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Carry on winning: The gamblers’ fallacy creates hot hand effects in online gambling

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People suffering from the hot-hand fallacy unreasonably expect winning streaks to continue whereas those suffering from the gamblers’ fallacy unreasonably expect losing streaks to reverse. We took 565,915 sports bets made by 776 online gamblers in 2010 and analyzed all winning and losing streaks up to a maximum length of six. People who won were more likely to win again (apparently because they chose safer odds than before) whereas those who lost were more likely to lose again (apparently because they chose riskier odds than before). However, selection of safer odds after winning and riskier ones after losing indicates that online sports gamblers expected their luck to reverse: they suffered from the gamblers’ fallacy. By believing in the gamblers’ fallacy, they created their own hot hands.
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Brief article
Carry on winning: The gamblers’ fallacy creates hot hand effects
in online gambling
Juemin Xu
, Nigel Harvey
Department of Cognitive, Perceptual and Brain Sciences, University College London, UK
article info
Article history:
Received 12 October 2012
Revised 16 January 2014
Accepted 17 January 2014
Keywords:
Hot-hand fallacy
Gamblers’ fallacy
Sports betting
abstract
People suffering from the hot-hand fallacy unreasonably expect winning streaks to con-
tinue whereas those suffering from the gamblers’ fallacy unreasonably expect losing
streaks to reverse. We took 565,915 sports bets made by 776 online gamblers in 2010
and analyzed all winning and losing streaks up to a maximum length of six. People who
won were more likely to win again (apparently because they chose safer odds than before)
whereas those who lost were more likely to lose again (apparently because they chose risk-
ier odds than before). However, selection of safer odds after winning and riskier ones after
losing indicates that online sports gamblers expected their luck to reverse: they suffered
from the gamblers’ fallacy. By believing in the gamblers’ fallacy, they created their own
hot hands.
Ó 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC
BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
1. Introduction
The hot-hand fallacy and gamblers’ fallacy are assumed
to be common among gamblers because it is thought that
they believe that outcomes for future bets are predictable
from those of previous ones.
1.1. Belief in a hot-hand: ‘‘If you have been winning, you are
more likely to win again.’’
The term a ‘‘hot hand’’ was initially used in basketball to
describe a basketball player who had been very successful
in scoring over a short period. It was believed that such a
player had a ‘‘hot hand’’ and that other players should pass
the ball to him to score more. This term is now used more
generally to describe someone who is winning persistently
and can be regarded as ‘‘in luck’’. In gambling scenarios, a
player with a genuine hot hand should keep betting and
bet more.
There have been extensive discussions about the exis-
tence of the hot hand effect. Some researchers have failed
to find any evidence of such an effect (Gilovich, Vallone,
& Tversky, 1985; Koehler & Conley, 2003; Larkey, Smith,
& Kadane, 1989; Wardrop, 1999). Others claim there is evi-
dence of the hot hand effect in games that require consid-
erable physical skill, such as golf, darts, and basketball
(Arkes, 2010, 2011; Gilden & Wilson, 1995; Yaari &
Eisenmann, 2011).
People gambling on sports outcomes may continue to
do so after winning because they believe they have a hot
hand. Such a belief may be a fallacy. It is, however, possible
that their belief is reasonable. For example, on some occa-
sions, they may realize that their betting strategy is pro-
ducing profits and that it would be sensible to continue
with it. Alternatively, a hot hand could arise from some
change in their betting strategy. For example, after win-
ning, they may modify their bets in some way to increase
their chances of winning again.
http://dx.doi.org/10.1016/j.cognition.2014.01.002
0010-0277/Ó 2014 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Corresponding author. Address: Department of Cognitive, Perceptual
and Brain Sciences, University College London, Gower Street, London
WC1E 6BT, UK. Tel.: +44 (0)2076797570.
E-mail address: juemin.xu@ucl.ac.uk (J. Xu).
Cognition 131 (2014) 173–180
Contents lists available at ScienceDirect
Cognition
journal homepage: www.elsevier.com/locate/COGNIT
1.2. The gamblers’ fallacy: ‘‘If you have been losing, you are
more likely to win in future.’’
