Winning Isn't Everything: Corruption in Sumo Wrestling

Winning Isn’t Everything: Corruption in Sumo Wrestling

By MARK DUGGAN AND STEVEN D. LEVITT*

There is a growing appreciation among econ-

omists of the need to better understand the role

that corruption plays in real-world economies.

Although some have argued that it can be w el-

fare enhancing (Nathaniel Leff, 1964), most

commentators believe that a willingness to ac-

cept bribes (or similar forms of corruption) in

either the public or the private sector reduc es

economic ef ciency (Andrei Shleifer and

Robert W. Vishny, 1 993). As a result, g overn-

ments and  rms often create incentives to mo-

tivate their employees to be honest (Gary S.

Becker and George J. Stigler, 1974).

While it is generally agreed that corruption is

widespread, th ere is little rigorous empirical

research on the subject. Because of corruption’s

illicit nature, those who engage in corruption

attempt not to leave a trail. As a consequence,

much of the existing evidence on corruption is

anecdotal in nature. More systematic empirical

substantiation of corrupt practices is unlikely to

appear in typical data sources. Rather, research-

ers must adopt nonstandard approaches in an

attempt to ferret out indirect evidence of

corruption.

To date, there have been only a handful of

studies that attempt to systematically document

the impact of corruption on economic o ut-

comes. The  rst empirical study of corruption

dates to 1846 when Quetelet documented th at

the height distribution among French males

based on measurements taken at conscription

was normally distributed ex cept for a puzzling

shortage of men measuring 1.57–1.597 meters

(roughly 5 feet 2 inches to 5 feet 3 inches) and

an excess number of men below 1.57 meters.

Not coincidentally, the minimum height for

conscription into the Imperial army was 1.57

meters (Stephen Stigler, 1986). More recent em-

pirical work on corruption includes R obert H.

Porter and J. Douglas Zona (1993), which  nds

evidence that construction companies collude

when bidding for state highway contracts by

meeting before the auction, designating a seri-

ous bidder, and having other cartel members

submit correspondingly higher bids. R. Preston

McAfee (1992) details a wid e variety of bid-

rigging schemes. Paulo Mauro (1995) uses sub-

jective indices of corruption across countries to

demonstrate a correlation between corrupt gov-

ernments and lower rates of economic growth,

although the relationship may not be causal.

Ray Fisman (2001) analyzes how stock prices

of Indonesian  rms  uctuate with changes in

former Prime Minister Suharto’s health status.

Firms with close connections to Suharto, which

presumably bene t from corruption within the

regime, decline substantially more than other

Indonesian  rms when Suharto’s health weak-

ens. Whether the rents accruing to those close to

Suharto are due to corruption or simply bad

policy, however, is hard to determine. Rafael Di

Tella and Ernesto Schargrodsky (2000) docu-

ment that the prices paid for b asic inputs at

public hospitals in Buenos Aires fall by 10–20

percent after a corruption crackdown.

In this paper we look for corruption among

Japan’s elite sumo wrestlers. While acknowl-

edging th at sumo wrestling is not itself a subject

of direct interest to economists, we believe that

this case study nonetheless provides potentially

valuable insights. First, if corrupt practices

thrive here, one might suspect that no institution

is safe. Sumo wrestling is the national sport of

Japan, with a 2,000-year tradition and a focus

on honor, ritual, and history that may be unpar-

alleled in athletics.

Moreover, Japan is generally

* Duggan: Department of Economics, University of Chi-

cago, 1126 East 59th Street, Chicago, IL 60637, and National

Bureau of Economic Research (e-mail: mduggan@midway

.uchicago.edu); Levitt: American Bar Foundation and De-

partment of Economics, University of Chicago, 1126 East

59th Street, Chicago, IL 60637 (e-mail: slevitt@midway

.uchicago.edu). We would like to thank Gary Becker, Casey

Mulligan, Andrei Shleifer, Stephen Stigler, Mark West, two

anonymous referees, seminar participants, and especially

Serguey Braguinsky for helpful comments. Kyung-Hong

Park provided truly outstandin g research assistance. Levitt

gratefully acknowledges the research su pport of the Na-

tional Science Foundation and Slo an Foundation.

See Mark West (1997) for an examination of the legal

rules and informal norms that govern sumo wrestling in Japan.

1594

found to have relatively low rates of corruption

in cross-country comparisons (Transparency In-

ternational, 20 00).

Second, because of the sim-

plicity of the institutional framework, it is easy

to understand and model t he incentives facing

participants. Third, data to test for match rig-

ging are readily available. While the exact tech-

niques we utilize for studying corrupt behavior

in sumo wrestling will require modi cation be-

fore being applied to more substantive a pplica-

tions, our analysis may nonetheless aid future

researchers in that task.

