The hot hand (also known as the hot hand phenomenon or hot hand fallacy) is the putative tendency for an athlete to have streaks of success higher than their average performance. The concept is often applied to sports and skill-based tasks in general and originates from basketball, where a shooter is assumed to be more likely to score if their previous attempts were successful – i.e., while having the "hot hand". Researchers for many years did not find evidence for a "hot hand" in practice, dismissing it as fallacious. However, later research questioned whether the belief is indeed a fallacy. Some recent studies using modern statistical analysis have observed evidence for the "hot hand" in some sporting activities; however, other recent studies have not observed evidence of the "hot hand". Moreover, evidence suggests that only a small subset of players may show a "hot hand" and, among those who do, the magnitude (i.e., effect size) of the "hot hand" tends to be small.

The fallacy was first described in a 1985 paper by Thomas Gilovich, Amos Tversky, and Robert Vallone. The "Hot Hand in Basketball" study questioned the hypothesis that basketball players have "hot hands", which the paper defined as the claim that players are more likely to make a successful shot if their previous shot was successful. The study looked at the inability of respondents to properly understand randomness and random events; much like innumeracy can impair a person's judgement of statistical information, the hot hand fallacy can lead people to form incorrect assumptions regarding random events. The three researchers provide an example in the study regarding the "coin toss"; respondents expected even short sequences of heads and tails to be approximately 50% heads and 50% tails. The study proposed two biases that are created by the kind of thought pattern applied to the coin toss: it could lead an individual to believe that the probability of heads or tails increases after a long sequence of either has occurred (known as the gambler's fallacy); or it could cause an individual to reject randomness due to a belief that a streak of either outcome is not representative of a random sample.

The first study was conducted via a questionnaire of 100 basketball fans from the colleges of Cornell and Stanford. The other looked at the individual records of players from the 1980–81 Philadelphia 76ers. The third study analyzed free-throw data and the fourth study was of a controlled shooting experiment. The reason for the different studies was to gradually eliminate external factors around the shot. For example, in the first study there is the factor of how the opposing team's defensive strategy and shot selection would interfere with the shooter. The second and third take out the element of shot selection, and the fourth eliminates the game setting and the distractions and other external factors mentioned before. The studies primarily found that the outcomes of both field goal and free throw attempts are independent of each other. In the later studies involving the controlled shooting experiment the results were the same; evidently, the researchers concluded that the sense of being "hot" does not predict hits or misses.

A 2018 study by Alon Daks, Nishant Desai, and Lisa R. Goldberg at the University of California, Berkeley, reexamined the hot-hand phenomenon using detailed shooting data from the Golden State Warriors during the 2016–2017 NBA season, including performances by Stephen Curry, Klay Thompson, and Kevin Durant. Building on a correction to the original 1985 study identified by Joshua Miller and Adam Sanjurjo, the researchers accounted for a statistical bias caused by the “law of small numbers”—a tendency for reversals to appear more likely than continuations in short sequences of data.

Gilovich offers two different explanations for why people believe hot hands exist. The first is that a person may be biased towards looking for streaks before watching a basketball game. This bias would then affect their perceptions and recollection of the game (confirmation bias). The second explanation deals with people's inability to recognize chance sequences. People expect chance sequences to alternate between the options more than they actually do. Chance sequences can seem too lumpy, and are thus dismissed as non-chance (clustering illusion).

There are many proposed explanations for why people are susceptible to the hot-hand fallacy. Alan D. Castel, and others investigated the idea that age would alter an individual's belief in the fallacy. To test this idea researchers conducted a cross-sectional study where they sampled 455 participants ranging in age from 22 to 90 years old. These participants were given a questionnaire preceded by a prompt that said in college and professional basketball games no players make 100% of their attempted shots. Then the questionnaire asked two important questions: (1) Does a basketball player have a better chance of making a shot after having just made the last two or three shots than after having missed the last two or three shots? (2) Is it important to pass the ball to someone who has just made several shots in a row?

The main interest of the questionnaire was to see if a participant answered yes to the first question, implying that they believed in the hot-hand fallacy. The results showed that participants over 70 years of age were twice as likely to believe the fallacy than adults 40–49, confirming that the older individuals relied more on heuristic-based processes. Older adults are more likely to remember positive information, making them more sensitive to gains and less to losses than younger adults.

One study looked at the root of the hot-hand fallacy as being from an inability to appropriately judge sequences. The study compiled research from dozens of behavioral and cognitive studies that examined the hot-hand and gambler's fallacies with random mechanisms and skill-generated streaks. In terms of judging random sequences the general conclusion was that people do not have a statistically correct concept of random. It concluded that human beings are built to see patterns in sensory and conceptual data of all types.