Bias reduced estimation of a fixed effects model for Expected Goals in association football

In recent years, there has been an increasing interest in the scientific evaluation of association football. This paper addresses the issue of assessing the scoring probabilities of shots, commonly named as Expected Goals, by specifying a suitable generalized linear model. In particular, in order to account for different players abilities, a fixed effects model is considered. This has the advantage of avoiding the potential bias induced by endogeneity in a random effects specification. On the other hand, it is well known that in fixed effects models standard likelihood inference is not reliable, due to the large dimension of the parameter. Therefore, we propose to estimate the model using Firth’s bias reduction method. Recent theoretical results guarantee that bias reduced estimates are accurate even in this extreme scenario.