Most people who watch basketball believe

in the "hot hand": Players who make a shot

are more likely to hit the next shot than

players who miss a shot (i.e., shots are positively

autocorrelated rather than independent).

Almost everyone in the sample studied

by Thomas Gilovich, Robert Vallone,

and Amos Tversky (1985), including several

successful professionals, believed in the hot

hand

Camerer, Colin F.

English

Caltech Authors - Main

American Economic Association
Does the Basketball Market Believe in the `Hot Hand,'?
Author(s): Colin F. Camerer
Source: The American Economic Review, Vol. 79, No. 5 (Dec., 1989), pp. 1257-1261
Published by: American Economic Association
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Does the Basketball Market Believe in the 'Hot Hand,'? 
By COLIN F. CAMERER* 
Most people who watch basketball believe 
in the "hot hand": Players who make a shot 
are more likely to hit the next shot than 
players who miss a shot (i.e., shots are posi- 
tively autocorrelated rather than indepen- 
dent). Almost everyone in the sample stud- 
ied by Thomas Gilovich, Robert Vallone, 
and Amos Tversky (1985), including several 
successful professionals, believed in the hot 
hand. 
There is no hot hand in basketball shoot- 
ing. Gilovich et al. found that the outcomes 
of consecutive shots are approximately inde- 
pendent. (In fact, outcomes are slightly neg- 
atively autocorrelated). They rejected many 
explanations of their surprising finding. For 
instance, the hot hand might be masked be- 
cause players defend more aggressively after 
a player has made a shot. But shots are also 
independent during free-throw shooting and 
in experiments with college players in which 
there is no defensive pressure. (Their paper 
contains several other clever demonstrations; 
the still-skeptical reader should consult it). 
Belief in the hot hand is a mistake gener- 
ated by persistent misunderstanding of ran- 
domness. People usually expect more alter- 
nations and fewer long streaks than actually 
occur in a random series (Willem Wagenaar, 
1972). They expect properties of large sam- 
ples, like convergence of the relative fre- 
quency of heads to the population parameter 
0.5, to hold in small samples too (see Tver- 
sky and Daniel Kahneman, 1971). While 
watching a random process, it is therefore 
easy to believe that the expected alternations 
do not occur because observations are actu- 
ally positively autocorrelated.' 
Does Belief in the Hot Hand Matter for 
Economics? The important question for eco- 
nomics is whether mistaken beliefs like the 
hot hand fallacy make allocations of re- 
sources suboptimal. Every basketball game 
provides casual evidence that belief in the 
hot hand affects coaches' choices of which 
players should shoot or leave the game, but 
it is difficult to tell whether these decisions 
are important mistakes without an experi- 
mental comparison of coaching techniques 
(which no team owner would allow!) 
While a study of coaching decisions is 
virtually impossible, a resource-allocation 
question that can be answered is whether 
belief in the hot hand affects betting. It does. 
Gilovich et al. had college players take shots 
while the players (and other observers) bet 
small or large amounts on the outcome.2 
Both players and observers made larger bets 
after players had just made shots, as the hot 
hand theory prescribes, but bet size and ac- 
tual performance were uncorrelated. 
If people believe that players have hot 
hands within a game, and belief in the hot 
hand stems from misunderstanding of ran- 
dom sequences in general, then bettors 
should also believe teams have hot and cold 
streaks across games. (For instance, suppose 
bettors expect that teams with losing streaks 
are due for wins. When they lose more often 
than expected, bettors will come to believe in 
cold and hot hands). This conjecture can be 
tested by examining point spreads and ac- 
tual results. 
The point spread is the number of points 
the favored team is expected to win by. If 
