This work is one of the first studies in a new interdisciplinary research field in which team sports are considered from the perspective of collective behavior. Previous studies are scarce, but in one nice recent study, Yokoyama and Yamamoto [9] analyzed spatiotemporal coupling and synchronization of humans playing a 3 vs. 1 football possession game. Our current study goes beyond previous attempts and the coordination of all the players (and also of the ball) are analyzed in formal football
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## Chaos, Solitons & Fractals

# Collective movement analysis reveals coordination tactics of team players in football matches

Author links open overlay panelRuiMarcelinoab, JaimeSampaioac, GuyAmichaydef, BrunoGonçalvesghi, Iain D.Couzindef, MátéNagydefjk

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## Highlights

- •
  Complex collective actions in team sport.

- •
  High spatiotemporal data from professional football matches.

- •
  Individual and group-level behavioural patterns.

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  Characterising dynamics of winning and losing teams.

## Abstract

Collective behavior is a hallmark of every living system and utilizing methods from statistical physics (such as correlation functions) could aid in our understanding of their underlying rules. We analyzed five football (soccer) matches as this game provides a unique but yet mostly unexplored example to study a system of collective cooperation and competition. The aim of our study was to analyze the collective motion patterns exhibited by football players to unfold the underlying coordination among them in order to understand collective strategies associated with team performance. By analyzing pairwise relationships among all the players using spatio-temporal correlation functions we reveal that there exist identifiable collective dynamics that characterize winning and losing teams. Using our metric we find clear and robust differences between the players, indicating a difference in their behavior and their interactions. And this enables us to assign a unique behavioral pattern - a ‘fingerprint’ - for each individual and for each team. Furthermore, we reveal there exists a relationship between the market value of the players and the metrics introduced here, suggesting that these metrics could potentially serve as valuable performance indicators in the future, with applications ranging from talent identification to player scouting. In a broader context team sports could open up new directions for quantitative analyses of human collective behavior.

## Introduction

Collective behavior characterizes the way in which an individual's activity is influenced by other members of its group, and in turn how they influence it [1]. In a system consisting of many similar ‘units’ [2] (such as fish in a shoal, birds in a flock, or players of a team sport [3]) the interactions between them can be simple (attraction/repulsion) or more complex, and can occur between neighbours in space [4] or through an underlying social network [5]. In human behavior joint action is ubiquitous, such as during pedestrian traffic, teamwork ( e.g. bucket brigade or human chain), team sports, or group dance, where movements are adjusted according to the ongoing actions of others to fit the demands of the tasks at hand [6], [7], [8], [9]. Here, we investigate joint actions of football players (European association football; soccer) to understand how players perform as a collective and how this relates to team success.

Football is played between two opposing teams where players interact directly, indirectly and concurrently to achieve an objective that involves scoring goals while simultaneously preventing the opposition from scoring [10,11]. In this sense, football is composed of individuals who coordinate their movements and develop cooperative relations to outcompete their opponents [12]. Having this theoretical knowledge as a base ground, a set of metrics have already been developed to incorporate a wide range of complex behaviors and explore how these impact and be impacted by group structures. For instance, the teammates’ displacement synchronization, computed through the relative phase [11], have been used to assess the dynamic players’ interpersonal coordination [13,14]. Preliminary results have shown that, by being more synchronized in positioning with teammates, players decreased their physical and physiological responses during the game [13]. Also, advances in knowledge have been made through the increased variety of processing techniques to assess regularities between whole teams and between individual players with their team as a function of time [15,16]. Entropy computations have been used to identify if individuals’ positioning dynamics express a predictable pattern which may, in turn, provide insights about the local information sources that are being used in movement decisions [17].

Historically, the analysis of football has focused on several descriptive indicators (with a preponderance to player movement characterization) and in the comparison of different single players’ performance according to different contexts [18]. In the behavioral sciences, by contrast, a paradigm shift has occurred in the study of group behavior, shifting focus from the study of single ‘focal’ individuals to the quantitative study of simultaneous interactions among organisms, and the resulting collective properties exhibited by groups. As a result of advances that allow automatic player identification and tracking [19], [20], [21], [22], [23], some recent works started to explore group behaviour analyses [24], [25], [26] (for a systematic review see [27]). These analyses mostly relied on metrics that gave overall collective scores (for example: “team centroid” - geometric mean position from all team players, or “dispersion” - an indicator of how "compact" the team is, i.e. large dispersion means players are more distant from each other) and less detailed insight to players’ individual contributions to the collective behaviour (i.e. how players coordinate with each other). Thus, and since the literature has already explored some collective indicators that result from the spatial relationships of the players, it only makes sense to move towards more fine-tuned analyses to understand the individual role of each ‘unit’ (player) on the behaviour of the remaining ‘units’ of the same system (teammates and opponents).

