A Bayesian inference approach for determining player abilities in football

We consider the task of determining a football player's ability for a given event type, for example, scoring a goal. We propose an interpretable Bayesian model which is fit using variational inference methods. We implement a Poisson model to capture occurrences of event types, from which we infer player abilities. Our approach also allows the visualisation of differences between players, for a specific ability, through the marginal posterior variational densities. We then use these inferred player abilities to extend the Bayesian hierarchical model of Baio and Blangiardo (2010) which captures a team's scoring rate (the rate at which they score goals). We apply the resulting scheme to the English Premier League, capturing player abilities over the 2013/2014 season, before using output from the hierarchical model to predict whether over or under 2.5 goals will be scored in a given game in the 2014/2015 season. This validates our model as a way of providing insights into team formation and the individual success of sports teams.