Philadelphia is favored by 6 over Boston, a 
*Department of Decision Sciences, University of 
Pennsylvania, Philadelphia, PA 19104. Thanks to Mike 
Chernew, Ben Maserang, Robye Frankel, Alan Frost, 
David Goldstein, and especially Lisabeth Miller for 
research assistance. 
'That is, if one creates a "random" series which 
actually has negative autocorrelation-too few long 
runs-then a truly random series with zero autocorrela- 
tion will seem to have positive autocorrelation and too 
many long runs. 
2All the bets paid a positive amount if the shot was 
made and a negative amount if the shot was missed, so 
the shooter had no incentive to miss deliberately. 
1257 
1258 THE AMERICAN ECONOMIC REVIEW DECEMBER 1989 
bet on Philadelphia wins only if they win the 
game by 7 points or more. (A win by 6 
points is a tie, neither a win nor a loss). 
If bettors overestimate the magnitude of 
the hot hand, teams with winning (losing) 
streaks will have point spreads which are too 
high (low) compared to actual results. 
Point spreads are set by bookmakers to 
balance the dollar amount bet on each team, 
thus minimizing their risk and guaranteeing 
revenue. (Their revenue comes from charging 
a percentage of losing bets). While point 
spreads are offered by bookmakers, they are 
an expression of the dollar-weighted average 
opinion of the public. If most fans believe in 
the hot hand but a few high rollers do not, 
then point spreads might reflect no hot hand 
fallacy even if most people believe in it. This 
test thus makes a small contribution to the 
empirical and theoretical debate about 
whether judgment errors by individuals 
matter for economics (for example, Robin 
Hogarth and Melvin Reder, 1987; my 1987 
paper and my 1989 paper with George 
Loewenstein and Martin Weber). 
The Data. The data are actual results and 
published betting odds on professional bas- 
ketball games between 1983-86.3 (Betting on 
such games is illegal in the United States, 
except in Nevada and Atlantic City, but is 
common anyway). Playoff games were ex- 
cluded because data were more difficult to 
find and systematic elimination of teams 
meant that most streaks were short. 
In each game both teams have a previous 
winning or losing streak of some length. We 
take the game as data for the team with the 
longest streak.4 Point spreads are forecasts, 
so the difference between the point spread 
and the actual outcome is a forecast error. 
We take the performance of the team with 
the longest streak against the point spread 
(the forecast error) and put it in a sample 
with forecast errors in games played by teams 
with streaks of identical length. Thus, one 
sample consists of the forecast errors of 
games played by teams with 1-game winning 
streaks, another sample consists of errors 
from games with 2-game streak teams, etc. 
Subsamples of games in which teams with 
winning streaks played teams with losing 
streaks were created. These subsamples are 
useful because the hot hand effect might be 
strongest when a team with a winning streak 
plays a team with a losing streak (instead of 
playing a team with a shorter winning streak). 
In each sample, the mean forecast error and 
the fraction of positive forecast errors (ex- 
cluding ties, which were rare) were calcu- 
lated. 
The Results. Statistics for games involving 
winning streaks are shown in Table 1. Super- 
scripts a, b, and c denote statistical signifi- 
cance (by t-tests for means and binomial 
tests for fractions) at the 0.10, 0.05, and 0.01 
levels. 
Consider the 1983-84 season (left col- 
umns). There were 59 times when teams with 
1-game winning streaks played teams with 
streaks that were shorter or equal in length. 
The teams with 1-game streaks beat the 
spread 59 percent of the time, by an average 
of 1.44 points. 
If point spreads reflect mistaken belief in 
the hot hand, teams with winning streaks 
should do worse than expected; forecast er- 
rors should be negative. They are mostly 
negative-teams with winning streaks are 
