Hot hand phenomenon

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Hot hand phenomenon (from English hot hand, happy hand) describes the positive expectation towards the occurrence of an event that has already been preceded by a consequence of the same event. In the game one speaks of a lucky streak. It is not determined whether this expectation is correct. In contrast, a hot hand is used when a repeated event actually increases the likelihood of a recurrence. In sport one speaks of a run. The event is then referred to as “hot”.

The existence of the hot hand is rejected from a mathematical point of view if the events under consideration are independent of one another. The probability of an event occurring does not change in the repetition, which is why a previous sequence has no effect on the next event. On the other hand, if the events are positively dependent on one another, then their probability of occurrence in the repetition increases. That is why proponents speak of a hot hand that can be masked by disruptive factors. Critics accuse them of failing to recognize independence from events.

The hot-hand phenomenon has been discussed from a mathematical and psychological point of view since 1985 . The hot hand phenomenon occurs in areas such as sports , business and gambling.

Origin and development

In 1985 Thomas Gilovich , Robert Vallone and Amos Tversky dealt with the hot hand phenomenon for the first time . In her work, "The Hot Hand in Basketball: On the misperception of random sequences" (dt .: The Hot Hand in Basketball: On the misperception of random sequences ) they inquired about how people random sequences misjudge and they therefore non-random Attributing Attributes .

In several field and laboratory experiments , the researchers investigated whether a player was more likely to score a hit in basketball if he was successful in previous throws. The work comprises four studies that approach the hot hand phenomenon from different perspectives: The survey of 100 fans, the analysis of the Philadelphia 76ers team in the 1980/81 season and the evaluation of the free throws were carried out. Finally, the predictions of the players about the occurrence of a hot hand were evaluated. Overall, Gilovich, Tversky and Vallone showed in their studies that the hot hand does not exist in basketball.

The results of this study have been discussed since 1985. Today, the findings are also used in other disciplines outside of sport: In areas such as decision theory , sport science , economics, legal literature or religion , the work of Gilovich et al. cited many times.

The hot hand phenomenon in sports

A player has a hot hand who achieves successes several times in quick succession and therefore has an increased probability of success on the next attempt compared to his average performance. Since the first study, research has focused primarily on basketball, from which the phenomenon owes its name. But the hot hand phenomenon is also important in other sports: studies on baseball and tennis appeared around 1990, and later also on golf , darts , bowling and horseshoe throwing.

basketball

A basketball hot hand is when the basket is more likely to be hit by a player because he has scored several baskets immediately before . Studies have shown that fans as well as players and coaches believe in the existence of the hot hand. Nevertheless, this could not be proven in various studies. The comparison of the probability of a hit after a successful and an unsuccessful throw showed no connection. The calculation of the performance stability of the players over several games also did not reveal any evidence of a hot hand. In addition, the number of changes between hits and misses was analyzed. Accordingly, the existence of the hot hand in basketball has not been proven.

Although the existence of the hot hand has not been established, the belief in the hot hand has an indirect effect on the gameplay.

  • Accepting a hot hand with a player means that his fellow players will allude to him more often. Because the opponents anticipate this, this player is better covered. This increases the difficulty of the next throwing attempt by him and decreases the chances of a hit. So accepting the hot hand can negatively impact a team's performance.
  • Accepting a hot hand can increase the team's probability of hitting the ball if the ball is passed to another equally good player without an alleged hot hand. The chance of a hit is higher because this player is poorly covered and can therefore use free space on the field.

Soccer

In football one speaks of the hot foot phenomenon. As in basketball, the interviewed players assume the occurrence of the hot foot ; When examining the hit rates of twelve strikers in the English Premier League , no correlation was found between a number of hits already scored and the next attempt in football.

volleyball

In volleyball , positive dependencies between successive shots were found in 50% of the cases. For the other half, no influence of previous successes was found.

One reason for the positive connection is the hot hand. Due to the separation of the teams by a net, players cannot be covered directly by the opponent. The performance of a player with a hot hand can only be partially reduced by the improved cover of the opponent. This makes the hot hand visible and directly influences the course of the game . Coaches use them in strategy development as do players who make decisions about who to pass the ball to. The team in which the hot hand occurs more often scores more points.

