Extending the Dixon and Coles model: an application to women's football data

TL;DR

This paper extends the Dixon and Coles model for football scores by introducing a more flexible family of models based on the Sarmanov distribution, tailored to women's football data characteristics.

Contribution

It generalizes the Dixon and Coles model using the Sarmanov family, allowing for better modeling of women's football scores with alternative score probabilities and distributions.

Findings

New models better fit women's football score data

Demonstrates flexibility of Sarmanov family in sports modeling

Provides insights into scoring patterns in women's football

Abstract

The prevalent model by Dixon and Coles (1997) extends the double Poisson model where two independent Poisson distributions model the number of goals scored by each team by moving probabilities between the scores 0-0, 0-1, 1-0, and 1-1. We show that this is a special case of a multiplicative model known as the Sarmanov family. Based on this family, we create more suitable models by moving probabilities between scores and employing other discrete distributions. We apply the new models to women's football scores, which exhibit some characteristics different than that of men's football.