Predicting draws and number of fouls in football matches using Bayesian network classifiers

Abstract

This study proposes a unified approach to predicting two specific events in football-the number of fouls committed and the probability of a draw-using Naive Bayes (NB) classifiers optimized through discretization strategies aimed at effective class separation. First, a model is introduced to anticipate the number of fouls in a match, discretized into intervals determined by historical percentiles, thereby capturing the ordinal distribution of these infractions. To evaluate the classification performance, the RPS is employed. The proposed discretization attains an overall RPS = 0.0093, outperforming k-means (0.0098) and Fayyad-Irani (0.0098). Second, the prediction of draws is addressed by incorporating subjective factors such as the significance of regional derbies and teams’ historical rankings. Given the class imbalance inherent in this task, weighted accuracy (WAP) and weighted recall (WAR) metrics are used. Our model reaches WAP = 0.424 and WAR = 0.565, versus 0.413/0.539 with k-means and 0.406/0.539 with Fayyad-Irani. These results show that discretizations specifically designed for NB substantially improve the performance of both models compared to other standard discretizers, providing a comprehensive and computationally efficient framework for modeling rare events in the football domain.