The hot hand phenomenon and profit-maximizing action

One approach to explaining economic upswings and downturns is based on the hot-hand phenomenon. A good is “hot” when an increase in value leads to a renewed increase in value. This happens because investors are asking for goods that are increasing in value. These investments are intended to maximize the difference between purchase and sales price, i.e. profit. From a simplified economic point of view, the increased demand for the good leads to a price increase, since the good is becoming increasingly scarce. As a result, the value of the good increases and in turn attracts investors. This cycle is repeated throughout an upswing. In a downturn, the opposite is predicted. Investors invest their money in other goods after a loss in value, as a further decline in value is assumed. This leads to a decline in demand and a reduction in prices. Investment continues to decline and exacerbate the downturn.

These cycles can also be applied to other consumer markets such as the housing market . The transition between an upswing and a downswing is explained by the Gambler's Fallacy .

In sports betting with variable odds and teams of equal strength, profit can be maximized if the other bettors assume a team's hot hand. You invest in the team that has repeatedly achieved successes in direct succession, although the theoretical success probability of the teams is the same. It is rational to bet on the opposing team because this team is as likely to win as the one with the supposed hot hand. If a win occurs , the bet payout does not have to be shared with other bettors. If, on the other hand, the team wins with the alleged hot hand, the payout must be divided among the bettors. The expected profit is higher when investing in the team that is not said to have the hot hand.

The hot hand phenomenon and the gambler's fallacy phenomenon

Like the hot-hand phenomenon, the gambler's fallacy phenomenon describes the misconception that events become predictable. This assessment is based on a consecutive event. In contrast to the hot-hand phenomenon, after such a sequence, the same event is not expected with a higher probability (positive expectation), but the counter-event (negative expectation).

Both phenomena are attributed to mathematical fallacies : the law of large numbers is wrongly applied to small observation sequences.

Under which circumstances the Gambler's Fallacy or the Hot Hand is accepted, explains on the one hand the expectations towards human or static performance and on the other hand the motivational mechanism.

Human and static performance

The difference in expectations in the hot hand and gambler's fallacy phenomenon is based on the fact that human performance is ascribed less randomness than static. The results in sport are met with positive expectations, as they are the result of human performance. In gambling , it is not believed that results can get "hot"; this leads to negative expectations. In both cases, the error is that the random probability distribution is not recognized.

Motivational mechanism

Events that have a positive or helpful effect on an intended goal are foreseen or motivated with a higher probability. If they have a negative effect on a target, they are less likely to be expected.

  • In sport, hits by a team contribute to success and are motivated according to the hot hand phenomenon.
  • In the game of roulette, when betting on colors, the opposing color is motivated after frequent occurrences of a color, if this was bet on according to the Gambler's Fallacy.

The motivational mechanism is applied to both the hot hand phenomenon and the gambler's fallacy phenomenon. To win a prize, a total of 12 out of 20 coin tosses must be heads. After each throw, the next result is predicted. After the “head” event, “head” is anticipated again (motivated). The basis for decision-making is the hot-hand phenomenon, according to which events that have occurred several times in a row are expected with a higher probability. If the unwanted event, ie “tails”, occurs, according to the gambler's fallacy phenomenon, a “head” is also forecast. In this case, the counter-event is motivated.

Approaches to explaining the hot hand phenomenon

The assumption of the hot hand is based on psychological biases based on the representativeness heuristic , the availability heuristic and the anchor heuristic . At the same time, the lack of ability to assess statistical properties leads to the acceptance of a hot hand. This can be seen in the mistaken application of the law of large numbers to small sequences.

Mathematical fallacies

The law of large numbers states that the greater the number of observed events, the smaller the difference between the relative frequency and the theoretical expected value . The expected value is formed by theoretical considerations and is the decision-making basis for identifying the hot hand. If an event occurs more than average compared to the theoretical expected value, one concludes that it is a hot hand. Here the law of large numbers is applied incorrectly: the theoretical expected value is viewed as a relative frequency, although this assumption only applies to large sequences . Deviations from this consideration are assessed as an anomaly and explained by the occurrence of a hot hand.