The key institutional feature of sumo wres-

tling that makes it ripe for corruption is the

existence of a sharp nonlinearity in the payoff

function for competitors. A sumo tournament

(

basho

) involves 66 wrestlers (

rikishi

) partici-

pating in 15 bouts each. A wrestler who

achieves a winning record (eight wins or more,

known as

kachi-koshi

) is guaranteed to rise up

the of cial ranking (

banzuke

); a wrestler with a

losing record (

make-koshi

) falls in the rankings.

A wre stler’s rank is a source of prestige, the

basis for salary determination, and also in u-

ences the perks that he enjoys.

Figure 1 demonstrates empirically the impor-

tance of an eighth win t o a wrestler. The hori-

zontal axis of the  gure is the number of wins a

wrestler achieves in a tournament; the vertical

axis is the average change in rank as a conse-

quence of the tournament. The change in rank is

a positive function of the number of wins. With

the exception of the eighth win, th e relationship

is nearly linear: each additional victory is worth

approximately three sp ots in the rankings. The

critical eighth win—which results in a substan-

tial promotion i n rank rather than a demotion—

garners a wrestler approximately 11 spots in the

ranking, or roughly four times the value of the

typical victory. Consequently, a wrestler enter-

ing the  nal match of a tournament with a 7-7

record has far more to gain from a victory than

an opponent wit h a record of, say, 8-6 has to

lose. There will also b e incentives for forward-

looking wrestlers to rig matches o n earlier days

of the tournament.

According to our rough

calculations, moving up a single spot in the

rankings is worth on average approxima tely

$3,000 a year to a wrestler, so the potential

gains to trade may be substantial if the wrestlers

 x a match.

Of course, no legally binding

contract can be written.

In this paper, we examine more than a decade

of data for Japan’s sumo e lite in search of

evidence demonstrating or refuting claims of

match rigging. We u ncover overwhelming evi-

dence that match rigging occurs in the  nal days

of sumo tournaments. Wrestlers who are on the

margin for attaining their eighth victory win far

more often than would be expected. Hi gh win-

ning percentages by themselves, however, are

Nevertheless, in recent years, sumo wrestling has been

dogged by allegations of rigged matches, none of wh ich

have been substantiated. Of cials from the Japanese Sumo

Association dismiss these complaints as fabrications on the

part of disgraced former wrestlers. Ultimately, despite years

of allegations, no formal disciplinary actions have been

taken towar ds any wrestler.

For instance, the lowest-ranked wrestlers in the heya

must rise early each morning to clean the building and

prepare the food for the main meal of the day. When a

wrestler reaches the rank of juryo, placing him among the

top 66 sumo wrestlers in Japan, he no longer is required to

do chores for other rikishi. Those in the top 40 with ranks of

maegashira or better have their own servants.

An earlier version of this paper, Duggan and Levitt

(2001), derive a formal model of the incentives facing partic-

ipants. For wrestlers on the bubble, the incentive to rig matches

increases monotonically over the co urse of a tournament.

Wrestlers ranked between  fth and tenth earn an annual

income—including only of cial wages, bonuses, and prize

money—of roughly $250,000 per year. The fortieth -ranked

wrestler earns approximately $170,000. The seventieth-

ranked wrestler receives only about $15,000 per year (no

of cial salary, just a small stipend to cover tournament

expenses, some prize money, and room and board). All

information on annual salaries are based on the authors’

calculations and information provided in Mina Hall (1997).

Unof cial sources of income such as endorsements would

likely increase the disp arity between the top and bottom

wrestlers.

FIGURE 1. PAYOFF TO TOURNAMENT WINS

1595VOL. 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING

far from conclusive proof of match rigging.

Those wrestlers who are on the margin for

achieving the eighth win may exert greater ef-

fort because their reward for winning is larger.

We offer a number o f pieces of evid ence a gainst

this alternative hypothesis. First, whereas th e

wrestler who is on the margin for an eighth win

is victorious with a surprisingly high frequency,

the next time that those same two wrestlers face

each other, it is the

opponent

who has an un-

usually high win percentage.

This result sug-

gests that at least part of the currency used in

match rigging is promises of throwing future

matches in return for taking a fall today. Sec-

ond, win rates for wrestlers on the bubble vary

in accordance with factors predicted by theory

to support implicit collusion. For example, suc-

cess rates for wrestlers on the bubble rise

throughout the career (consistent with the de-

velopment of repu tation), but fall in the last year

of a wrestler’s career. T hird, match rigging dis-

appears during times of increased media scru-

tiny. Fourth, some wrestling stables (known as

heya

) appear to have worked out rec iprocity

agreements with other st ables such that wres-

tlers from either stable do exceptionally well on

the bubble against one another.