People gambling on sports outcomes may continue to
do so after losing because they believe in the gamblers’ fal-
lacy. This is the erroneous belief that deviations from ini-
tial expectations are corrected even when outcomes are
produced by independent random processes. Thus, peo-
ple’s initial expectations that, in the long run, tosses of a
fair coin will result in a 50:50 chance of heads and tails
are associated with a belief that deviations from that ratio
will be corrected. Hence, if five tosses of a fair coin have
produced a sequence of five heads, the chance of tails on
the next toss will be judged to be larger than 50%. This is
because the coin ‘‘ought to’’ have a 50:50 chance of heads
and tails in the long run and, as a result, more tails are
‘‘needed’’ to correct the deviation from that ratio produced
by the first five tosses.
1.3. Odds and stake size: A conflict between belief in a hot
hand and the gambler’s fallacy
Betting strategies are often based on the previous bet-
ting results (Oskarsson, Van Boven, McClelland, & Hastie,
2009). The strategies based on a belief in a hot hand and
gamblers’ fallacy may conflict. For example, when trying
to decide what odds to select in the next round, a belief
in the gamblers’ fallacy would result in betting on higher
odds and with more money after losing than after winning.
A believer in the hot hand would do the opposite.
2. Method and data
To date, there is little research on real gambling. Our re-
search (1) demonstrates the existence of a hot hand, (2)
investigates gamblers’ beliefs in a hot hand and the gam-
blers’ fallacy, and (3) explores the causal relationship
between a hot hand and the gamblers’ fallacy.
2.1. Analysis methods
We used a large online gambling database. First, we
counted all the sports betting results to see whether win-
ning was more likely after a streak of winning bets or after
a streak of losing ones. Second, we examined the record of
those gamblers who has long streaks of wins to see
whether they had higher returns; this could be a sign of
real skill. Third, we used the odds and the stake size to
predict the probability of winning.
2.2. Data set
The complete gambling history of 776 gamblers be-
tween 1 January 2010 and 31 December 2010 was ob-
tained from an online gambling company. In total,
565,915 bets were placed by these gamblers during the
year. Characteristics of the samples are shown in Table 1.
Each gambling record included the following informa-
tion: game type (e.g., horse racing, football, and cricket),
game name (e.g. Huddersfield v West Bromwich), time,
stake, type of bet, odds, result, and payoff. Each person
was identified by a unique account number. All the bets
they placed in the year were arranged in chronological or-
der by the time of settlement, which was precise to the
minute. The time when the stake was placed was not avail-
able but, according to the gambling house, there is no rea-
son to think that stakes are placed long before the time of
settlement. Each account used one currency, which was
chosen when the account was opened; no change of cur-
rency was allowed during the year.
If there is a hot hand, then, after a winning bet, the
probability of winning the next bet should go up. We com-
pared the probability of winning after different run lengths
of previous wins (Fig. 1). If the gamblers’ fallacy is not a fal-
lacy, the probability of winning should go up after losing
several bets. We also compared the probability of winning
in this situation.
3. Results and analysis
3.1. The hot hand
To produce the top panel of Fig. 1, we first counted all
the bets in GBP; there were 178,947 bets won and
192,359 bets lost. The probability of winning was 0.48.
Second, we took all the 178,947winning bets and
counted the number of bets that won again; there were
88,036 bets won. The probability of winning was 0.49. In
comparison, following the 192,359 lost bets, the probability
of winning was 0.47. The probability of winning in these two
situations was significantly different (Z = 12.10, p < .0001).
Third, we took all the 88,036 bets, which had already
won twice and examined the results of bets that followed
these bets. There were 50,300 bets won. The probability
of winning rose to 0.57. In contrast, the probability of
winning did not rise after gambles that did not show a
winning streak: it was 0.45. The probability of winning
in these two situations was significantly different
(Z = 60.74, p < .0001).
Fourth, we examined the 50,300 bets which had already
won three times and checked the result of the bets followed
them. We found that 33,871 bets won. The probability of
winning went up again to 0.67. In contrast, the bets not hav-
ing a run of lucky predecessors showed a probability of win-
ning of 0.45. The probability of winning in these two
situations was significantly different (Z = 90.63, p < .0001).
Fifth, we used the same procedure and took all the
33,871 bets which had already won four times. We
checked the result of bets followed these bets. There were
24,390 bets that won. The probability of winning went up
again to 0.72. In contrast, the bets without a run of previ-
ous wins showed a probability of winning of only 0.45.
The probability of winning in these two situations was sig-
nificantly different (Z = 91.96, p < .0001).
