A Cold Shower for the Hot Hand Fallacy: Robust Evidence that Belief in the Hot Hand is Justified

Abstract

The hot hand fallacy has long been considered a massive and widespread cognitive illusion with important implications in economics and finance. We develop a novel empirical strategy to correct for several fundamental limitations in the canonical study and replications, conduct an improved field experiment to test for the hot hand in its original domain (basketball shooting), and gather all extant controlled shooting data. We find strong evidence of hot hand shooting in every dataset, including on the individual level. Also, in a novel study of beliefs, we find that expert observers can predict (out-of-sample) which shooters are hotter.

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

“…23 The median number of shots taken is 197, with a minimum of 100 (multiple players) and a maximum of 454 (Craig Hodges). As is the case in all extant controlled studies (Miller and Sanjurjo 2014), as well as free throw shooting (Arkes 2010; Yaari and Eisenmann 2011), players perform relatively (and significantly) worse on their first two shot attempts, shooting 32 percent on their first shot, 41 percent on the second, and 56 percent thereafter. Omitting the first two shots, players do not shoot significantly better or worse, on average, from any of the five rack locations.…”

“…Once the bias is corrected for in Gilovich et al (1985)'s analysis, the results of their controlled shooting experiment reverse, yielding strong evidence of hot hand shooting. Further, this evidence has now been replicated across several controlled shooting experiments (Miller andSanjurjo 2014, 2018).…”

“…Throughout our analysis we report one-sided p-values for all of our tests, as the alternative hypothesis of hot hand shooting establishes a clear ex ante directional prediction for the statistical measures that we define. Due to the relatively small number of shots in each round (25), and the well-documented power issues concerning small samples of binary data (Miller and Sanjurjo 2014), in our primary analysis we take a similar approach to Koehler and Conley (2003) and measure each statistic across an individual shooter's multiple shooting rounds. Further, in order to reduce the noisiness of our estimates, and allow at least a minimal number of instances in which a player has hit three or more shots in a row, in our primary analysis we restrict the sample of shooters to those who took at least 100 shots, which is the same number used in Gilovich et al (1985)'s controlled test of hot hand shooting.…”

March Madness? Underreaction to Hot and Cold Hands in Ncaa Basketball

“…The distinction between actual and perceived hot and cold hands is neglected by much of this literature, as pointed out by Miller and Sanjurjo (); we discuss this issue further later in the paper.…”

“…Offerman and Sonnemans () refer to what we call HH underreaction as the cold‐hand effect (“the decision‐maker could underestimate the autocorrelation ... would fall prey to the so‐called cold‐hand effect”); as discussed above, we believe the term “cold hand bias” is more appropriately used to refer to over‐estimation of coldness based on poor recent performance. Miller and Sanjurjo () also use the term this way.…”