Discrete Weibull regression for modeling football outcomes

We propose the use of the discrete Weibull distribution for modeling football match results, as an alternative to existing Poisson and generalized Poisson models. The number of goals scored by the two teams playing a football match are regarded as a pairwise observation and are modelled first through two independent discrete Weibull variables, and then through two dependent discrete Weibull variables, using a copula approach that accommodates non-null correlation. The parameters of the bivariate discrete Weibull distributions are assumed to depend on covariates such as the attack and defense abilities of the two teams and the `home effect'. Several discrete Weibull regression models are proposed and then applied to the 2015-2016 Italian Serie A. Even if the interpretation of parameters is less immediate than in the case of bivariate Poisson models, nevertheless these models represent a suitable alternative, which can be applied also in other fields than sport data analysis.