# Comparing probabilistic predictive models applied to football

## TL;DR

This paper compares Bayesian multinomial-Dirichlet models with traditional models for predicting football match outcomes, demonstrating their competitive accuracy and good calibration on Brazilian league data.

## Contribution

Introduces two Bayesian multinomial-Dirichlet models for football outcome prediction and evaluates their performance against existing models using real match data.

## Key findings

- Multinomial-Dirichlet models are competitive with standard models.
- Models are well calibrated and have good goodness of fit.
- Predictive accuracy is comparable to established approaches.

## Abstract

We propose two Bayesian multinomial-Dirichlet models to predict the final outcome of football (soccer) matches and compare them to three well-known models regarding their predictive power. All the models predicted the full-time results of 1710 matches of the first division of the Brazilian football championship and the comparison used three proper scoring rules, the proportion of errors and a calibration assessment. We also provide a goodness of fit measure. Our results show that multinomial-Dirichlet models are not only competitive with standard approaches, but they are also well calibrated and present reasonable goodness of fit.