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A simple way to understand this illusion is to imagine casting ten pennies in a one foot square space. Unless all of the pennies fall in an exactly even distribution, which is extremely improbable, some pennies will be closer to each other than others and seem to form a cluster or group solely from the random distribution.
It's sometimes called the "hot hand fallacy" due to the belief common among basketball coaches and players that it was best to use players on a hot streak (i.e., those who had a "hot hand"). A study demonstrated that the hot hand was a matter of coaches picking a short run of baskets out of a larger sequence that was more or less random. Though there some dispute that the researchers defined "hot hand" (i.e., making exactly one basket following another) differently than basketball players actually conceptualize it (in a vaguer sense).
A similar idea cropped up among birders, known as the Patagonia Picnic Table Effect, that once a rare bird is spotted in one area, other rare birds will soon be spotted in the same area. An analysis of the birding database eBird however showed that this is unlikely to be a real effect.
- Thomas Gilovich, Robert Vallone, and Amos Tversky. The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology vol. 17, pp. 295-314, 1985.
- Scientists who claim ‘hot hand’ is a myth have never had one by Tom Siegfried
- A rare bird sighting doesn't lead to seeing more kinds of rare birds: The so-called Patagonia Picnic Table Effect is a myth, an analysis of bird sightings suggests by Anushree Dave (February 16, 2021 at 12:57 pm) Science News.
- The influence of rare birds on observer effort and subsequent rarity discovery in the American birdwatching community by Jesse A. Laney et al. (January 21, 2021) Peerj 9:e10713 https://doi.org/10.7717/peerj.10713.
- Random Number, Wolfram Math