Can the hot hand phenomenon be modelled? A Bayesian hidden Markov approach

Abstract Sports data analytics has been gaining importance over recent years as an essential topic in applied statistics. Specifically, basketball has emerged as one of the iconic sports where the use and immediate collection of data have become widespread. Within this domain, the hot hand phenomenon has sparked a significant scientific controversy, with sceptics claiming its non-existence while other authors provide evidence for it. We propose a Bayesian longitudinal hidden Markov model that examines the hot hand phenomenon in consecutive shots of a basketball team, each of which can be either missed or made. We assume two states (cold or hot) in the hidden Markov chains associated with each math and model the probability of success for each shot with regard the hidden state, the random effects related the match, and the covariates. This model is applied to real data sets of three teams from the USA National Basketball Association: the Miami Heat team and the Toronto Raptors team in the 2005–2006 season, and the Chicago Bulls in the 2022–2023 season. We show that this model is a powerful tool for assessing the overall performance of a team during a game and, in particular, for quantifying the magnitude of team streaks in probabilistic terms.