The “hot hand” revisited: A nonstationarity argument Yanlong Sun and Hongbin Wang School of Biomedical Informatics, University of Texas Health Science Center at Houston, Houston, Texas, USA Abstract: The “hot hand belief,” that a basketball player would experience elevated performance for a certain period of time, during which consecutive shots are made in streaks, has been suggested to be a “cognitive illusion,” because, from the basketball-shooting data, no significant evidence has been found to reject the simple binomial model. The present study raises concerns about the statistical methods used to support this claim. It is argued that nonstationarity may manifest as a residual effect when the changes in shooting accuracy are interrupted by activities such as shot selection and defense effort. Reanalyses of the field goal data from the earlier study showed that the serial correlation varied substantially between positive (“hot hand shooting”) and negative (“over-alternation shooting”). In addition, a nested model comparison revealed that when a player’s shooting accuracy fluctuated substantially in a short period of time, it was unlikely to be detected by the binomial model. Our results suggest that paying special attention to streak patterns in the hot hand belief may be an adaptive strategy in detecting changes in the environment. Keywords: hot hand belief; perception of randomness; stationarity Correspondence: DrYanlong Sun, School of Biomedical Informatics, University of Texas Health Science Center at Houston, 7000 Fannin, Suite 600, Houston, TX 77030, USA. Email: yanlong.sun@uth.tmc.edu Received 23 November 2011. Accepted 22 February 2012. The “hot hand” in the game of basketball has raised many interesting questions about human perceptions of probabil- istic events outside the psychological laboratory. Many people hold the “hot hand belief,” which is a manifestation about nonstationary shooting accuracy or positive depen- dence in basketball shooting sequences. For example, a player would experience elevated performance for a certain period of time, during which consecutive shots are made in streaks. However, regarding the statistical validity of the hot hand belief, a long-lasting debate has been triggered by three articles written by Gilovich, Vallone, and Tversky (1985), and Tversky and Gilovich (1989a, 1989b). If we think of the case of randomly tossing a biased coin, we would expect that the outcome of each toss has the same probability to be a head. As a consequence, it would be unlikely to observe that in some periods of time most of the tosses are heads, but in other periods of time most of the tosses are tails. That is, such a process should be stationary. Moreover, if we encode each head as 1 and each tail as 0, then calculate the serial correlation between consecutive tosses, we should expect the correlation to be close to 0, rather than 1 (e.g. if we had a streak of heads or tails) or -1 (heads and tails were perfectly alternating with each other). That is, such a process should also be independent. In the case of basketball shooting, it is clear that the hot hand belief has violated either the stationarity or the independence or both of the properties as in the case of coin tossing, namely, the properties of the simple binomial model. However, after a number of statistical analyses of the data from actual basketball games and a controlled shooting experiment, Gilovich et al. concluded that actual basketball shooting records “may be adequately described by a simple binomial model” (Gilovich et al., 1985, p. 313), and “perhaps, then, the belief in the hot hand is merely one manifestation of this fundamental misconception of the laws of chance” (Tversky & Gilovich, 1989a, p. 16). This conclusion has had a con- siderable impact on a variety of fields, such as judgment and decision making, sports, and particularly behavioral eco- nomics. Many researchers seem to be convinced that the hot hand is just a myth and the hot hand belief is indeed a fallacy PsyCh Journal 1 (2012): 28–39 doi: 10.1002/pchj.2 © 2012 The Institute of Psychology, Chinese Academy of Sciences and Blackwell Publishing Asia Pty Ltd