Fractal Analysis of Ball Movement Maps for Team Performance Evaluation in Association Football

Spatiotemporal analysis has become a foundation of modern football analytics, particularly in evaluating team performance. However, the complex, dynamic nature of association football makes objective performance evaluation a persistent challenge. While recent studies have explored event distribution randomness and player-to-player interactions, these approaches often overlook the role of ball movement trajectories, which can offer crucial insights into team effectiveness. To address this gap, this study proposes a novel method for quantifying spatial complexity in team ball movement as a measure of offensive performance. A time-series feature extraction approach is introduced, wherein the fractal dimension of 2D ball movement maps are computed to represent spatial complexity across defined time intervals. Correlation analysis reveals a positive association between spatial complexity and match-winning outcomes, particularly during the early phases of play. Furthermore, a Random Forest classification model trained exclusively on spatial complexity features achieved an AUC-ROC of 0.8180 in predicting match winners, underscoring the potential of spatial complexity as a valuable and interpretable time-series metric for evaluating team performance in association football.