Detecting the Hot Hand: An Alternative Model

Detecting the Hot Hand: An Alternative Model Yanlong Sun (Yanlong.Sun@uth.tmc.edu) University of Texas Health Science Center at Houston School of Health Information Sciences, 7000 Fannin Suite 600 Houston, TX 77030 USA Abstract The belief in the hot hand was suggested to be a “cognitive illusion” since no significant evidence was found in the basketball-shooting data to reject the simple binomial model (Gilovich, Vallone & Tversky, 1985). The present study argues that in order to evaluate the validity of human perception and cognition such as the hot hand belief, a data- driven approach is needed to compare multiple alternative models. A hot hand model with nonstationary shooting accuracy was tested and showed significantly better approximation to the data than the binomial model, indicating that the simple binomial model may not be accurate enough to serve as a normative model. This finding suggests that the hot hand might indeed have existed, and weakens the argument that the hot hand belief might be “seeing patterns out of randomness. ” The Hot Hand and the Perception of Randomness The “hot hand” in the game of basketball has received much attention in cognitive psychology because it touches an interesting topic about human perception and cognition of random and non-random events outside the psychological laboratory. A long-lasting debate about whether the hot hand exists, hence, whether the hot hand belief is a valid cognitive activity, was triggered by three articles by Gilovich, Vallone and Tversky (1985), and Tversky and Gilovich (1989a, 1989b) (later “GVT” refers to these three articles as a group, unless specified otherwise). The researchers interpreted the hot hand belief as a manifestation about statistically significant deviations from what is expected by the simple binomial model, namely, nonstationary shooting accuracy or positive dependence in basketball shooting sequences. However, no statistical evidence was found to support such belief. After a number of statistical analyses on a large set of data, the researchers found that actual basketball shooting sequences were “indistinguishable from that produced by a simple binomial model” (Gilovich et al., 1985, p. 297). They concluded, “perhaps, then, the belief in the hot hand is merely [italics added] one manifestation of this fundamental misconception of the laws of chance” (Tversky & Gilovich, 1989a, p. 16). Since GVT, many studies have been carried out to investigate the hot hand in basketball or other sports such as baseball. These studies roughly fell into four categories: a) studies that conducted null hypothesis tests but failed to reject the binomial model (e.g., Adams, 1992; Albright, 1993; Chatterjee, Yilmaz, Habibullah, & Laudato, 2000), (b) studies that raised concerns about the power of significance tests conducted by Gilovich et al. (1985) and Albright (1993) (e.g., Miyoshi, 2000; Stern & Morris, 1993; Sun, 2001, 2003; Wardrop, 1999), (c) studies that proposed alternative models that may support the hot hand belief (e.g., Albert, 1993; Albert & Bennett, 2001; Larkey, Smith, & Kadane, 1989), (d) a study that addressed the adaptive value of the hot hand belief, assuming the accuracy of the binomial model (Burns, 2001). The present paper takes a step further and examines the accuracy of the simple binomial model in a side-by-side comparison with an alternative model that assumes the existence of the hot hand. The importance of such a comparison is obvious since which model is more accurate would inevitably affect researchers’ opinion about the validity of the hot hand belief. As Brunswik (1956) and Simon (1982) suggested, the environment in which human perception and cognition originate and operate must be carefully studied. On one hand, it is possible that the hot hand does not exist and the hot hand belief is another example of misperceptions of randomness outside the psychological laboratory, in addition to many previous findings when random events were clearly defined (e.g., Falk, 1981; Kahneman and Tversky, 1972; Tversky & Kahneman, 1971, 1974; Wagenaar, 1972). On the other hand, it is possible that the hot hand does exist, even with a substantial effect size (e.g., substantial changes in shooting accuracy), and traditional statistical tests are generally low in power thus not capable of detecting the effect. The fact is that a truly random process can produce seemingly non- random “patterns,” but a truly non-random process can produce seemingly random events as well. Lopes and Oden (1987) demonstrated that although human subjects sometimes misidentified random events as nonrandom (i.e., false alarms), they could also correctly detect truly nonrandom signals (i.e., correct hits). Thus, it is important to find out whether the simple binomial model is accurate enough to serve as a normative model. Then, researchers might be able to answer the question whether the hot hand belief is more about signal detections, or, just “seeing something out of randomness. ”