What is The Hot Hand Fallacy?
The Hot Hand Fallacy, also known as streak shooting, is the belief that the probability of a made shot is greater following a previously made shot rather than a miss. 
This belief is of course irrational. All statistical analysis collected on the subject, first conducted by Thomas Gilovich, show that the outcome of a shot has no positive correlation with the outcome of the previous shots taken. 
Irrational Belief that is Predictable, Pervasive, and Powerful
When asked if a player “has a better chance of making a shot after having just made his last two or three shots than he does after having just missed his last two or three shots,” 91% of fans surveyed responded “Yes.” When surveyed professional players and coaches like basketball fans alike show equal levels of belief in the hot hand fallacy. Moreover, these results are pervasive even when shown the data proving otherwise. When the results of Gilovich’s first studies where published the overwhelming public response was of disbelief. Most famously famed Boston Celtics' Coach Red Auberbach's response to the study was, “Who is this guy? So he makes a study. I couldn’t care less.”
Irrational Belief That Cannot Be Explained By Lack of Proper Incentives
One may argue that the average fan may not have the proper incentives to correct for this fallacy. After-all, the root of irrational beliefs caused by biases and heuristics is commonly (but misleadingly) believed to be a “lazy and inattentive minds.” This explanation should be resisted in light of the evidence that even trained professionals are prone to the streak shooting belief. Conceivably, in the context of the multi-billion dollar NBA industry there are strong incentives to pay attention and devote full cognitive resources to understanding the phenomenon of “streak shooting.” Failure to be understand streak shooting can be costly! As Gilovich explains,
“Passing the ball to the player who is ‘hot’ is a common strategy endorsed by basketball players. It is also anticipated by the opposing team who can concentrate on guarding the ‘hot’ player. If another player, who is less ‘hot’ on that particular day, is equally skilled, then the less guarded player would have a better chance of scoring. Thus the belief in the ‘hot hand’ is not just erroneous, it could be costly.” 
The occurrence of even well incentivized people still falling prey to this fallacy is not a surprise. As researchers Camerer and Hogarth have found, “no replicated study has made rationality violations disappear purely by raising incentives.”
Why Does the Erroneous Belief of Streak Shooting Exist?
We Are Associative Machines Built To See Patterns Where None Exist
The hot hand fallacy is caused by the representatitiveness bias. We have a positive association bias in which the likelihood of a made shot is incorrectly perceived to be greater following a made basket. This occurs because we are built to see patterns where none exist. When we see two shots being hit, we assume the successive shots thereafter similarly will go in. In other words, we judge the likelihood of successive shots based on the representatitiveness of the outcomes of the most recent shot attempts. The association of the recently made or missed basket is still so fresh in our head!
We Lack the Ability to Intuitively Grasp Random Sequences
Moreover, the associative machine seeks to explain perceived abnormalities of random sequence. This is because we lack the ability to intuitively grasp random sequences.  A random sequence is a sequence of events in which the outcome of each individual event cannot be predicted with certainty. Basketball shots are indeed random sequences similar to coin tosses. The comparison seems intuitively unreasonable because the chance of a shot is dependent on other parameters which may not be the same in every instance, such as defensive intensity, player skill, and shot selection. Nevertheless, the probability of each individual shot is largely independent on the outcome of the previous shots taken. Similarly with coin tosses, although the probability of getting heads when you flip a coin is dependent on other parameters such as “the initial position of the coin, and it’s angular and vertical momentum,” it is nevertheless independent on the outcome of the previous flips taken.
Like a random sequence of shots resulting in 3 baskets made in a row, it is not inconceivable (and in fact quite probable) to have a random sequence of coin flips come up heads 3 times in a row. However, our associative machine upon viewing such a pattern inaccurately seeks to make use of this seemingly logical pattern within the random sequence, leading us to a mistaken perception on how random sequences work.
Findings Do Not Make Basketball a Game of Chance, and Not Skill
Of course, these findings do not make basketball a game of chance as oskill. It merely means that the likelihood of a make on successive shots is independent of the outcomes of the previous shots taken. Strategy, skill, and other variables still play a part in deciding which shots to take and the likelihood you are to make it.
