Modeling Tactical Free Energy and Shot Decision-Making in Professional Football Using Spatiotemporal Event Data

Abstract

This study proposes a physics-inspired framework for analyzing shooting decision-making in professional football through the concept of tactical free energy. Drawing on energy landscape theory from statistical mechanics, we model the tactical influence exerted by surrounding players on the ball as an abstract, configuration-dependent scalar field rather than a physical force. A derivative-based formulation is introduced to quantify the rate of change in tactical free energy around the ball, incorporating spatial factors such as distance to goal, shooting angle, opponent density, and tactical entropy representing decision variability.

The framework is evaluated using open-source StatsBomb event and freeze-frame data. Due to the absence of continuous tracking information, temporal derivatives are approximated using discrete positional snapshots within a short pre-shot window. An exploratory empirical analysis of 20 open-play shots reveals a moderate negative correlation (Pearson r = −0.62) between the tactical free energy derivative and expected goals (xG), indicating that players tend to attempt shots during moments of decreasing tactical resistance. Spatial heatmap visualizations further show that successful shots are concentrated in regions characterized by lower tactical energy influence. These findings suggest that shooting decisions can be interpreted as transitions toward local minima in a tactical energy landscape. The proposed approach contributes to football analytics by introducing an energy-based interpretation of tactical decision-making, bridging concepts from statistical physics and spatiotemporal football data, and providing a reproducible application using publicly available datasets. While exploratory in nature, the framework demonstrates potential for extension to larger datasets and integration into predictive and decision-support systems.