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

Marcus Nolan; Wagner Barreto-Souza; Luiza S. C. Piancastelli; Raanju R. Sundararajan

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arXiv · 2608.07168

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

Marcus Nolan·Wagner Barreto-Souza·Luiza S. C. Piancastelli·Raanju R. Sundararajan

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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.

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Marcus Nolan, Wagner Barreto-Souza, Luiza S. C. Piancastelli, Raanju R. Sundararajan. 2026-08-07. A Bayesian bivariate conditional Poisson regression for goal dependence in the English Premier League. https://arxiv.org/abs/2608.07168

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