Modelling soccer matches using bivariate discrete distributions with general dependence structure

In this paper copulas are used to generate novel bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots-for and shots-against, exhibit negative dependence; thus in particular we develop bivariate Poisson-related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a 1-dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within-match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the “beautiful game” is an effective strategy—more passes and crosses contribute to more effective play and more shots on goal.