thought to have hotter hands than they actu- 3The source was the NBA Pointspread Handbook 
sold by Tony Salinas' High Roller Inc., Las Vegas. Two 
seasons of data were checked against point spreads 
published in the Philadelphia Inquirer; no discrepancies 
of more than a point were found. Salinas's data are 
"closing lines," reflecting bookmakers' adjustment of 
the initial "opening line" for imbalances in betting. 
For instance, if Philadelphia has a winning streak of 
6 games and plays Boston, which has a losing streak of 
3 games, the outcome is only used as evidence of how 
teams with 6-game winning streaks perform. To use the 
same observation as evidence for streaks of + 6 and - 3 
would cause statistical dependence across streak cate- 
gories. This procedure also shifts observations from 
short streaks to long streaks, which improves overall 
statistical power because short streaks are common and 
long streaks are rare. (Indeed, basketball is useful to 
study because it contains more long streaks than most 
other sports, and point spreads are used rather than 
odds). When two teams had equal-length streaks of 
opposite sign, the observation was randomly assigned to 
streaks of one of the two signs. 
VOL. 79 NO. 5 CAMERER: BASKETBALL AND THE HOT HAND 1259 
TABLE 1-MARKET FORECAST ERRORS (OUTCOMES MINUS POINT SPREADS) 
FOR TEAMS WITH WINNING STREAKS 
1983-84 1984-85 1985-86 All Years 
Streak Mean Fraction Mean Fraction Mean Fraction Mean Fraction 
Length Error Positive n Error Positive n Error Positive n Error Positive n 
Against All Teams 
+ 1 1.44 0.59 59 1.07 0.49 61 - 1.30 0.47 53 0.47 0.52 173 
+ 2 1.47 0.55 113 1.25 0.50 106 0.84 0.47 118 1.18b 0.51 337 
? 3 -2.33a 0.49 103 -1.51 0.40a 81 1.36 0.53 83 -0.93 0.47 267 
? 4 0.28 0.51 51 -0.55 0.48 58 -2.02 0.38a 50 -0.75 0.46 159 
? 5 - 2.54 0.40 35 - 2.47 0.47 32 -0.31 0.51 35 -1.75 0.46 102 
? 6 -3.21 0.26a 19 1.38 0.54 24 0.44 0.44 18 -0.33 0.43 61 
? 7 - 0.81 0.54 13 2.31 0.63 16 - 2.92 0.23 13 -0.27 0.48 42 
+ 8 -4.86 0.14 7 2.67 0.50 12 -2.10 0.30 10 -0.79 0.34a 29 
> 9 - 9.50 0.00 3 -2.10 0.41 17 - 3.11 0.50 18 - 3.16b 0.42 38 
Total - 0.49 0.50 403 0.08 0.48 407 - 0.19 0.46 398 - 0.20 0.479 1208 
Against Teams with Losing Streaks 
+ 1 1.44 0.59 59 1.07 0.49 61 - 1.30 0.47 53 0.47 0.52 173 
+ 2 4.26c 0.64b 56 0.66 0.49 61 -0.27 0.44 62 1.46a 0.52 179 
+ 3 -2.75 0.49 53 -1.74 0.38a 50 0.51 0.49 43 -1.44 0.45 146 
+ 4 1.43 0.59 29 0.47 0.52 31 - 1.52 0.48 25 0.21 0.53 85 
+ 5 - 3.44 0.39 18 - 2.5 0.47 17 1.13 0.60 15 -1.78 0.48 50 
+ 6 - 3.36 0.29 7 3.16 0.63 16 1.42 0.50 12 1.26 0.51 35 
+ 7 2.31 0.75 8 - 6.17 0.33 6 - 1.25 0.50 4 -1.31 0.56 18 
+ 8 - 7.00 0.33 3 - 0.50 0.33 3 2.00 0.50 4 - 1.45 0.40 10 
> 9 - 18.50 0.00 1 - 4.83 0.44 9 - 5.75 0.50 8 - 6.00c 0.44 18 
Total 0.48 0.56a 234 -0.17 0.47 254 -0.49 0.48 226 -0.06 0.501 714 
p < 0.10. 
p < 0.05. 
'p < 0.01. 
ally do-when data from all three seasons 
are pooled. However, the effects are very 
small, they do not increase much with streak 
length (except for the striking results for 
streaks of 9 wins or more), and the effects 
are not stronger when teams with winning 
streaks played teams with losing streaks. 
Data from teams with losing streaks, 
shown in Table 2, also provide some evi- 
dence of hot hand fallacy. The forecast er- 
rors are mostly positive-losing-streak teams 
do better than expected-and pooled means 
are often statistically significant. But the ef- 
fects are still small in magnitude. 
The asymmetry in results between winning 
and losing streaks is curious. It is reminis- 
cent of Werner De Bondt and Richard 
Thaler's (1985) finding that stocks of firms 
which have lost market value (" losers") re- 
bound in price more than stocks of winner 
firms drop. People seem to believe there is 
more permanence to losing than to winning, 
and they overestimate this permanence. 
Bookmakers profit by charging a percent- 
age of losing bets (usually 10 percent). Bet- 
tors must therefore win 52.4 percent of their 
bets to break even.5 Table 2 shows that 
