Is it a Fallacy to Believe in the Hot Hand in the NBA Three-Point Contest?

Abstract

The NBA Three-Point Contest has been considered an ideal setting to study the hot hand, as it showcases the elite professional shooters that hot hand beliefs are typically directed towards, but in an environment that eliminates many of the confounds present in game action. We collect 29 years of NBA Three-Point Contest television broadcast data , apply a statistical approach that improves on those of previous studies, and find considerable evidence of hot hand shooting in and across individuals. Our results support fans' and experts' widely held belief in the hot hand among NBA shooters.

Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers

“…However, as in GVT and Avugos et al (), the conditional probability tests that the authors conducted are vulnerable to the bias. By contrast, Miller and Sanjurjo () collected 28 years of data, which yield 33 players that have taken at least 100 shots; using this data set, we find that the average bias‐corrected difference across players is +8 percentage points (). Further, 8 of the 33 players exhibit significant hot hand shooting (), which itself is statistically significant (, binomial test).…”

“…We illustrate how the results of Avugos et al (), a close replication of GVT, similarly reverse when the bias is corrected for. Miller and Sanjurjo () showed that the results of Koehler and Conley (), which has been referred to as “an ideal situation in which to study the hot hand” ( Thaler and Sunstein ()), reverse when an unbiased (and more powered) analysis is performed. These results in turn agree with the unbiased analyses performed on all remaining extant controlled shooting datasets in Miller and Sanjurjo ().…”

A Visible (Hot) Hand? Expert Players Bet on the Hot Hand and Win

“…To illustrate, imagine a hypothetical shooter who shoots 12 percentage points better in his "hot" state than in his "normal" state, and is in the hot state on 10 percent of his shots. Such a hot hand effect would be considerable for basketball standards, and is roughly equal to the conservative estimate of the (average) hot hand effect reported in Miller and Sanjurjo (2018). 12 Now, suppose that there is a predictor who can perfectly detect the shooter's hot hand whenever it occurs, so always bets "high" when the shooter is in the hot state and "low" when the shooter is not in the hot state.…”

“…Here, we provide the first such evidence. Our finding of profitable hot hand beliefs is of particular relevance in light of the recent finding of strong evidence of hot hand performance (Miller and Sanjurjo 2018). 7 We test for the ability of decision makers to predict sequential performance outcomes in an incentivized field betting task.…”

“…10 GVT also administer an unincentivized survey in which 8 NBA players and a coach express an almost unanimous belief in the hot hand. However, these beliefs can no longer be considered fallacious (Miller and Sanjurjo 2018). See Appendix C for more on GVT's survey of beliefs.…”