Sixth, we used the same method to check the 24,390
bets which had already won five times in a row. There
were 18,190 bets that won, giving a probability of winning
of 0.75. After other bets, the probability of winning was
0.46. The probability of winning in these two cases was sig-
nificantly different (Z = 86.78, p < .0001).
174 J. Xu, N. Harvey / Cognition 131 (2014) 173–180
Seventh, we examined the 18,190 bets that had won
six times in a row. Following such a lucky streak, the
probability of winning was 0.76. However, for the bets
that had not won on the immediately preceding
Table 1
Sample characteristics for sports bets placed in each of three currencies for the year 2010.
GBP EUR USD
Number of bets 371,306 162,077 32,532
Number of gamblers 407 318 51
Mean stake £145 (1482) 395 (5555) $50 (321)
Median stake £14 18 $15
Maximum stake £313,900 1,492,000 $20,500
Mean number of bets placed by a single account 917 517 641
Median number of bets placed by a single account 171 88 153
Number of horse racing bets 260,550 34,659 8290
Number of soccer bets 69,863 90,415 12,058
Number of greyhound racing bets 28,859 6660 9159
Fig. 1. Probability of winning after obtaining winning streaks of different lengths (o) and after not obtaining winning streaks of those lengths (
D
).
J. Xu, N. Harvey / Cognition 131 (2014) 173–180
175
occasion, the probability of winning was only 0.47. These
two probabilities of winning were significantly different
(Z = 77.50, p < .0001).
The hot hand also occurred for bets in other currencies
(Fig. 1). Regressions (Table 2) show that, after each succes-
sive winning bet, the probability of winning increased by
0.05 (t(5) = 8.90, p < .001) for GBP, by 0.06 for EUR
(t(5) = 8.00, p < .001), and by 0.05 for USD (t(5) = 8.90,
p < .001).
3.2. The gamblers’ fallacy
We used the same approach to analyze the gamblers’
fallacy. The first step was same as in the analysis of the
hot hand. We counted all the bets in GBP; there were
178,947 bets won and 192,359 bets lost. The probability
of winning was 0.48 (Fig. 2, top panel).
In the second step, we identified the 192,359 bets that
lost and examined results of the bets immediately after
them. Of these, 90,764 won and 101,595 lost. The probabil-
ity of winning was 0.47. After the 178,947 bets that won,
the probability of winning was 0.49. The difference be-
tween these two probabilities were significant (Z = 12.01,
p < 0.001).
In the third step, we took the 101,595 bets that lost and
examined the bets following them. We found that 40,856
bets won and 60,739 bets lost. The probability of winning
after having lost twice was 0.40. In contrast, for the bets
that did not lose on both of the previous rounds, the prob-
ability of winning was 0.51. The difference between these
probabilities was significant (Z = 58.63, p < 0.001).
In the fourth step, we repeated the same procedure.
After the 60,739 bets that had lost three times in a row,
there were 19,142 winning bets won and losing 41,595
bets ones, giving a probability of winning of 0.32. For other
bets, this probability was 0.51 (Z = 88.26, p < 0.001).
The fifth, sixth and seventh steps were carried out in an
analogous way. They showed that the probability of win-
ning after four lost bets was 0.27, after five lost bets was
0.25, and after six lost bets was 0.23.
The pattern was similar for bets in other currencies
(Fig. 2). Regressions (Table 2) showed that each succes-
sive losing bet decreased the probability of winning 0.05
(t(5) = 9.71, p < .001) for GBP, by 0.05 for EUR
(t(5) = 9.10, p < .001) and by 0.02 for USD (t(5) = 7.56,
p < .001). This is bad news for those who believe in the
gamblers’ fallacy.
3.3. Do gamblers with long winning streaks have higher
payoffs?
One potential explanation for the appearance of the hot
hand is that gamblers with long winning streaks consis-
tently do better than others. To examine this possibility,
we compared the mean payoff of these gamblers with
the mean payoff of the remaining gamblers.
Among 407 gamblers using GBP, 144 of them had at
least six successive wins in a row on at least one occasion.
They had a mean loss of £1.0078 (N = 279,162, SD = 0.47)
for every £1 stake they placed. The remaining 263 gam-
blers had a mean loss of £1.0077 (N = 92,144, SD = 0.38)
for every £1 stake they placed. The difference between
these two was not significant.
