The gambler's fallacy in penalty shootouts

A well-known bias in subjective perceptions of chance is the gambler's fallacy: people typically believe that a streak generated by a series of independent random draws, such as a coin toss, becomes increasingly more likely to break when the streak becomes longer. In a fascinating study, Misirlisoy and Haggard analysed sequential behavior of kickers and goalkeepers in penalty shootouts. They report that goalkeepers are prone to the gambler's fallacy: after a series of three kicks in the same direction, goalkeepers are more likely to dive in the opposite direction at the next kick. Here we argue, first, that a binomial test is more appropriate for testing gambler's fallacy than the tests employed by Misirlisoy and Haggard, and second, that penalty shootouts may not be well-suited to analyze the gambler's fallacy. Using a binomial test, we neither find statistically significant evidence for gambler's fallacy in Misirlisoy and Haggard's original data, nor in extended data, nor in data from an idealised laboratory experiment that we ran to address the second point. In line with Misirlisoy and Haggard's original result, we do, however, find evidence for a systematic pattern of goalkeeper's behavior that kickers could exploit.