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[Plutarch] "It is no great wonder if in the long process of time, while fortune takes her course, hither and thither... numerous coincidences should spontaneously occur".
Avoid the pits by following the pendulum, Niederhoffer and Kenner, 2002
NBA teams ride the shooter with the hot hand, and baseball players live and die with hitting streaks. But are these examples of hot hands real, or do they just seem that way because of the vagaries of memory? Most researchers who have studied hot hands conclude the concept is a myth. The expert in this field, Cornell University psychology professor Gilovich, concluded that "detailed analyses provided no evidence for a positive correlation between the outcomes of successive shots". An excellent book that reports tests for streakiness of batters and teams in baseball is "Curve Ball" by Jim Albert and Jay Bennett. They found that in one year, only six of 30 teams showed streakiness, a result consistent with chance.
The Hot Hand in Basketball: Fallacy or Adaptive Thinking?, Burns
In basketball, players believe that they should "feed the hot hand", by giving the ball to a player more often if that player has hit a number of shots in a row. However, Gilovich, Vallone & Tversky (1985) analyzed basketball players' successive shots and showed that they are independent events. Thus the hot hand seems to be a fallacy. Taking the correctness of their result as a starting point, I suggest that if one looks at the hot hand phenomena from Gigerenzer & Todd's (1999) adaptive thinking point of view, then the relevant question to ask is does belief in the hot hand lead to more scoring by a basketball team? By simulation I show that the answer to this question is yes, essentially because streaks are predictive of a player's shooting percentage. Thus belief in the hot hand may be an effective, fast and frugal heuristic for deciding how to allocate shots between member of a team.
When it is adaptive to follow streaks: Variability and stocks, Burns, 2003
"Streaks of events are ubiquitous yet understanding the behavioral effects of them has been restricted by the lack of testable hypotheses concerning the most basic question: When do we tend to follow streaks (positive recency), and when do we tend to go against streaks (negative recency)? From an analysis of positive recency in terms of adaptivity, I develop two elements of people's representation of the process generating a sequence which should be predictive of people's use of positive recency. The first factor is randomness, which has already been tested empirically, and the second is variability which is tested here. The context used is stocks because not only do people seem to give weight to streaks in the stockmarket, but recent evidence suggests that it may be beneficial to do so. Participants were told that a small company (more variable price) and a large company (less variable price) had experienced a streak of six months of increased/decreased stock prices. As predicted, participants were more likely to predict that the small company would continue the streak next month. However, regardless of the initial streak, participants tended to switch which company would do better between six months and ten years. The results show that there are interesting behavioral phenomena associated with streaks".
Heuristics as beliefs and as behaviors: The adaptiveness of the "hot hand", Burns, 2004

"Belief in the "hot hand" in basketball suggests that players experiencing streaks should be given more shots, but this has been seen as a fallacy due to Gilovich, Vallone & Tversky's (1985) failure to find dependencies between players' shots. Based on their findings, I demonstrate by Markov modeling and simulation that streaks are valid allocation cues for deciding who to give shots to, because this behavior achieves the team goal of scoring more. Empirically I show that this adaptive heuristic is supported by the fallacious belief in dependency, more so as skill level increases. I extend the theoretical analysis to identify general conditions under which following streaks should be beneficial. Overall, this approach illustrates the advantages of analyzing reasoning in terms of adaptiveness".
Randomness and inductions from streaks: "Gambler's fallacy" versus "Hot hand", Burns, 2004
"Sometimes people believe a run of similar independent events will be broken (belief in the "gambler's fallacy"), but other times that such a run will continue (belief in the "hot hand"). These opposite inductions have both been explained as due to belief in a law of small numbers. We argue one factor that distinguishes these phenomena is people's beliefs about the randomness of the underlying process generating the events. We gave participants information about a streak of events, but varied the scenarios such that the mechanism generating the events should vary in how random participants judged it to be. A manipulation check confirmed our assumptions about the scenarios. We found that in less random scenarios participants were more likely to continue a streak".