We did same analysis for bets made in EUR. Among 318
gamblers using this currency, 111 of them had at least one
winning streak of six. They had a mean loss of 1.005
(N = 105,136, SD = 0.07) for every 1 of stake. The remain-
ing 207 EUR gamblers had a mean loss of 1.002
(N = 56,941, SD = 0.22). The difference between these two
returns was significant (t (162,075) = 4.735, p < 0.0001).
Those who had long winner streaks actually lost more than
others.
The results in USD were similar. Seventeen gamblers
had at least one winning streak of six and 34 did not. For
those who had, the mean loss was $1.022 (N = 23,280,
SD = 0.75); for those who had not, it was $1.029
(N = 9,252, SD = 0.35). There was no significant difference
between the two (t (32,530) = 0.861, p = 0.389). The gam-
blers who had long winning streaks were not better at win-
ning money than gamblers who did not have them.
3.4. The effects of winning and losing streaks on level of odds
selected
To determine whether the gamblers believed in the hot
hand or gamblers’ fallacy, we examined how the results of
their gambling affected the odds of their next bet. Among
all GBP gamblers, the mean level of selected odds was
7.72 (N = 371,306, SD = 37.73). After a winning bet, lower
odds were chosen for the next bet. The mean odds dropped
to 6.19 (N = 178,947, SD = 35.02). Following two consecu-
tive winning bets, the mean odds decreased to 3.60
(N = 88,036, SD = 24.69). People who had won on more
consecutive occasions selected less risky odds. This trend
continued (Fig. 3, top panel).
Table 2
Regression for length of streaks predicting the probability of winning.
BSEBb t Sig. (p) FR
2
GBP
Winning streak 0.475 0.021 0.053 (0.006) 8.902 <0.001 79.25 0.928
Losing streak 0.489 0.018 0.047 (0.004) 9.711 <0.001 94.31 0.940
EUR
Winning streak 0.439 0.026 0.059 (0.007) 8.223 <0.001 67.62 0.917
Losing streak 0.508 0.021 0.053 (0.006) 9.100 <0.001 82.8 0.932
USD
Winning streak 0.315 0.025 0.054 (0.007) 7.996 <0.001 63.93 0.913
Losing streak 0.386 0.010 0.022 (0.003) 7.560 <0.001 57.15 0.904
Note: Independent variable is the number of bets taken into consideration.
176 J. Xu, N. Harvey / Cognition 131 (2014) 173–180
After a losing bet, the opposite was found. People who
had lost on more consecutive occasions selected riskier
odds. After six lost bets in a row, the mean odds went up
to 17.07 (N = 22,694, SD = 50.62). In comparison, after win-
ning six times in a row, the figure for mean odds was 0.85
(N = 18,252, SD = 9.82). From the odds that they selected,
we can infer that gamblers believed in the gamblers’ fal-
lacy but not in the hot hand.
The gambling results were affected by the gamblers’
choice of odds. One point of odds increase reduced the
probability of winning by 0.035 (SD = 0.003, t(36) =
13.403, p < .001).
3.5. The effects of winning and losing streaks on stake size
Among all GBP gamblers, the median stake was £14
(N = 371,306, Interquartile Rang = 4.80–53.29). After
winning once, the median stake went up to £18.47
(N = 178,947, Interquartile Range = 5.04–66.00). After win-
ning twice in a row, the median stake rose to £20.45
(N = 88,036, Interquartile Range = 8.00–80.00) (Fig. 4, top
panel).
For the losing side, the opposite was found. People who
had lost on more consecutive occasions decreased stakes.
After losing once, the median stake went down to £10.89
(N = 192,359, Interquartile Range = 4.00–44.16). In
comparison, after losing twice in a row, the median stake
dropped to £10.00 (N = 101,595, Interquartile
Range = 3.33–30.00). These trends continued (Fig. 4, top
panel).
Gamblers increased stake size after winning and
decreased stake size after losing. This could be the result
of more money available after winning and less money
available after losing.
Fig. 2. Probability of winning after obtaining losing streaks of different lengths (o) and after not obtaining losing streaks of those lengths (
D
).
J. Xu, N. Harvey / Cognition 131 (2014) 173–180
177
We examined EUR and USD bets. Findings for selected
odds were similar (Fig. 3) but those for stake size were less
robust (Fig. 4), perhaps because of the reduced sample size.
