A regularized hidden Markov model for analyzing the 'hot shoe' in football

Abstract

Although academic research on the 'hot hand' effect (in particular, in sports, especially in basketball) has been going on for more than 30 years, it still remains a central question in different areas of research whether such an effect exists. In this contribution, we investigate the potential occurrence of a 'hot shoe' effect for the performance of penalty takers in football based on data from the German Bundesliga. For this purpose, we consider hidden Markov models (HMMs) to model the (latent) forms of players. To further account for individual heterogeneity of the penalty taker as well as the opponent's goalkeeper, player-specific abilities are incorporated in the model formulation together with a LASSO penalty. Our results suggest states which can be tied to different forms of players, thus providing evidence for the hot shoe effect, and shed some light on exceptionally well-performing goalkeepers, which are of potential interest to managers and sports fans.