Analyzing performance with the aim of revealing the dynamics and complexity of team sports is largely an unexplored area and will likely lead to new avenues with theoretical and practical implications [28], [29], [30]. The integrated use of positional data, for example, may make it possible to develop performance indicators capable of describing and understanding the mechanisms that underlie players’ collective movements [31,32] and to describe their coordination when performing different tasks together, or how their individual and collective behavior adapts to that of their opponents. The practical implications of applying this type of analysis may have an impact, for example, in the assessment of talent in a sports context, with the immediate consequences in the transfer of players between teams. It is public knowledge that each year players are being transferred between clubs for record-breaking fees. Nevertheless, it is especially surprising that the evaluation of talented players relies on very few performance indicators (such as the number of goals scored) and circumstantial, subjective impressions [33], and there is no indication of the existence of performance indicators that consider the way in which players cooperate and/or compete, considering their spatial movements during competitions.

The aim of our study was to analyze collective patterns in the motion of football players to reveal the underlying coordination among players within teams as well as between players at different teams in order to reveal collective strategies associated with team performance. To do so we used directional correlation with time delay analysis [34] - which detects similarity/difference between concurrent motion patterns among players. Using high-spatiotemporal resolution positional data of the players (and of the ball), we demonstrated how football players dynamically adapt their behavior depending on different contexts, such as changing their movements relative to their teammates and opponents according to their playing position (goalkeepers, defenders, midfielders or forwards) and according to the match phase (offense vs. defense). This work opens up new possibilities for quantifying the performance of sport teams which can serve as an innovative method for applications from design and development of team strategies to the screening of players with tactical talent.

## Section snippets

## Study design

This study followed a cross-sectional design in which the spatial coordinates of all players were collected, during the entire duration of the analyzed matches. For each player from his high resolution trajectory, spatio-temporal correlation based metrics were calculated with the other players (teammates and opponents) and the ball, in order to identify the highly correlated segments (HCS) . After calculating the HCS for each pair of players, individual scores and team scores were produced and

## Results

We analyzed high spatio-temporal resolution positional data of players and the balls from 5 official football matches between 9 different top level teams (hereafter referred to as tA to tI to preserve their anonymity), including one team that played twice (Table 1). In order to quantify the joint actions among players in these matches, we calculated correlations between path segments of pairs of players to detect co-occurring similar motion patterns. We defined highly correlated segments (HCS)

## Discussion

This work is one of the first studies in a new interdisciplinary research field in which team sports are considered from the perspective of collective behavior. Previous studies are scarce, but in one nice recent study, Yokoyama and Yamamoto [9] analyzed spatiotemporal coupling and synchronization of humans playing a 3 vs. 1 football possession game. Our current study goes beyond previous attempts and the coordination of all the players (and also of the ball) are analyzed in formal football

## Conclusions

In this work we aimed to advance the emerging field of analysis of football on a collective scale. By understanding what makes some teams better than others, we can inspire both coaches and football staff on their decision-making, and hopefully will also push football as a ‘model-system’ of collective action in general. With our pairwise analysis - focusing on the interactions between the players, we were able to find clear differences between the different roles on the pitch. In a nutshell,

## CRediT authorship contribution statement

Rui Marcelino: Conceptualization, Resources, Data curation, Formal analysis, Funding acquisition, Validation, Investigation, Methodology, Writing - original draft, Project administration, Writing - review & editing. Jaime Sampaio: Supervision, Writing - review & editing. Guy Amichay: Validation, Writing - original draft, Writing - review & editing. Bruno Gonçalves: Data curation, Investigation. Iain D. Couzin: Supervision, Funding acquisition, Writing - review & editing. Máté Nagy:

## Declaration of Competing Interest

The authors declare no conflict of interest

## Acknowledgments

We thank Raphael Reiners (head of data collection, PERFORM, Opta Sports) for support with the data acquisition, Fritz Francisco and Michael Smith for commenting on our manuscript, and Tamás Vicsek and David Sumpter for valuable discussion. This work was supported by the Portuguese Foundation for Science and Technology (FCT) and European Social Fund (ESF), through a Post Doctoral grant endorsed to R.M. (SFRH/BPD/89806/2012), under the Human Potential Operating Program (POPH); and through the

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