Information-Theoretical Analysis of Team Dynamics in Football Matches.

Team dynamics significantly influence the outcomes of modern football matches. This study employs an information-theoretical approach, specifically causal emergence, combined with graph theory to explore how team-level dynamics arise from complex interactions among players, utilizing tracking data from 34 J-League matches. We focused on how collective behaviors arise from the interdependence of individual actions, examining team coordination and dynamics through player positions and movements to identify emergent properties. Specifically, we selected relative distance to the field's center, center of mass (CoM) and clustering coefficients based on velocity similarity and inverse distance as macroscopic features to capture the key aspects of team structure, coordination, and spatial relationships. Relative distance and CoM represent the collective positioning of the team, while clustering coefficients provide insights into localized cooperation and movement similarity among the players. The results indicate that average causal emergence with relative distance and CoM as a macroscopic feature across entire games shows a strong correlation with differences in ball possession rate between home and away teams. In contrast, clustering coefficients based on inverse distance and velocity similarity showed moderate to weak correlations with ball possession rate, indicating that these metrics may capture localized interactions that are less directly tied to team-level emergent behavior compared to CoM. Additionally, relative distance and CoM as macroscopic features yield higher causal emergence in attacking phases than in defending phases before shooting, suggesting that the collective positioning of players may play a more significant role in facilitating successful attacks than in defensive stability. This study offers a novel perspective on team coordination in football, suggesting that effective team coordination may be characterized by emergent patterns arising from collective positioning. These findings have practical implications for understanding coordinated team behaviors and inform coaching and performance analysis focused on enhancing team dynamics.