  • The fair coin toss game is an example of a random binary game where the “heads” (“K”) or “tails” (“Z”) events have a probability of 0.5. This corresponds to the theoretical expected value. If a short sequence with the events “KKKKZ” is implemented, “K” occurs more often than the average compared to the theoretical expected value 0.5. The deviation is attributed to a hot hand. An equal distribution of “K” and “Z” is expected, although according to the law of large numbers this only shows up in very large sequences.

In addition, people often think in terms of conditional probabilities and do not consider event probabilities in an abstract manner. The theoretical expected value is conditioned on the previous event, which means that incorrect probability distributions are assigned to the population . The next event is therefore expected with a false probability.

  • The coin tossing game is considered again. The conditional probability is incorrectly calculated for the ten occurrences of “head”:
The actually assumed probability of this is independent of the previous results and is:
The event “head” has already been realized nine times with the probability 1, the tenth time it occurs with the probability 0.5.
The larger the sequence of the coin tossing game, the clearer the law of large numbers becomes: the difference between the relative frequency and the expected value decreases.

Heuristics

Often mathematical control processes are not recognized, which is why psychological heuristics are used. These are judgment guidelines that are applied in the same scheme in different decision-making situations with a lack of time and information. Once the hot hand has been accepted, heuristics consolidate the systematic distortion of reality in quick and frugal decisions.

  • The availability heuristic shows that the persistence of the assumption of a hot hand is based on the cognitive bias of the memories. The easier an event can be evoked from memory, the higher the expectations regarding the occurrence of the event in similar situations. In sport, fans remember successes of the sports team more consistently than failures. These events are therefore easier to call up and are expected with a higher probability in similar game situations.
  • The representativity heuristic assumes that two events belong together if their characteristics are similar. Once a hot hand is accepted, similar events are associated with the hot hand.
  • With the anchor heuristic , an initial assessment influences the final decision. This assessment forms the “anchor” of the judgment, in the direction of which one finally decides. If the belief in the existence of the hot hand forms the “anchor”, then the repeated occurrence of the same event is assessed as a hot hand.

Belief in the hot hand is stronger in older people than in younger people. With increasing life experience, situations as a result of heuristics are increasingly attributed to a hot hand. The predominant memory of positive experiences of the Hot Hand strengthens the belief in them, which is further reinforced by emotions . The heuristics confirm the existence of the hot hand and lead to repeated application. Decreasing cognitive performance is a crucial factor in making biases a reality.

Reasons for the existence of the hot hand

The most cited experiments do not fully control the confounding factors , which is why results cannot be directly traced back to examined variables. The internal validity is correspondingly low. Under uncontrolled circumstances, no correlation can be recognized between the previous hit rate and the expected probability of a next hit. For example, the selection of throws, strategic action or the length of time between throws is not controlled. At the same time, uncontrollable influences such as psychological states, innate advantages and the ability to learn are important factors.

In sports, for example, uncontrolled disruptive factors lead to the disguise of a hot hand. Disruptive factors such as better coverage by the opponent after a success reduce the additional performance from the hot hand. Even if it exists, the hot hand cannot be detected. Studies can only conclude that a hot hand does not exist if all confounding factors are fully controlled.

  • Evidence for the existence of the hot hand: Due to the same conditions at the World Championships in horseshoe throwing in 2000 and 2001, data were acquired that control disruptive factors more closely. The same prerequisites for each player such as identical throwing distances, regulated time intervals between throws and no possibility of strategic action lead to a controlled amount of data. Compared to the results after a series of failures, players achieved more successes if they had already achieved positive results several times in a row.

Evidence of the existence of a hot hand could also be gathered from investigations in bowling and volleyball. In both studies it is justified with the control of confounding factors.

