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

The article focuses on extending the Dixon and Coles model for predicting football match scores by framing it as a special case of the Sarmanov family of bivariate discrete distributions. This extension allows shifting probabilities across a broader range of scorelines and incorporating marginal distributions beyond the Poisson, such as the negative binomial, to better capture characteristics observed in women's football, including pronounced overdispersion and stronger negative correlation between home and away goals. Using data from four major European women's leagues, the authors demonstrate that their proposed models, particularly the Alternative Negative Binomial Sarmanov (ANS) model, outperform classical models in terms of fit and predictive accuracy. The framework also accommodates team-specific attacking and defensive effects and can be adapted for other applications involving dependent count data with differing marginal distributions.