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=What is Hot Hand Fallacy?= The hot hand fallacy is a belief that particularly applies to the sport of basketball. In relation to basketball the hot hand is the belief that a player is more likely to make their next shot given that they have mad e the previous two or three shots in a row. But this is not true research has shown that a players shots are each independent in and of themselves, 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. According to game theory, when an ideal player shoots a basketball he hits about 50% of his shots. When he shoots 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. Hot hand is also prevalent in many different sports, not just basketball. In volleyball, it is widely accepted that hot hands exist and can influence allocation decisions by coaches and players. Hot hands can change the psychological behavior and the success or failure rates of a player. Belief in the hot hand affects a player's perceptions of success.

Discovery
The discovery of the hot hand fallacy was brought to light by three men Thomas Gilovich, and Amos Tversky are the primary investigators into the hot hand fallacy. Gilovich's research primarily focuses on judgement and decision making behaviors and heuristics. He combined with Amos Tversky, a cognitive and mathematical psychologist, with Robert Vallone, a cognitive psychologist helped pioneer studies on the hot hand fallacy. Their study, The Hot Hand in Basketball: On the Misperception of Random Sequences (1985), investigated the validity of peoples thoughts on "hot" shooters in basketball. This study provided a large body of evidence that disproves the hot hand. The study looks at people's inability to properly understand randomness and random events, much like innumeracy can impair a person's judgement of statistical information, the hot hand can lead people to incorrect assumptions regarding random events. For instance, people expect even short sequences of heads and tails to reflect the fairness of a coin and contain roughly 50% heads and 50% tails. But the study states that there are two biases that are created by this kind of thought pattern. The first is that it could lead an individual to believe that the probability of heads or tails increases after a long sequence after the other has occurred ( gambler's fallacy ) and the second is causes an individual to reject randomness of a sequence of the occurrence of a streak of either heads or tails 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 was looking at the individual records of players from the Philadelphia 76ers during the 1980 - 81 season. 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 surround the shot. For example in the first study there is the factor of 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 fourth eliminate the game setting and the distractions and all of the interferences mention before. The results that were found in the studies primarily displayed 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.

=Hot Hand in Sports=

The NBA is 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. We 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 acquired from the review of film from the 3-point contests and use a technique called 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 HHHHH has one run and the sequence HMHMH has five runs. According to the hot hand a player should have very few run and instead their makes and misses should be in clusters. In their research there were only two players who had a significantly smaller amount of runs then 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 compare the shooters makes and misses. The data came be more in accordince with chance than the hot hand. Through their analysis of the data the conclusion was draw that there was nothing that supported the hot hand.

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 hot hand is changed to account for a player’s ability to predict the outcome of his next shot.

Hot Hand Consumers
There are more places then sport that can be affected by the hot hand fallacy. A study conducted by Johnson, J. et al. examined the characteristics of an individuals 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 that is influenced by a belief that a small sample is able to represent the underlying process. To inspect the effect of the hot hand and gambler's heuristic on the buying and selling behaviors of consumers three hypotheses were made. Hypothesis one states, consumers that are given stocks with positive and negative trends in earning will be more likely to buy a stock that is positive when it is first getting started but will become less likely to do so as the trend lengthens. Hypothesis two, says consumers will be more likely to sell a stock with negative earnings as the trend length initially increases but will decrease as the trend length increases more. Finally the third hypothesis is that consumers in the buy condition are more likely to choose winning stock over those in the selling condition.

The results of the experiment were not supportive of the first hypothesis but was in support of hypothesis two and three. suggesting that that use of these heuristics are dependent on are buying or selling and the length of the sequence. which means that those who had the shorter length and the buying condition would fall under the influence of the hot hand. The opposite would be in accordance with the gambler's 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 affects on other aspects of consumers potential behavior especially when selling instead of buying, because it is more complex of a task.

Hot Hand and Gamblers Fallacy
A study was conducted to examine the difference between 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 when people feel that an event is random such as rolling a pair of dice on a craps table or the number or color you will land on on 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 the hot hand fallacy is when an individuals expect a run to continue. There is a much larger aspect of the hot hand that relies on the individual. That being stated to hot hand is evident when it relates to peoples own ability to predict random events, which is impossible you cannot predict something that is random. The fact that people see that they have this abililty is in line with the illusion of control.

In this study the researchers wish to test if they could manipulate a coin toss in-order to counter the gambler's fallacy by having the particpant focus on the person tossing the coin. In contrast they attempt to initiate the hot hand by centering the participants 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.

The 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 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 attention to the person who was actively flipping the coin. It is important to note that this counteraction of the gambler's fallacy only happend if the person tossing the coin remained the same. This study shed light on the idea that gambler's and hot hand at time fight for dominance when people try yo make predictions about the sameevent.

=Explanation=

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 effect 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).

In attempting to explain the phenomenon that is the hot hand fallacy there are many avenues of thought and potential influences to why we fall pray to the hot hand. Castel, D.A., et. al investigated the idea that age would alter an individuals belief in the hot hand. The researchers cite various studies such as 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 adavaptive dependance on heuristic based judgments. To test this idea researchers conducted a cross sectional study where they sampled 455 participants ranging from ages 22 to 90 years old. These participants were given a questionnaire. the questionnaire was proceeded by a prompt that said in college and professional basketball games no play makes 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. That means that if a person answered yes to the first question then they believed in the hot hand. The results showed that participants over 70 years of age did believe the hot hand and were twice as likely to do so than adults aging 40 - 49. confirming the idea posed earlier that older individuals rely 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. But it is important to note that in this study they did bring up an important point that hot hand may be adaptive because in basketball in could influence the passing of the ball to a player that has a higher shooting percentage. This is knowledge that is can be accumulated over time and thus would increase with age. There are limitations to this study however. That it is only a cross sectional study it only makes the case that there a differences in ages not individual levels of change with regard to the hot hand.

One study looks at the root of the hot hand fallacy as being from our inability to appropriately judge sequences. This analytical study compile the research from dozens of behavioral and cognitive studies. Studies that examined hot hand and gambler's fallacy with random mechanisms and skill generated streaks. In terms of judging random sequences the general conclusion was that people do not a 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 sequence to show the ways in which we as humans interpret and seek to understand information such as s streaks random sequences in relation to furthering research of hot hand and hot hand belief. This study drew the conclusion that human beings are built to see patterns in sensory and conceptual data of all types (gawande, 1999; Gilvich, 1993). In furthering this type of research we have the capability to change the way we as humans conceptualize our surroundings. To understand and predict details of behavior one needs to understand the cognitive representation of the outside world. ultimately this study makes clear that in order to better understand binary sequence we must find a way to bridge the gap between how we categorize the mechanisms that generate random sequences.

=References=