literature

  • Age, AL; Oppenheimer, DM (2006): From a fixation on sports to an exploration of mechanism. The past, present, and future of hot hand research. In: Thinking & Reasoning 12 (4), pp. 431-444. doi: 10.1080 / 13546780600717244 , last checked on June 16, 2015.
  • Ayton, P .; Fischer, I. (2004): The hot hand fallacy and the gambler's fallacy. Two faces of subjective randomness? In: Memory & Cognition 32 (8), pp. 1369-1378. doi: 10.3758 / bf03206327 .
  • Badarinathi, R .; Kochman, L. (1996): Football Betting and the Efficient Market Hypothesis. In: The American Economist (Vol. 40, No. 2), pp. 52–55, last checked on June 20, 2015.
  • Burns, BD (2001): The Hot Hand in Basketball: Fallacy or Adaptive Thinking? In: CogSci: 23rd Annual Conference of the Cognitive Science Society, last checked on June 16, 2015.
  • Burns, BD (2004): Heuristics as beliefs and as behaviors: the adaptiveness of the “hot hand”. In: Cognitive Psychology (48), pp. 295–331, last checked on June 16, 2015.
  • Burns, BD; Corpus, B. (2004): Randomness and inductions from streaks. “Gambler's fallacy” versus “hot hand”. In: Psychonomic Bulletin & Review 11 (1), pp. 179-184. doi: 10.3758 / BF03206480 .
  • Camerer, CF (1989): Does the Basketball Market Believe in the `Hot Hand, '? In: The American Economic Review (Vol. 79, No. 5), pp. 1257–1261, last checked on June 19, 2015.
  • Castel; DR; McGillivray (2012): Beliefs About the “Hot Hand” in Basketball Across the Adult Life Span. In: Psychology and Aging (Vol 27., No. 3), pp. 601–605, last checked on June 16, 2015.
  • Choi, BY; Oppenheimer, DM; Monin, B. (2003): Motivational biases in judgments of streaks in random sequences (poster presented at "Subjective probability, utility, and decision making").
  • Dorsey-Palmateer, R .; Smith, G. (2004): Bowlers' hot hands. In: The American Statistician (58), pp. 38-45.
  • G. Gigerenzer, P. Todd; the ABC Research Group (Ed.) (1999): Simple heuristics that make us smart. New York: Oxford University Press.
  • Gigerenzer, G .; Todd, PM (1999): Fast and frugal heuristics: The adaptive tool box. In: P. Todd G. Gigerenzer and the ABC Research Group (Eds.): Simple heuristics that make us smart. New York: Oxford University Press, pp. 3-34.
  • Gilovich, T .; Tversky, A. & Vallone, R. (1985): The Hot Hand in Basketball: On the Misperception of Random Sequences. In: Cognitive Psychology 3 (17), pp. 295-314.
  • Gould, SJ (1989): The Streak of Streaks. In: Chance (2), pp. 10-16.
  • Huber, J .; Kirchler, M .; Stöckl, T. (2010): The hot hand belief and the gambler's fallacy in investment decisions under risk. In: Theory Decis 68 (4), pp. 445-462. doi: 10.1007 / s11238-008-9106-2 .
  • Johnson, J .; Tellis, GJ; Macinnis, DJ (2005): Losers, Winners, and Biased Trades. In: Journal of Ronsumer Research 2 (32).
  • Koehler, JJ; Conley, C. (2003): The 'Hot Hand' Myth in Professional Basketball. In: Journal of Sport & Exercise Psychology (25), pp. From 253, last checked on June 18, 2015.
  • Basket, KB; Stillwell, M. (2003): The Story of The Hot Hand: Powerful Myth or Powerless Critique? last checked on June 18, 2015.
  • Plous, S. (ed.) (2010): Tom Gilovich. Wesleyan University , last updated December 21, 2010, last reviewed June 18, 2015.
  • Raab, M .; Gula, B .; Gigerenzer, G. (2012): The hot hand exists in volleyball and is used for allocation decisions. In: J Exp Psychol Appl 18 (1), pp. 81-94. doi: 10.1037 / a0025951 .
  • Rao, JM (2009): Experts' Perceptions of Autocorrelation: The Hot Hand Fallacy Among Professional Basketball Players. San Diego, last checked June 20, 2015.
  • Schütz, A. (Ed.) (2011): Psychology: an introduction to its basics and fields of application. With the collaboration of Kohlhammer. Stuttgart.
  • Smith, G. (2003): Horseshoe pitchers' hot hands. In: Psychonomic Bulletin & Review 10, pp. 753-758.
  • Stanford News Service (ed.) (1996): Amos Tversky, leading decision researcher, dies at 59 , last checked on June 18, 2015.
  • Tversky, A .; Kahneman, D. (1974): Judgment under Uncertainty: Heuristics and Biases. In: Science 185 (4157), pp. 1124-1131. doi: 10.1126 / science.185.4157.1124 .
  • Yaari, G .; Eisenmann, S. (2011): The hot (invisible?) Hand: can time sequence patterns of success / failure in sports be modeled as repeated random independent trials? In: PLoS ONE 6 (10). doi: 10.1371 / journal.pone.0024532 .