4. Discussion
We found evidence for the hot hand but not for the
gamblers’ fallacy. Gamblers were more likely to win after
winning and to lose after losing.
After winning, gamblers selected safer odds. After los-
ing, they selected riskier odds. After winning or losing, they
expected the trend to reverse: they believed the gamblers’
fallacy. However, by believing in the gamblers’ fallacy, peo-
ple created their own luck. The result is ironic: Winners
worried their good luck was not going to continue, so they
selected safer odds. By doing so, they became more likely
to win. The losers expected the luck to turn, so they took
riskier odds. However, this made them even more likely
to lose. The gamblers’ fallacy created the hot hand.
Ayton and Fischer (2004) found that people believed in
the gamblers’ fallacy for natural events over which they
had no control. Our gamblers displayed the gamblers’ fal-
lacy for actions (i.e. bets) that they took themselves. This
may indicate that they did not believe that bets were under
their control. Fong, Law, and Lam (2013) reported Chinese
gamblers believed their luck would continue. Does this
mean they felt they had more control over their bets? By
believing their luck would continue, did they help to bring
it to an end?
Fig. 3. Mean preferred odds after winning (o) and losing (
D
) streaks of different lengths.
178 J. Xu, N. Harvey / Cognition 131 (2014) 173–180
5. Implications
There are likely to be other domains (e.g., financial trad-
ing) where people reduce their preference for risk in the
wake of chance success and thereby give the impression
of a hot hand. Furthermore, they may attribute their suc-
cesses to skill rather than chance (Langer, 1975) and may
not be aware of their change in risk preference. In such cir-
cumstances, they may develop the illusion that they are
becoming better at the task and able to persuade others
that this is so. In the financial domain, this would have
clear implications for people’s selection of investment
strategies.
Acknowledgements
This research was supported by a scholarship awarded
by the Responsible Gambling Fund to Juemin Xu. We thank
Peter Ayton for invaluable comments on earlier drafts of
the manuscript.
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... Third, universities emphasize sports and sports-related activities in the context of websites, recruiting materials, and as a social or community event. Fourth, winning games is considered important to most people either because it is fun to do so (Wann & Branscombe, 1990) or fruitful to do so (Xu & Harvey, 2014). As such, coaching decisions are crucial to athletic administrators, fans, and athletes. ...
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Using data streams from ESPN.com (n.d.), we identified possible contingencies on timeout calling for 594 timeouts in 117 games for four Division 1 NCAA college basketball teams. We found that the probability of calling a timeout increased as the relative points scored by the opposing team increased. In addition to analyzing all timeouts inclusively, we analyzed timeouts called within the last 2 min of each half separately from those called in the rest of the game. Regardless of the window of analysis, the probability of calling a timeout increased as the relative points scored by the opposing team increased. To the extent that shots made and points scored by the opposing team were aversive to the coach (and players), the reductions that immediately followed the timeout may have functioned as negative reinforcement.
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In recent years, gambling harm has been considered a significant public health concern due to its increasing socioeconomic costs. Although the adverse effects of gambling have attracted research interest, evidence of its effect on financial stress remains largely anecdotal. This study empirically examines the link between individual problem gambling severity and financial stress using panel data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey. After addressing endogeneity, we find that problem gambling severity is positively associated with self-reported financial stress. Thus, problem gambling severity tends to increase financial stress. This finding is robust to alternative measures of financial stress and gambling behaviour-whether gambling is measured using the Problem Gambling Severity Index (PGSI), gambling risk statuses, number of gambling activities, or gambling expenditure. The positive effect of gambling on financial stress is largely driven by gambling activities involving scratch cards and poker machines. Although males exhibit higher levels of problem gambling severity, females are more financially stressed than males. Our findings also suggest that gambling widens the gender gap in financial stress. Further analysis reveals that financial resilience mediates the gambling-financial stress relationship. This implies that promoting policies that enhance financial resilience can help to insulate individuals against the effects of gambling on financial stress.
