Statistical Tests for the Hot-Hand in Basketball in a Controlled Setting

When I watch basketball on television, it is a common occurrence to have an announcer state that some player has the hot-hand. This raises the question: Are Bernoulli trials an adequate model for the outcomes of successive shots in basketball? This paper addresses this question in a controlled (practice) setting. A large simulation study examines the power of the tests that have appeared in the literature as well as tests motivated by the work of Larkey, Smith, and Kadane (LSK). Three test statistics for the null hypothesis of Bernoulli trials have been considered in the literature; one of these, the runs test, is effective at detecting one-step autocorrelation, but poor at detecting nonstationariy. A second test is essentially equivalent to the runs test, and the third is shown to be worthless. The LSK-motivated tests are shown to be effective at detecting nonstationarity. Finally, a case study of 2,000 shots by a single player is analyzed. For this player, the model of Bernoulli trials is inadequate.