Modeling outcomes of soccer matches

TL;DR

This paper evaluates different statistical models, including extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model, for predicting soccer match outcomes, using a novel temporal validation framework.

Contribution

It introduces a comprehensive comparison of multiple models for soccer outcome prediction and proposes a new validation method for assessing their performance.

Findings

Models show similar predictive performance.

The novel validation framework accurately estimates test error.

Hierarchical Poisson and Bradley-Terry models are comparably effective.

Abstract

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalized version of it, while the posterior densities of the parameters of the hierarchical Poisson log-linear model are approximated using integrated nested Laplace approximations. The prediction performance of the various modeling approaches is assessed using a novel, context-specific framework for temporal validation that is found to deliver accurate estimates of the test error. The direct modeling of outcomes via the various Bradley-Terry extensions and the modeling of match scores using the hierarchical Poisson log-linear model demonstrate similar behavior in terms of predictive performance.