Maximizing ball movement unpredictability in association football: A Rényi entropy-based approach to optimizing event distribution randomness

Abstract

Modern football prioritizes team play and tactical strategies over individual brilliance. However, its low-scoring nature makes evaluating team performance challenging. Unpredictable ball movement enhances offensive play while complicating defensive setups. To better capture this dynamic nature, authors’ prior work has proposed entropy-based time-series metric to assess unpredictable ball movement by quantifying Spatial Event Distribution Randomness (EDRan). However, some teams may prefer to dominate specific areas with unpredictability, while others utilize the entire field. Existing literature has not examined whether emphasizing dominant (frequently used field regions for ball movement) or considering all regions equally, including rarely used areas, is a more effective approach for computing randomness in event distribution. Moreover, existing research has not investigated the underlying patterns of event distribution randomness, particularly how these variations differ between winning and losing teams, both in terms of overall field coverage and concentration within dominant regions. This study addresses these gaps by analyzing event distribution randomness using Rényi entropy with varying alpha values ( 0 ≤ α ≤ 2 0).Correlation analysis indicated that assigning equal weight to all field regions, including rarely used areas, with Max entropy ( α = 0 alpha) was most strongly associated with match-winning performance. In men’s data, machine learning models trained with α = 0 , 0.1 , alpha and 0.5 achieved statistically significant improvements over models trained with the traditionally used Shannon entropy ( α → 1 alpha). These results suggest that unpredictability distributed across the entire field, maximizing the use of diverse regions, is more strongly associated with success than randomness restricted to dominant areas. The best-performing model, obtained with α = 0 alpha, significantly outperformed both the baseline and existing models in the literature, achieving an accuracy of 80.61% in predicting match winners.