The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of variability likely to appear in a small sample of random or semi-random data.
Thomas Gilovich, an early author on the subject, argued that the effect occurs for different types of random dispersions, including two-dimensional data such as clusters in the locations of impact of World War II V-1 flying bombs on maps of London; or seeing patterns in stock market price fluctuations over time. Although Londoners developed specific theories about the pattern of impacts within London, a statistical analysis by R. D. Clarke originally published in 1946 showed that the impacts of V-2 rockets on London were a close fit to a random distribution.
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 referred to by sportcasters 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.
Using this cognitive bias in causal reasoning may result in the Texas sharpshooter fallacy. More general forms of erroneous pattern recognition are pareidolia and apophenia. Related biases are the illusion of control which the clustering illusion could contribute to, and insensitivity to sample size in which people don't expect greater variation in smaller samples. A different cognitive bias involving misunderstanding of chance streams is the gambler's fallacy.