A mixed effects model for identifying goal scoring ability of footballers

Abstract

The paper presents a model that can be used to identify the goal scoring ability of footballers. By decomposing the scoring process into the generation of shots and the conversion of shots to goals, abilities can be estimated from two mixed effects models. We compare several versions of our model as a tool for predicting the number of goals that a player will score in the following season with that of a naive method whereby a player's goals-per-minute ratio is assumed to be constant from one season to the next. We find that our model outperforms the naive model and that this outperformance can be attributed, in some part, to the model's disaggregating a player's ability and chance that may have influenced his goal scoring statistic in the previous season. © 2013 Royal Statistical Society.