The ecological dynamics approach to interpersonal relationships provides theoretical support to the use of kinematic data, obtained with sensor-based systems, in which players of a team are linked mainly by information from the performance environment. Our goal was to capture the properties of synergic behavior in football, using spatiotemporal data from one match of the 2018 FIFA WORLD CUP RUSSIA, to explore the application of player-ball-goal angles in cluster phase analysis. Linear mixed effects models were used to test the statistical significance of different effects, such as: team, half(-time), role and pitch zones. Results showed that the cluster phase values (synchronization) for the home team, had a $3.812\times {10}^{-2}\pm 0.536\times {10}^{-2}$ increase with respect to the away team (${\mathcal{X}}^2\left(41\right)=259.8, p<0.001$) and that changing the role from with ball to without ball increased synchronization by $16.715\times {10}^{-2}\pm 0.283\times {10}^{-2}$ (${\mathcal{X}}^2\left(41\right)=12227.0, p<0.001$). The interaction between effects was also significant. The player-team relative phase, the player-ball-goal angles relative frequency and the team configurations, showed that variations of synchronization might indicate critical performance changes (ball possession changes, goals scored, etc.). This study captured the ongoing player-environment link and the properties of team synergic behavior, supporting the use of sensor-based data computations in the development of relevant indicators for tactical analysis in sports.

This article clarifies the distinctive role of eco-physical variables in analyzing and modeling the dynamics of goal-directed behavior in sports. While behavior in sport is inherently purposeful and context-dependent, most current performance metrics neglect how athletes direct their actions toward task-relevant environmental properties. Although traditional indicators and continuous variables (e.g., collective, compound, and order parameters) have been widely used to quantify performance, they often conflate different constructs and remain neutral to situated intentionality. A conceptual clarification is necessary, as these metrics are frequently used interchangeably in the literature, leading to confusion among researchers and practitioners. Rooted in the theoretical approach of ecological dynamics, the concept of eco-physical variables seeks to address these issues by capturing how performers intentionally perceive and act in their environment to achieve task goals. These variables reflect how athletes act toward task goals, shaped by the socio-material properties of their performance environment. To our knowledge, this is the first article to focus exclusively on eco-physical variables, define them as a distinct class of metrics in sport, and outline their theoretical, methodological, and practical implications. It resolves conceptual ambiguity around similar terms and offers theory-informed guidance for developing variables that preserve dynamics and context. Specifically, this article: (a) reviews existing sports performance metrics; (b) overviews the ecological dynamics approach to sport performance; (c) defines eco-physical variables and reviews their application; (d) provides recommendations for their development and measurement; (e) explores their role in dynamical systems and artificial intelligence modeling; and (f) identifies debates, challenges, and future research.

Anticipation is essential for successfully performing in dynamic environments, yet it is often framed as mentally inferring a future state without considering how action is embodied and embedded. This paper introduces an action-based approach to anticipation and team synergies based on perception-action couplings. Using football as a case study, we measured anticipation as the players’ prospective coordination with the match environment towards task objectives. We explored how team synergic behavior emerged from players’ anticipatory movements, guiding the teams’ ability to maintain goal directed behavior. Defender-ball-goal angles were computed from game positional data and submitted to cluster phase analysis to develop a team coherence model expressing how defenders collectively blocked the progression of the ball towards goal. Cross-correlation analysis measured defender-ball coupling strength and delay (ρ), capturing how defenders coordinated with the ball to sustain and interchange among blocking roles, so the team could maintain coherence. Results showed that higher coupling strengths (ρ) were associated with defenders’ anticipatory movements in relation to the ball, exhibited by negative coupling delays (median lag = -1.02 s). This indicates that defenders coordinated their movements with future ball positions to assume and interchange among blocking roles. Regression analysis showed a strong association (R² = .74) between blocking role interchanges and team coherence stability. This action-based approach helped clarify how perception-action is coordinated among team members to foster team synergies, offering a comprehensive framework for studying anticipation as an embodied and embedded human skill, while providing a tool for its broader application across group performance domains.

Sports coaches play a vital role in enhancing athletic performance by shaping learning environments; this process is inherently complex and dynamic, requiring an understanding of how performance em...