Predicting Football Results: a Bayesian Approach with a ZeroModified Poisson Distribution

Abstract

Football is a global phenomenon, and as such, it was only a matter of time until statistics joined the field. This dissertation explores the application of the Zero-Modified Poisson (ZMP) model within a Bayesian framework for predicting football match outcomes. Traditional Poisson-based approaches often fail to account for irregularities in goal distributions, such as zero inflation or zero deflation, which are common in football scoring patterns. The incorporation of the Zero-Modified Poisson model provides the flexibility to handle varying frequencies of zero outcomes while accommodating unequal means and variances in contrast with the standard Poisson, which assumes equaldispersion. Using match data from the 2022/23 Italian Serie A, a Bayesian hierarchical model is implemented via the NIMBLE r package, where team-specific parameters for attack, defense, and home advantage were estimated using Markov Chain Monte Carlo (MCMC) techniques. After the parameter estimation, two simulation methods were employed to generate probabilistic forecasts: a round-by-round and a full-season one. In order to check the performance of the model the first simulation method was replicated with 3 other Poisson models to check if the handling of zero inflation and deflation really gave an advantage in the predictive power of the ZMP