Fractal Ball Movement Complexity: Spatiotemporal Analysis for Team Performance Evaluation in Association Football

Abstract Spatiotemporal techniques are increasingly integral to football analytics for assessing team performance, yet the inherently dynamic and interactive nature of association football continues to hinder fully objective evaluation. Although existing research has examined the randomness of match events and patterns of player interactions, the contribution of ball movement trajectories has received comparatively limited attention despite its tactical significance. This study addresses this shortcoming by introducing a novel framework to quantify the spatial complexity of team ball movement as an indicator of offensive performance. Using a time-series feature extraction methodology, the fractal dimension of two-dimensional ball trajectory representations is calculated over predefined temporal windows to capture spatial complexity. The findings indicate a positive relationship between higher spatial complexity and match success, particularly in the early stages of play. In addition, a multi-scale fractal analysis reveals scale-dependent effects, with coarse- and mid-scale spatial complexity showing positive correlations with match-winning outcomes, while fine-scale complexity exhibits an inverse relationship, indicating that spatial structure at broader scales may be more influential for effective team performance than high-frequency local variations in ball movement. Finally, a Random Forest classification model trained solely on spatial complexity features achieved an AUC–ROC score of 0.8180 in predicting match outcomes, demonstrating that spatial complexity serves as an informative, interpretable, and effective time-series metric for evaluating team performance in association football.