Individual evidence

  1. ↑ Plous, S. (2010) (ed.): Tom Gilovich . Wesleyan University, last updated December 21, 2010, last reviewed June 18, 2015.
  2. ^ [1] Stanford News Service (ed.) (1996): Amos Tversky, leading decision researcher, dies at 59, last checked on June 18, 2015.
  3. ↑ a b [2] Gilovich, T .; Tversky, A. & Vallone, R. (1985): The Hot Hand in Basketball: On the Misperception of Random Sequences. In: Cognitive Psychology 3 (17), pp. 295-314.
  4. ↑ [3] Camerer, CF (1989): Does the Basketball Market Believe in the `Hot Hand, '? In: The American Economic Review (Vol. 79, No. 5), pp. 1257–1261, last checked on June 19, 2015.
  5. ↑ [4] Burns, BD (2001): The Hot Hand in Basketball: Fallacy or Adaptive Thinking? In: CogSci: 23rd Annual Conference of the Cognitive Science Society, last checked on June 16, 2015.
  6. ^ A b Smith, G. (2003): Horseshoe pitchers' hot hands. In: Psychonomic Bulletin & Review 10, pp. 753-758.
  7. ↑ a b c age, AL; Oppenheimer, DM (2006): From a fixation on sports to an exploration of mechanism. The past, present, and future of hot hand research. In: Thinking & Reasoning 12 (4), pp. 431–444, last checked on June 19, 2015. doi: 10.1080 / 13546780600717244 .
  8. ↑ Schütz, A. (Ed.) (2011): Psychology: an introduction to its basics and fields of application. With the collaboration of Kohlhammer. Stuttgart.
  9. ↑ a b Raab, M .; Gula, B .; Gigerenzer, G. (2012): The hot hand exists in volleyball and is used for allocation decisions. In: J Exp Psychol Appl 18 (1), pp. 81-94. doi: 10.1037 / a0025951 .
  10. ↑ a b Johnson, J .; Tellis, GJ; Macinnis, DJ (2005): Losers, Winners, and Biased Trades. In: Journal of Ronsumer Research 2 (32).
  11. ↑ [5] Badarinathi, R .; Kochman, L. (1996): Football Betting and the Efficient Market Hypothesis. In: The American Economist (Vol. 40, No. 2), pp. 52–55, last checked on June 20, 2015.
  12. ↑ Ayton, P .; Fischer, I. (2004): The hot hand fallacy and the gambler's fallacy. Two faces of subjective randomness? In: Memory & Cognition 32 (8), pp. 1369-1378. doi: 10.3758 / bf03206327 .
  13. ↑ a b Burns, BD; Corpus, B. (2004): Randomness and inductions from streaks. “Gambler's fallacy” versus “hot hand”. In: Psychonomic Bulletin & Review 11 (1), pp. 179-184. doi: 10.3758 / BF03206480 .
  14. ↑ a b Choi, BY; Oppenheimer, DM; Monin, B. (2003): Motivational biases in judgments of streaks in random sequences (poster presented at "Subjective probability, utility, and decision making").
  15. ↑ a b Tversky, A .; Kahneman, D. (1974): Judgment under Uncertainty: Heuristics and Biases. In: Science 185 (4157), pp. 1124-1131. doi: 10.1126 / science.185.4157.1124 .
  16. ^ Gould, SJ (1989): The Streak of Streaks. In: Chance (2), pp. 10-16.
  17. ^ Alan D. Castel, Aimee Drolet Rossi, and Shannon McGillivray: Beliefs About the "Hot Hand" in Basketball Across the Adult Life Span. (PDF) In: Psychology and Aging (Vol 27., No. 3). 2012, pp. 601–605 , accessed on June 16, 2015 (English).
  18. ^ Justin M. Rao: Experts' Perceptions of Autocorrelation: The Hot Hand Fallacy Among Professional Basketball Players. (PDF) 2009, accessed on June 20, 2015 (English).
  19. ↑ Dorsey-Palmateer, R .; Smith, G. (2004): Bowlers' hot hands. In: The American Statistician (58), pp. 38-45.