Comparing probabilistic predictive models applied to football

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.

Keywords:

• Bayesian inference
• predictive inference
• probabilistic prediction
• scoring rules
• soccer prediction

Acknowledgements

The authors thank the very useful help of Rafael Bassi Stern.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Rafael Izbicki was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (2014/25302-2 and 2017/03363-8).