33. The Hot Hand in Basketball: On the Misperception of Random Sequences

Thomas Gilovich, Robert Vallone, and Amos Tversky

In describing an outstanding performance by a basketball player, reporters and spectators commonly use expressions such as "Larry Bird has the hot hand" or "Andrew Toney is a streak shooter." These phrases express a belief that the performance of a player during a particular period is significantly better than expected on the basis of the player's overall record. The belief in "the hot hand" and in "streak shooting" is shared by basketball players, coaches, and fans, and it appears to affect the selection of plays and the choice of players. In this chapter, we investigate the origin and the validity of these beliefs.

People's intuitive conceptions of randomness depart systematically from the laws of chance. It appears that people expect the essential characteristics of a chance process to be represented not only globally in the entire sequence, but also locally, in each of its parts. For instance, people expect even short sequences of heads and tails to reflect the fairness of a coin and contain roughly 50% heads and 50% tails. This conception of chance has been described as a "belief in the law of small numbers" according to which the law of large numbers applies to small samples as well (Tversky & Kahneman, 1971). A locally representative sequence, however, deviates systematically from chance expectation: It contains too many alternations and not enough long runs.

A conception of chance based on representativeness, therefore, produces two related biases. First, it induces a belief that the probability of heads is greater after a long sequence of tails than after a long sequence of heads – this is the notorious gambler's fallacy (see, e.g., Tversky & Kahneman, 1974). Second, it leads people to reject the randomness of sequences that contain the expected number of runs because even the occurrence of, say, four heads in a row – which is quite likely in a sequence of 20 tosses – makes the sequence appear nonrepresentative (Falk, 1981; Wagenaar, 1972).

Sequences of hits and misses in a basketball game offer an interesting context for investigating the perception of randomness outside the psychological laboratory. Consider a professional basketball player who makes 50% of his shots. This player occasionally hits four or more shots in a row. Such runs can be properly called streak shooting, however, only if their length or frequency exceeds what is expected on the basis of chance alone. The player's performance, then, can be compared to a sequence of hits and misses generated by tossing a coin. A player who produces longer sequences of hits than those produced by tossing a coin can be said to have a hot hand or be described as a streak shooter. Similarly, these terms can be applied to a player who has a better chance of hitting a basket after one or more successful shots than after one or more misses.

This analysis does not attempt to capture all that people might mean by the hot hand or streak shooting. Nevertheless, we argue that the common use of these notions – however vague or complex – implies that players' performance records should differ from sequences of heads and tails produced by coin tossing in two essential respects. First, these terms imply that the probability of a hit should be greater following a hit than following a miss (i.e., positive association). Second, they imply that the number of streaks of successive hits or misses should exceed the number produced by a chance process with a constant hit rate (i.e., nonstationarity).

It may seem unreasonable to compare basketball shooting to coin tossing because a player's chances of hitting a basket are not the same on every shot. Lay-ups are easier than 3-point field goals and slam dunks have a higher hit rate than turnaround jumpers. Nevertheless, the simple binomial model is equivalent to a more complicated process with the following characteristics: Each player has an ensemble of shots that vary in difficulty (depending, for example, on the distance from the basket and on defensive pressure), and each shot is randomly selected from this ensemble. This process provides a more compelling account of the performance of a basketball player, although it produces a shooting record that is indistinguishable from that produced by a simple binomial model in which the probability of a hit is the same on every trial.

We begin with a survey that explores the beliefs of basketball fans regarding streak shooting and related phenomena. We then turn to an analysis of field goal and free-throw data from the NBA. Finally, we report a controlled experiment performed by the men and women of Cornell's varsity teams that investigates players' ability to predict their performance. These investigations, however, consistently found no evidence of streak shooting beyond what chance would produce—the hot hand is a cognitive illusion. This bias, now known as the hot hand fallacy, stems from the deep-seated human tendency to misperceive randomness as meaningful patterns. Despite its origin in basketball, the fallacy has broad implications: it affects decision-making in finance, gambling, and any domain where people interpret random sequences of events as patterned or predictable.