A Bayesian bivariate conditional Poisson regression for goal dependence in the English Premier League

2026-08-07

AI Summary

This study addresses the limitations of traditional soccer score models, which typically assume independence or only positive correlation between home and away goals, thereby failing to capture their true dependence structure. The authors propose the first Bayesian framework incorporating bivariate conditional Poisson regression to explicitly model the joint distribution of home and away goals, including potential negative correlations, while integrating covariates such as attendance and fouls. Applying this model to three English Premier League seasons, posterior inference reveals a significant negative correlation between home and away goals. Moreover, the influence of home crowd attendance on scoring exhibits asymmetry in both direction and magnitude between home and away teams. This approach enhances both the plausibility and interpretability of match score predictions.

Abstract

Understanding the relationship between home and away goal counts in football provides valuable insights into match-level dynamics. While the influence of home advantage is well-established, with historical records indicating roughly 50% of matches are won by home teams (versus about 30% by the away team), properly determining the joint goal distribution while accounting for key match factors remains under-explored. In this paper, we develop a Bayesian bivariate Conditional Poisson (BCP) regression model to explicitly capture the dependence between home and away goal counts, addressing a core limitation of traditional football scoring models that assume independence or only allow for positive correlation. The BCP regression is applied to the English Premier League (EPL) data spanning three seasons, incorporating stadium attendance and committed fouls by both teams as regressors. Inference is conducted within a Bayesian framework, enabling interpretable uncertainty quantification and model validation through posterior predictive checks. Our results reveal a negative correlation between home and away goal counts and highlight an asymmetry in how match attendance influences home versus away scoring.

Problem

• goal dependence
• bivariate modeling
• football scoring
• joint goal distribution
• home-away correlation

Innovation

• Bayesian bivariate Conditional Poisson regression
• goal dependence
• negative correlation
• home advantage
• posterior predictive checks