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The research on the relationship between wins and gambling behaviour most often focuses on winning considerably large amounts of money. It seems, however, that it is not the amount of the win that exerts a decisive influence on gambling behaviour but the significance that the player assigns to the win. Therefore, we adopted the concept of “significant win”, a win perceived by gamblers as important to them. The research aimed to discover what kind of wins are experienced as significant and what factors explain experiencing wins as significant. The research conducted in Poland (N = 3,143) and France (N = 5,692) also had a comparative goal: discovering intercultural differences in experiencing significant wins. The computer-assisted web survey was conducted among gamblers engaging in pure-chance gambling, selected from representative samples in both countries. Logistic regression models were used to examine predictors of significant win experience in both countries and cross-countries differences between them. The results demonstrated that Polish gamblers more frequently considered wins significant when accompanied by strong, often negative emotions and were objectively higher than French gamblers. A significant win was more frequently associated with a positive experience in the view of French gamblers. The common predictors of a significant win experience in both countries were: being in debt, experiencing the win of a close person, gambling in a game of pure chance other than lotteries, more systematic pursuit of gambling, enhancement and coping gambling motivations. The age of the initiation into gambling was a significant predictor only in the French sample, while financial motivation – in the Polish one. The results confirmed that the subjective perception of gambling wins is only partially related to the amounts of wins, which has practical implications for planning prophylactic strategies.
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Financial bubbles cause misallocation of resources and even systemic crises. Experimental finance has long studied both the determinants of bubbles and institutional measures to prevent them. Within the framework of the dual-process theory, we experimentally investigate whether traders under higher time pressure (Fast condition) behave differently than traders under lower time pressure (Slow condition). Relative to the Fast condition, the Slow condition dampens market price volatility, greatly reduces the spread between ask and bid limit orders, and leads to higher equality in payoffs.
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Chapter 3 of The Psychology of Foreign Policy concerns prospect theory, which originates from behavioural economics but has been increasingly applied to International Relations and Foreign Policy Analysis. It is one of the most influential cognitive psychological decision-making theories. The theory arose to challenge the straightforward expected utility-based rational choice theory. Prospect theory claims that people hardly ever make choices on the basis of the mathematical utility value of the available options, as the expected utility theory models the decision-making situation. Focusing on risky decision-making, the theory argues that the way in which a decision is framed, that is, whether it is understood to be in the realms of loss or gain, defines whether the decision-maker is a risk-taker or risk-averse. After carefully considering the generic theory, the chapter presents its applications to foreign policy decision-making. In addition to methodological challenges, the critical discussion deals with the issue of whether a theory based on average behaviour and tested by small monetary values in controlled circumstances can be applied to foreign policy decision-making.
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The NBA Three-Point Contest has been considered an ideal setting to study the hot hand, as it showcases the elite professional shooters that hot hand beliefs are typically directed towards, but in an environment that eliminates many of the confounds present in game action. We collect 34 years of NBA Three-Point Contest television broadcast data (1986-2020), apply a statistical approach that improves on those of previous studies, and find considerable evidence of hot hand shooting in and across individuals. Our results support fans’ and experts’ widely held belief in the hot hand among NBA shooters.
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When I watch basketball on television, it is a common occurrence to have an announcer state that some player has the hot-hand. This raises the question: Are Bernoulli trials an adequate model for the outcomes of successive shots in basketball? This paper addresses this question in a controlled (practice) setting. A large simulation study examines the power of the tests that have appeared in the literature as well as tests motivated by the work of Larkey, Smith, and Kadane (LSK). Three test statistics for the null hypothesis of Bernoulli trials have been considered in the literature; one of these, the runs test, is effective at detecting one-step autocorrelation, but poor at detecting nonstationariy. A second test is essentially equivalent to the runs test, and the third is shown to be worthless. The LSK-motivated tests are shown to be effective at detecting nonstationarity. Finally, a case study of 2,000 shots by a single player is analyzed. For this player, the model of Bernoulli trials is inadequate.
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No previous study on momentum in team sports has found any valid evidence for a momentum effect—i.e., an effect of success in the past few games, over and above the effect of team quality. We develop an econometric model to determine if there is a momentum effect in the NBA by examining how success over the past few games leads to a higher probability of winning the next game. The model takes into account the home vs. away strengths of the teams in the current game as well as their opponents in the previous games (to calculate measures of “adjusted success over the past few gamesâ€). Thus, success in previous games is adjusted for quality of the wins or losses. In addition, we account for rest days before the current game for both teams. Using data over three NBA seasons (2007-2009), we find strong evidence for a positive momentum effect.
