Mar-Co: a new dependence structure to model match outcomes in football

The approaches commonly used to model the number of goals in a football match are characterised by strong assumptions about the dependence between the number of goals scored by the two competing teams and about their marginal distribution. In this work, we argue that the assumptions traditionally made are not always based on solid arguments and sometimes they can be hardly justified. In light of this, we propose a modification of the Dixon and Coles (1997) model by relaxing the assumption of Poisson-distributed marginal variables and by introducing an innovative dependence structure. Specifically, we define the joint distribution of the number of goals scored during a match by means of thoroughly chosen marginal (Mar-) and conditional distributions (-Co). The resulting Mar-Co model is able to balance flexibility and conceptual simplicity. A real data application involving five European leagues suggests that the introduction of the novel dependence structure allows to capture and interpret fundamental league-specific dynamics. In terms of betting performance, the newly introduced Mar-Co model does not perform worse than the Dixon and Coles one in a traditional framework (i.e. 1-X-2 bet) and it outperforms the competing model when a more comprehensive dependence structure is needed (i.e. Under/Over 2.5 bet).