The clustering illusion is the tendency to erroneously perceive small samples from random distributions to have significant “streaks” or “clusters”, caused by a human tendency to under-predict the amount of variability likely to appear in a small sample of random or semi-random data due to chance.

Gilovich, an early author on the subject, argues the effect occurs for different types of random dispersion’s, including 2-dimensional data such as seeing clusters in the locations of impact of V-1 flying bombs on 2 dimensional maps of London during World War II or seeing streaks in stock market price fluctuations over time. Although Londoners developed specific theories about the pattern of impacts within London, in a statistical analysis by R. D. Clarke originally published in 1946 the impacts of V-2 rockets on London is a close fit to the Poisson distribution, meaning it closely resembles the expected result from a chance dispersion (colloquially known as “random”).

The clustering illusion is central to the “hot hand fallacy”, the first study of which was reported by Gilovich, Robert Vallone and Amos Tversky. They found that the idea that basketball players shoot successfully in “streaks”, sometimes called by sportscasters as having a “hot hand” and widely believed by Gilovich et al.’s subjects, was false. In the data they collected, if anything the success of a previous throw very slightly predicted a subsequent miss rather than another success.

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