Continuous-time state-space modelling of the hot hand in basketball

TL;DR

This paper uses a continuous-time state-space model to analyze the hot hand phenomenon in NBA free throws, finding evidence of its existence with a small effect size.

Contribution

It introduces a continuous-time state-space approach with an Ornstein-Uhlenbeck process to study serial dependence in basketball shooting success.

Findings

Supports existence of hot hand phenomenon

Effect size of hot hand is small

Method accounts for uneven time intervals

Abstract

We investigate the hot hand phenomenon using data on 110,513 free throws taken in the National Basketball Association (NBA). As free throws occur at unevenly spaced time points within a game, we consider a state-space model formulated in continuous time to investigate serial dependence in players' success probabilities. In particular, the underlying state process can be interpreted as a player's (latent) varying form and is modelled using the Ornstein-Uhlenbeck process. Our results support the existence of the hot hand, but the magnitude of the estimated effect is rather small.