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The long lasting debate initiated by Gilovich, Vallone and Tversky in [Formula: see text] is revisited: does a "hot hand" phenomenon exist in sports? Hereby we come back to one of the cases analyzed by the original study, but with a much larger data set: all free throws taken during five regular seasons ([Formula: see text]) of the National Basketball Association (NBA). Evidence supporting the existence of the "hot hand" phenomenon is provided. However, while statistical traces of this phenomenon are observed in the data, an open question still remains: are these non random patterns a result of "success breeds success" and "failure breeds failure" mechanisms or simply "better" and "worse" periods? Although free throws data is not adequate to answer this question in a definite way, we speculate based on it, that the latter is the dominant cause behind the appearance of the "hot hand" phenomenon in the data.
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Despite the conventional wisdom of the existence of the “hot hand" in basketball, studies have found no or weak evidence for the hot hand in game situations, although stronger evidence in controlled settings. Almost all studies have tested for the hot hand in univariate frameworks, often with inadequate power. I use a sample based on all free throws during the 2005-06 NBA season. With a multivariate framework with individual fixed effects, I find evidence for the “hot hand" in that making the first free throw is associated with a significantly higher probability of making the second free throw.
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The authors review research on judgments of random and nonrandom sequences involving binary events with a focus on studies documenting gambler's fallacy and hot hand beliefs. The domains of judgment include random devices, births, lotteries, sports performances, stock prices, and others. After discussing existing theories of sequence judgments, the authors conclude that in many everyday settings people have naive complex models of the mechanisms they believe generate observed events, and they rely on these models for explanations, predictions, and other inferences about event sequences. The authors next introduce an explanation-based, mental models framework for describing people's beliefs about binary sequences, based on 4 perceived characteristics of the sequence generator: randomness, intentionality, control, and goal complexity. Furthermore, they propose a Markov process framework as a useful theoretical notation for the description of mental models and for the analysis of actual event sequences.
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Gambling is a leisure activity, which is enjoyed by many people around the world. Among these people, Chinese are known for their high propensity to gamble and are highly sought after by many casinos. In this exploratory study, the effect of two types of fallacy bias-positive recency and negative recency-on the betting behavior of Chinese gamblers is investigated. Although the influence of fallacy bias on a betting decision is well documented, little is known about the interaction of the factors that dictate fallacy bias. Drawing from an analysis of 2,645 betting decisions, the results show that Chinese gamblers primarily endorse positive recency, especially when the latest outcome is more frequent. This is contrary to most findings on Western subjects in which negative recency is more common. Current findings have meaningful implications to casino gaming entertainment businesses and public policymakers.
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Conducted a series of 6 studies involving 631 adults to elucidate the "illusion of control" phenomenon, defined as an expectancy of a personal success probability inappropriately higher than the objective probability would warrant. It was predicted that factors from skill situations (competition, choice, familiarity, involvement) introduced into chance situations would cause Ss to feel inappropriately confident. In Study 1 Ss cut cards against either a confident or a nervous competitor; in Study 2 lottery participants were or were not given a choice of ticket; in Study 3 lottery participants were or were not given a choice of either familiar or unfamiliar lottery tickets; in Study 4, Ss in a novel chance game either had or did not have practice and responded either by themselves or by proxy; in Study 5 lottery participants at a racetrack were asked their confidence at different times; finally, in Study 6 lottery participants either received a single 3-digit ticket or 1 digit on each of 3 days. Indicators of confidence in all 6 studies supported the prediction. (38 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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The 'hot hand' describes the belief that the performance of an athlete, typically a basketball player, temporarily improves following a string of successes. Although some earlier research failed to detect a hot hand, these studies are often criticized for using inappropriate settings and measures. The present study was designed with these criticisms in mind. It offers new evidence in a unique setting, the NBA Long Distance Shootout contest, using various measures. Traditional sequential dependency runs analyses, individual level analyses, and an analysis of spontaneous outbursts by contest announcers about players who are 'on fire' fail to reveal evidence of a hot hand. We conclude that declarations of hotness in basketball are best viewed as historical commentary rather than as prophecy about future performance.
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We investigate the origin and the validity of common beliefs regarding “the hot hand” and “streak shooting” in the game of basketball. Basketball players and fans alike tend to believe that a player's chance of hitting a shot are greater following a hit than following a miss on the previous shot. However, 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 belief in the hot hand and the “detection” of streaks in random sequences is attributed to a general misconception of chance according to which even short random sequences are thought to be highly representative of their generating process.