Combining historical data and bookmakers\u2019 odds in modelling football scores

Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial pro\ufb01ts. Despite the strong connection existing between football models and the bookmakers\u2019 betting odds, no authors have used the latter for improving the \ufb01t and the predictive accuracy of these models. We have developed a hierarchical Bayesian Poisson model in which the scoring rates of the teams are convex combinations of parameters estimated from historical data and the additional source of the betting odds. We apply our analysis to a nine-year dataset of the most popular European leagues in order to predict match outcomes for their tenth seasons. In this article, we provide numerical and graphical checks for our model