across the three seasons, bets on teams with 
losing streaks would exactly break even. Bets 
against teams with winning streaks (see Table 
1) win 52.1 percent of the time, almost 
breaking even. 
Discussion. The answer to my title ques- 
tion is Yes, but the market's error is too 
small to be profitably exploited. The data 
5The break-even winning probability p is determined 
by p+(l-p)(-l.l)=0, which implies p=1.1/2.1= 
0.524. 
1260 THE AMERICAN ECONOMIC REVIEW DECEMBER 1989 
TABLE 2-MARKET FORECAST ERRORS (OUTCOMES MINUS POINT SPREADS) FOR TEAMS WITH LOSING STREAKS 
1983-84 1984-85 1985-86 All Years 
Streak Mean Fraction Mean Fraction Mean Fraction Mean Fraction 
Length Error Positive n Error Positive n Error Positive n Error Positive n 
Against All Teams 
- 1 1.89 0.39a 59 1.76 0.57 56 1.53 0.62a 58 1.73b 0.53 173 
- 2 0.39 0.53 111 1.22 0.55 95 -0.42 0.48 118 0.34 0.52 324 
- 3 1.08 0.51 89 2.16a 0.55 83 1.12 0.49 76 1.45a 0.52 248 
- 4 0.19 0.53 59 - 0.76 0.55 51 1.88 0.54 48 0.40 0.54 158 
- 5 - 0.61 0.39 36 - 0.64 0.45 29 1.36 0.52 33 0.04 0.45 98 
- 6 6.30b 0.65 20 0.33 0.60 20 0.06 0.53 17 2.34a 0.60 57 
- 7 0.44 0.44 9 - 2.23 0.55 11 -1.00 0.38 16 - 1.02 0.44 36 
- 8 1.92 0.67 6 -4.00 0.40 5 11.11c 1.00 9 4.58a 0o75b 20 
< - 9 11.00 1.00 2 1.21 0.58 19 0.80 0.60 5 1.88 0.62 26 
Total 1.03 0.50 391 0.87 0.55b 369 0.92 0.53 380 0.94 0.524a 1140 
Against Teams with Winning Streaks 
- 1 1.89 0.39 59 1.76 0.57 56 1.53 0.62a 58 1.73a 0.53 173 
- 2 0.14 0.55 60 2.15 0.57 54 - 0.98 0.46 59 0.39 0.53 173 
- 3 0.31 0.51 51 0.70 0.58 40 2.74 0.47 38 1.15 0.52 129 
- 4 - 1.38 0.44 32 0.17 0.56 27 3.68 0.64 25 0.62 0.54 84 
- 5 - 5.13a 0.25 12 1.78 0.58 19 2.13 0.60 15 0.09 0.50 46 
- 6 6.83 0.78 9 1.44 0.56 9 - 0.44 0.56 9 2.61 0.65 26 
- 7 - 1.13 0.50 4 - 6.80 0.40 5 - 3.17 0.33 6 - 3.84 0.40 15 
- 8 - 6.25 0.50 2 - 4.17 0.33 3 1l.50C 1.00 6 4.00 0.73 11 
< -9 - - 0 1.25 0.60 10 3.33 0.67 3 1.73 0.62 13 
Total 0.33 0.48 229 1.17 0.57b 223 1.44 0.55 219 0.97 0.531a 670 
ap < 0.10. 
p < 0.05. 
cp < 0.01. 
suggest psychological and economic explana- 
tions of betting behavior are both useful. 
Psychological prediction of hot hand fallacy 
suggests the direction of the systematic fore- 
cast error correctly. However, the economic 
thesis that errors should be too small for 
traders to profit predicts the size of the 
forecast errors (placing an upper bound on 
their frequency). 
The novelty in this test is that psychologi- 
cal evidence suggested where to find a bias, 
and found one. There are many other studies 
of betting; some conclude that simple bet- 
ting strategies which exploit judgment error 
are profitable. A profitable rule for football 
betting, related to the hot hand fallacy, is to 
bet against favorites who beat the spread by 
a wide margin in the previous week (John 
Gandar et al., 1988, rule 7). Richard Thaler 
and William Ziemba (1988) reviewed many 
studies of betting in parimutuel markets. 
Betting on heavy favorites in horse races can 
be profitable, either because people overesti- 
mate the chance of high-odds long shots 
winning or because they prefer the positive 
skewness of long-shot bets. Betting in purely 
random lotteries can be profitable too be- 
cause people overbet certain numbers. 
In basketball betting, the hot hand fallacy 
exists but it is slight, perhaps because traders 
can study past data and exploit such errors 
easily. In other economic settings, rational 
traders cannot discipline less rational traders 
so easily-in labor markets, markets for 
housing, and illiquid assets, or in infrequent 
decisions about relationships, for instance. 
In such situations, biases like these might be 
especially important for economics. 
VOL. 79 NO. 5 CAMERER: BASKETBALL AND THE HOT HAND 1261 
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Does the Basketball Market Believe in the 'Hot Hand,'?

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Does the Basketball Market Believe in the 'Hot Hand,'?

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