The "hot-hand fallacy" (also known as the "hot hand phenomenon" or "hot hand") is the fallacious belief that a person who has experienced success with a random event has a greater chance of further success in additional attempts. The concept has been applied to gambling and sports, such as basketball. While a previous success at a skill-based athletic task, such as making a shot in basketball, can change the psychological behavior and subsequent success rate of a player, researchers have often found little evidence for a true "hot hand" in practice. It has been reported that a belief in the hot-hand fallacy affects a player's perceptions of success. However a 2015 examination of the original papers by Joshua Miller and Adam Sanjurjo found flaws in the methodology and showed that, in fact, the hot hand fallacy may not exist. It may be attributable to a misapplication of statistical techniques. 
Three researchers discovered the fallacy, with Thomas Gilovich and Amos Tversky acting as the primary investigators. Gilovich's primary focus was on judgment, decision-making behaviors and heuristics, while Amos Tversky came from a cognitive and mathematical psychology background. The pair collaborated with Robert Vallone, a cognitive psychologist, and all three became pioneers of the hot hand fallacy theory. Their study, "The Hot Hand in Basketball: On the Misperception of Random Sequences" (1985), investigated the validity of people's thoughts on "hot" shooters in basketball.
The "Hot Hand in Basketball" study provided a large body of evidence that disproved the theory the basketball players have "hot hands", that is, that they 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 sense of being "hot" does not predict hits or misses.
A 2003 paper noted that Gilovich et al. did not examine the statistical power of their own experiments. By performing power analysis on the 1985 data, the researchers concluded that even if the Philadelphia 76ers did shoot in streaks, it is highly unlikely that Gilovich, Vallone and Tversky would have discovered that fact.
Hot-hand in sports
In relation to basketball the hot hand is the belief that a player is more likely to make his next shot given that he has made the previous two or three shots in a row. However, research has shown that a player's shots are each independent statistical events, meaning that the chance that an athlete would make a shot (e.g., a free throw) was about the same regardless of whether the athlete made or missed one or more similar shots beforehand. According to probability theory, when an ideal player that hits about 50% of his basketball shots takes 20 shots, he will have a number of hits and misses that are a chance sequence. People that see chance sequences with lumps of hits and misses will say that he is shooting in streaks (having hot or cold hands) when the player actually is not.
The NBA is a place where people tend to place a lot of emphasis on streaks. A study by Koehler, J. J. & Conley C. A. was conducted to examine the hot hand myth in professional basketball. In this study the researchers examined film from the NBA shooting contests from 1994–1997. Through studying the film of the contests the researchers hoped to find evidence of sequential dependency within each shooter across all shots. They also searched for sequential dependencies within each shooter per set of 25 continuous shots, and employed a variety of novel techniques for isolating hot performance. To examine the data they used a runs analysis, which examined the streakiness of each individual player. A run is categorized as one or more hits and misses. Thus the sequence hit-hit-hit-hit-hit has one run and the sequence hit-miss-hit-miss-hit has five runs. According to the hot hand a player should have very few runs and instead their hits and misses should be in clusters. In their research there were only two players who had a significantly smaller amount of runs than expected by chance. No shooter had significantly more runs than would be expected by chance. About half of the shooters (12 of 23 = 52%) had fewer runs than expected, and about half (11 of 23 = 48%) had more runs than expected. The researchers also compared the shooters hits and misses. The data were more in accordance with chance than the hot hand. Through their analysis of the data the conclusion was drawn that there was nothing that supported the hot hand hypothesis.
In his 1991 book How We Know What Isn't So, Thomas Gilovich details his empirical investigation of the hot hand fallacy. By analyzing the shooting data of a professional basketball team over the course of a year, he discovered that a player’s performance on a shot is independent of his performance on the previous shot. This result is not expected if there is such a thing as a "hot hand". The result holds when considering players' free throw records, in which things such as defensive pressure and difficulty of the shot are constant. The result also holds when the definition of a hot hand is changed to account for a player’s ability to predict the outcome of his next shot.
There does, however, seem to exist some support for the basketball "hot hand" hypothesis, at least where the shooting of free throws are concerned. In a report published October, 2011 by Yaari and Eisenmann, a large data set of more than 300,000 NBA free throws were found to show "strong evidence" for the "hot hand" phenomenon at the individual level. They analyzed all free throws taken during five regular seasons NBA seasons from 2005 to 2010. They found that there was a significant increase in players' probabilities of hitting the second shot in a two-shot series compared to the first one. They also found that in a set of two consecutive shots, the probability of hitting the second shot is greater following a hit than following a miss on the previous one. Other studies have also confirmed a hot hand in basketball and baseball.
