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// Introduction in process //

The "hot hand" (also known as the "hot hand phenomenon," and "streak shooting," in the sports context, or the "hot hand fallacy," and "hot hand bias" in the context of cognitive psychology) is the belief that the probability an event, , will result in some outcome, , is significantly higher during a particular period than what is expected based on the average rate at which event produces outcome .[1] In situations where the outcome being observed is truly random (the result of an independent trial of a random process) this belief is false. A typical example is the event that a fair coin is flipped, and the outcome that the coin lands on heads (tails). Such an outcome is considered the result of a random process, because it is impossible to predict which side the coin will land on with absolute certainty. The true probability that each flip of a fair coin will land on heads (tails) is 50%. However, observers of a series of coin flips may come to believe the probability the next flip lands on heads (tails) is actually greater than 50% after watching the coin land on heads (tails) several times in a row.[2] Another typical example is the event that a basketball player takes a shot, and the outcome that the shot is a hit (miss). The basketball player, and the fans in the audience, may believe that the player is more likely to swish (brick) a shot that follows one or more successful (unsuccessful) shots than what one might expect based on that player's overall performance record. The outcome of a basketball player's shot is also the result of a random process, because it is impossible to predict whether the player will make or miss the shot with absolute certainty. While previous success at a task can indeed change the psychological attitude and subsequent success rate of a player, 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. Recent studies using modern statistical analysis show there is evidence for the "hot hand" in some sporting activities.

// Introduction under "Development of Theory" //

[placeholder for Tversky and Kahneman, 1971, belief in law of small numbers].[3] [placeholder for the representativeness heuristic, Tversky and Kahneman, 1974].[4][5] [placeholder for Bar-Hillel & Wagenaar, 1991].[6][7]

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Relationship between the "hot hand" and "gambler's" fallacies

[placeholder for Rabin, 2002][8]. [placeholder for Rabin & Vayanos, 2005, 2010].[9] [placeholder for Asparouhova, Hertzel, and Lemmon, 2009].[10]

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Financial markets

[placeholder for Barberis, Shleifer, and Vishny, 1998].[11]

// Below content needs to be updated with additional content, context, and references. Currently describes only one study, providing a very limited/biased view of the hot hand concept in the context of gambling //

Gambling[edit]

[placeholder for Clotfelter & Cook, 1993].[12] [placeholder for Croson & Sundali, 2005].[13]

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.[14] 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.[15] 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.[14]

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.[14]

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.[14] 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.[14] 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.[14]

  1. ^ Gilovich, Thomas; Vallone, Robert; Tversky, Amos (1985-07). "The hot hand in basketball: On the misperception of random sequences". Cognitive Psychology. 17 (3): 295–314. doi:10.1016/0010-0285(85)90010-6. ISSN 0010-0285. {{cite journal}}: Check date values in: |date= (help)
  2. ^ Tversky, Amos; Kahneman, Daniel (1971). "Belief in the law of small numbers". Psychological Bulletin. 76 (2): 105–110. doi:10.1037/h0031322. ISSN 1939-1455.
  3. ^ Tversky, Amos; Kahneman, Daniel (1971). "Belief in the law of small numbers". Psychological Bulletin. 76 (2): 105–110. doi:10.1037/h0031322. ISSN 1939-1455.
  4. ^ Kahneman, Daniel; Tversky, Amos (1972-07). "Subjective probability: A judgment of representativeness". Cognitive Psychology. 3 (3): 430–454. doi:10.1016/0010-0285(72)90016-3. ISSN 0010-0285. {{cite journal}}: Check date values in: |date= (help)
  5. ^ Tversky, Amos; Kahneman, Daniel (1974-09-27). "Judgment under Uncertainty: Heuristics and Biases". Science. 185 (4157): 1124–1131. doi:10.1126/science.185.4157.1124. ISSN 0036-8075. PMID 17835457.
  6. ^ Bar-Hillel, Maya (1973-06). "On the subjective probability of compound events". Organizational Behavior and Human Performance. 9 (3): 396–406. doi:10.1016/0030-5073(73)90061-5. ISSN 0030-5073. {{cite journal}}: Check date values in: |date= (help)
  7. ^ Bar-Hillel, Maya; Wagenaar, Willem A (1991-12). "The perception of randomness". Advances in Applied Mathematics. 12 (4): 428–454. doi:10.1016/0196-8858(91)90029-i. ISSN 0196-8858. {{cite journal}}: Check date values in: |date= (help)
  8. ^ Rabin, M. (2002-08-01). "Inference by Believers in the Law of Small Numbers". The Quarterly Journal of Economics. 117 (3): 775–816. doi:10.1162/003355302760193896. ISSN 0033-5533.
  9. ^ RABIN, MATTHEW; VAYANOS, DIMITRI (2010-04). "The Gambler's and Hot-Hand Fallacies: Theory and Applications". Review of Economic Studies. 77 (2): 730–778. doi:10.1111/j.1467-937x.2009.00582.x. ISSN 0034-6527. {{cite journal}}: Check date values in: |date= (help)
  10. ^ Asparouhova, Elena; Hertzel, Michael; Lemmon, Michael (2009-11). "Inference from Streaks in Random Outcomes: Experimental Evidence on Beliefs in Regime Shifting and the Law of Small Numbers". Management Science. 55 (11): 1766–1782. doi:10.1287/mnsc.1090.1059. ISSN 0025-1909. {{cite journal}}: Check date values in: |date= (help)
  11. ^ Barberis, Nicholas; Shleifer, Andrei; Vishny, Robert (1998-09). "A model of investor sentiment1We are grateful to the NSF for financial support, and to Oliver Blanchard, Alon Brav, John Campbell (a referee), John Cochrane, Edward Glaeser, J.B. Heaton, Danny Kahneman, David Laibson, Owen Lamont, Drazen Prelec, Jay Ritter (a referee), Ken Singleton, Dick Thaler, an anonymous referee, and the editor, Bill Schwert, for comments.1". Journal of Financial Economics. 49 (3): 307–343. doi:10.1016/s0304-405x(98)00027-0. ISSN 0304-405X. {{cite journal}}: Check date values in: |date= (help)
  12. ^ Clotfelter, Charles T.; Cook, Philip J. (1993-12). "Notes: The "Gambler's Fallacy" in Lottery Play". Management Science. 39 (12): 1521–1525. doi:10.1287/mnsc.39.12.1521. ISSN 0025-1909. {{cite journal}}: Check date values in: |date= (help)
  13. ^ Croson, Rachel; Sundali, James (2005-05). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos". Journal of Risk and Uncertainty. 30 (3): 195–209. doi:10.1007/s11166-005-1153-2. ISSN 0895-5646. {{cite journal}}: Check date values in: |date= (help)
  14. ^ a b c d e f Roney, Christopher J. R.; Trick, Lana M. (2009). "Roney, C. R., Trick, L. M. (2009)". Sympathetic magic and perceptions of randomness: the hot hand versus the gambler's fallacy. 15 (2): 197–210. doi:10.1080/13546780902847137.
  15. ^ Raab, Markus; Gula, B.; Gigerenzer, G. (2011). "The Hot hand Exists in Volleyball and Is Used for Allocation Decisions". Journal of Experimental Psychology: Applied. 18 (1): 81–94. doi:10.1037/a0025951.
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