The hot hand fallacy is just one of many ways in which a better understanding of behavioral science can help us. Failure to be aware of this heuristic based misperception of streak shooting can be costly. Nevertheless people, even in positions of great incentive, fail to consciously adjust their intuitive assessments in light of the research. In other words their system 2 (conscious thought) refuses to reassess the faulty information provided to them by their system 1 (subconscious thought, also known as intuition). They consciously reject the teachings of behavioral science in favor for beliefs that reconcile with our desire to see patterns, leading to incorrectly believing in the phenomenon of streak shooting. Therefore there is arbitrage to be had by those who do accept the teachings of behavioral science. In a world where every advantage helps, perhaps refusing to adopt strategies based on irrational beliefs can provide the necessary winning edge.
 Thomas Gilovich, Robert Vallone & Amos Tversky, The Hot Hand in Basketball: On the Misperception of Random Sequence, 295-314. 296 (1985).
 Id.at 295. In relevant part: “detailed analyses of the shooting records of the Philadelphia 76ers provided no evidence for a positive correlation between the outcomes of successive shots. The same conclusions emerged from free-throw records of the Boston Celtics, and from a controlled shooting experiment with the men and women of Cornell’s varsity teams. The outcomes of previous shots influenced Cornell players’ predictions but not their performance.” The different tests where done to control for and eliminate the various factors surrounding a shot such as skill, defensive intensity, and shot selection.
 Id. at 297.
 Id. at 310. In relevant part: “[Discussing surveyed 76ers players] Most of the players (six out of eight) reported that they have on occasion felt that after having made a few shots in a row they ‘know’ they are going to make their next shot-that they ‘almost can’t miss’… All of the players believed that it is important ‘for the players on a team to pass the ball to someone who has just made several (two, three, or four) shots in a row.’ Five players and the coach also made numerical estimates. Five of these six respondents estimated their field goal percentage for shots taken after a hit (mean: 62.5%) to be higher than their percentage for shots taken after a miss (mean: 49.5%).”
 Daniel Kahneman, Thinking Fast and Slow, 172.
 Thomas Gilovich, Dale Griffin, & Daniel Kahneman, Heuristics And Biases, 1-20, 2 (2002), The Psychology of Intuitive Judgment. In relevant part: “Automatic or Deliberate? There is another dichotomous aspect of the heuristics and biases approach that warrants discussion. Heuristics have often been described as something akin to strategies that people use deliberately in order to simplify judgmental tasks that would otherwise be too difficult for the typical human mind to solve. This use of the term fits with the ‘cognitive miser’ metaphor that proved popular in the field of social cognition (Fiske & Taylor, 1991). The metaphor suggests, perhaps unfortunately and unwisely, that the biases documented in the heuristics and biases tradition are the product of lazy and inattentive minds. The implication is unfortunate and potentially misleading because the biases identified in this tradition have not been appreciably reduced by incentives for participants to sit straight, pay attention, and devote their full cognitive resources to the task. After reviewing 74 studies, Camerer and Hogarth (1999) concluded that incentives can reduce self-presentation effects, increase attention and effort, and reduce thoughtless responding, but noted that ‘no replicated study has made rationality violations disappear purely by raising incentives.’”
 See Gilovich Hot Hand, supra note 1, at 313.
 See Gilovich Heuristics & Biases, supra note 7.
 See Gilovich Hot Hand, supra note 1, at 296.
 Id. at 296
 See Kahneman, supra note 5, at 169.
 See Gilovich Hot Hand¸supra note 1, at 311. In pertinent part: “We attribute this phenomenom to a general misconception of the laws of chance associated with the belief that small as well as large sequences are representative of their generating process. This belief induces the expectation that random sequences should be far more balanced than they are, and the erroneous perception of a positive correlation between successive shots.”
 Id. at 297. In relevant part: “It may seem unreasonable to compare basketball shooting to coin tossing because a player’s chances of hitting a basket are not the same on every shot. Lay-ups are easier than 3-point field goals and slam dunks have a higher hit rate than turnaround jumpers. Nevertheless, the simple binomial model is equivalent to a more complicated process with the following characteristics: Each player has an ensemble of shots that vary in difficulty (depending, for example, on the distance from the basket and on defensive pressure), and each shot is randomly selected from this ensemble. This process provides a more compelling account of the performance of a basketball player, although it produces a shooting record that is indistinguishable from that produced by a simple binomial model in which the probability of a hit is the same on every trial.”
 Id. 312-313.
 Id. at 312.