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

TL;DR

This paper investigates the existence of a 'hot shoe' effect in football penalty performance using a regularized hidden Markov model that accounts for player heterogeneity and provides insights into player states and goalkeeper performance.

Contribution

It introduces a regularized hidden Markov model with LASSO penalty to analyze latent player states and heterogeneity in football penalty data, revealing evidence of the 'hot shoe' effect.

Findings

States linked to different player forms suggest hot shoe effect.

Identification of well-performing goalkeepers.

Model accounts for individual heterogeneity.

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.