. Throughout these explanations, an example with simulated data is used. Finally, data from real life application are analyzed. This data corresponds to a rating task where the participants had to rate in real time the emotional expression of a person. The objectives of this practical example are (i) to point out how to manipulate the properties of the CWT method on real data, (ii) to show how to extract meaningful information from the results, and (iii) to provide a new way to analyze psychological attributes.