Modelling the dependence of goals scored by opposing teams in international soccer matches

This paper presents models for the number of goals scored by opposing teams in international soccer matches. The bivariate discrete distributions employed are defined in terms of the marginal distributions and a dependence copula. This copula representation allows dependence in the bivariate distribution to be modelled in a flexible manner by specifying a suitable family of copula functions and fitting this to the bivariate data using maximum likelihood. Marginal means are modelled with match covariates. The nature of the dependence in the number of goals scored is complex, and we develop the idea that the strength of dependence depends on the competitive balance of a match. Our analysis suggests that for games between closely matched teams, the overall dependence is low, and that the dependence becomes increasingly negative as the competitiveness of a match decreases. In this way, we relate dependence to competitive balance and suggest a method to measure the latter quantity. The models developed here may also offer better forecasts than those offered by match outcome models with independent marginal distributions.