There are more places than sport that can be affected by the hot-hand fallacy. A study conducted by Joseph Johnson et al. examined the characteristics of an individual's buying and selling behavior as it pertained to the hot hand and gambler's heuristic. Both of these occur when a consumer misunderstands random events in the market and is influenced by a belief that a small sample is able to represent the underlying process. To examine the effect of the hot hand and gambler's heuristic on the buying and selling behaviors of consumers, three hypotheses were made. Hypothesis one stated that consumers that were given stocks with positive and negative trends in earning would be more likely to buy a stock that was positive when it was first getting started but would become less likely to do so as the trend lengthened. Hypothesis two was that consumers would be more likely to sell a stock with negative earnings as the trend length initially increased but would decrease as the trend length increased more. Finally, the third hypothesis was that consumers in the buy condition would be more likely to choose a winning stock over those in the selling condition.
The results of the experiment did not support the first hypothesis but did support hypotheses two and three, suggesting that the use of these heuristics is dependent on buying or selling and the length of the sequence. This means that those who had the shorter length and the buying condition would fall under the influence of the hot-hand fallacy. The opposite would be in accordance with the gambler's fallacy which has more of an influence on longer sequences of numerical information. This particular study explores a portion of the possibilities that the hot hand and gambler's fallacies affect other aspects of consumers' potential behavior, especially when selling instead of buying, because it is a more complex task.
Hot-hand and the gambler's fallacy
A study was conducted to examine the difference between the hot-hand and gambler's fallacy. The gambler's fallacy is the expectation of a reversal following a run of one outcome. Gambler's fallacy occurs mostly in cases in which people feel that an event is random, such as rolling a pair of dice on a craps table or spinning the roulette wheel. It is caused by the false belief that the random numbers of a small sample will balance out the way they do in large samples; this is known as the law of small numbers heuristic. The difference between this and the hot-hand fallacy is that with the hot-hand fallacy an individual expects a run to continue. There is a much larger aspect of the hot hand that relies on the individual. This relates to a person's perceived ability to predict random events, which is not possible for truly random events. The fact that people believe that they have this ability is in line with the illusion of control.
In this study, the researchers wanted to test if they could manipulate a coin toss, and counter the gambler's fallacy by having the participant focus on the person tossing the coin. In contrast, they attempted to initiate the hot-hand fallacy by centering the participant's focus on the person tossing the coin as a reason for the streak of either heads or tails. In either case the data should fall in line with sympathetic magic, whereby they feel that they can control the outcomes of random events in ways that defy the laws of physics, such as being "hot" at tossing a specific randomly determined outcome.
They tested this concept under three different conditions. The first was person focused, where the person who tossed the coin mentioned that she was tossing a lot of heads or tails. Second was a coin focus, where the person who tossed the coin mentioned that the coin was coming up with a lot of heads or tails. Finally there was a control condition in which there was nothing said by the person tossing the coin. The participants were also assigned to different groups, one in which the person flipping the coin changed and the other where the person remained the same.
The researchers found the results of this study to match their initial hypothesis that the gambler's fallacy could in fact be countered by the use of the hot hand and people's attention to the person who was actively flipping the coin. It is important to note that this counteraction of the gambler's fallacy only happened if the person tossing the coin remained the same. This study shed light on the idea that the gambler's and hot hand fallacies at times fight for dominance when people try to make predictions about the same event.
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. The researchers cited various studies that found that younger adults are more capable of using complex, less heuristic-based decision-making strategies when the environment requires their use. By contrast, an older individual would be subject to an adaptive dependence on heuristic-based judgments. 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? Participants were then asked to rate their level of interest in basketball from 1 to 6, 1 being low and 6 being high.
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. The study did note that the fallacy may be adaptive because in basketball it could influence players to pass the ball to a player that has a higher overall shooting percentage. This is knowledge that can be accumulated over time and thus would increase with age. There are limitations to this study however. Since it is a cross-sectional study it only makes the case that there a differences in age cohorts, but not that individuals change in their belief in the fallacy as they age.
One study looked at the root of the hot-hand fallacy as being from our inability to appropriately judge sequences. This analytical 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. This paper covered concepts such as complex, cognitive mental models of sequence generators, folk theories about luck and randomness, and judgments of random sequences to show the ways in which humans interpret and seek to understand information such as streaks and random sequences in relation to the hot-hand fallacy. It concluded that human beings are built to see patterns in sensory and conceptual data of all types (Gawande, 1999; Gilvich, 1993).
Some sports video games have a version of hot hands, where the player will hit any move as long as they keep scoring. An example of this is NBA Jam, where the ball literally catches fire during combo streaks.
- Clustering illusion
- Gambler's fallacy
- Game theory
- Winning streak (sports)
- Poisson distribution
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- The Hot Hand in Basketball: Fallacy or Adaptive Thinking? - B.D. Burns
- The Hot Hand Fallacy: Taxonomy of the Logical Fallacies
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- Sports Streaks and The Hot Hand Phenomenon
- Prof. Alan Reifman's page "The Hot Hand in Sports"