Finally, wres-

tlers identi ed as “not corrupt” by two former

sumo wrestlers who have alleged match rigging

do no better in matches on the bubble than in

typical matches, whereas those accused of being

corrupt are extremely successful o n the bubble.

It is dif cult to reconcile any of these  ndings

with effort as the primary explanation.

The remainder of this paper is o rganized as

follows. Section I introduces the data used in

the analysis and presents the empirical evidence

documenting the strong performance of wres-

tlers on the bubble. Section II attempts to dis-

tinguish between increased effort and match

rigging as an explanation for the observed pat-

terns in the data and also considers the way in

which the market for rigged matches operates,

e.g., how contracts are enforced, the use of cash

payments versus promises of future thrown

matches, and individuals versus stables as the

level at which deals are brokered. Section III

concludes with a discussion of the broader eco-

nomic implications of our analysis.

I. Evidence of Strong Perfo rmanc e

on the Bubble

Our data set consists of almost every of cial

sumo match that took place in the top rank

(

Sekitori

) of Japanese sumo wrestling between

January 1989 and January 2000. Six tourna-

ments are held a year, with nearly 70 wrestlers

per tournament, and 15 bouts per wrestler.

Thus, our initial data set consists of over 64,000

wrestler-matches representing over 32,000 total

bouts (since there a re two wrestlers per bout). A

small number of observations (less than 5 per-

cent of the total data set) are discarded due to

missing data, c oding errors, or early withdrawal

from the tournament due to injury. A total of

281 wrestlers appear in our data, with th e aver-

age number of observations per wrest ler in a

randomly selected match equal to 554, and a

maximum of 990. The average number of total

matches betwee n the same two wrest lers com-

peting in a randomly selected match is 10; thus

we often have many observations involving the

same two wrestlers at different points in time.

For each observation, we know the identity of

the two competitors, who wins, the month and

year o f the tournament, and the day of the match

(tournaments last 15 days with one match per

wrestler per day). For roughly 98 percent of the

sample, we also know what wrestling stable the

wrestlers belong to; information is missing for

some wrestlers i n the early part of our sample

who had only a short stint in the top ranks.

We begin by looking at the distribution of

wins across wrestlers at the end of tournaments.

We expect that a disproportionate number of

wrestlers should  nish wit h eight wins because

of the high payoff associated with the eighth

win (see Figure 1). To the extent that wrestlers

are rigging matches not only on t he  nal day,

but also in the days immediately preceding the

end of the tournament, extra we ight should also

be observed on nine wins, as wrestlers who are

close to the margin on days 13 or 14 may buy

wins that ultimately were not needed to reach

eight wins due to subsequent victories. Figure

2 presents a histogram of  nal wins for the

60,000 wres tler-tournament observations in

which a wrestler completes exactly 15 matches.

For purposes of comparison, we also present the

By the second subsequent meeting, the winning per-

centages revert back to the exp ected levels, sug gesting that

deals between individual wrestlers span only two matches.

Wrestlers in the same stable do not wrestle each other.

1596 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

expected pattern of results assuming that all

wrestlers are identical and that match outcomes

are independently di stributed.

Figure 2 provides clear visual evidence in

support o f the model’s prediction. Approxi-

mately 26.0 percent of all wrestlers  nish with

exactly eight wins, compared to only 12.2 per-

cent with seven wins. The binomial distribution

predicts that these two outcomes should occur

with an equal frequency of 19.6 percent. The

null hypothesis that the probability of seven and

eight wins is equ al can be rejected at resounding

levels of statistical signi cance. Nine victories

also appears more often than would be ex-

pected. Although this d istortion is far less pro-

nounced visually, nine v ictories is signi cantly

more likely than six (16.2 percent versus 13.9

percent).

Further evidence that wrestlers on the bubble

win far more often than would be expected

comes fro m estimating regressions of the gen-

eral form

(1)

Win

ij t d

bBubble

ij td

Rankdiff

ijt

ijtd

where

and

represent the two wrestlers,

corresponds to a particular tournament, and

the day of the tournament. The unit of observa-

tion is a wrestler-match. Bubble is a vector of

indicator variables capturing whether wrestler

is on the margin for reaching eight wins in

the bout in question. The Bubble variables are

coded 1 if only the wrestler is on the margin,

1 if only the opponent is on the margin, and 0

if neither or both of the combatants are on the

margin in the match.

Rankdiff

is the gap be-

tween the of cial ranking of wrestlers

and

entering tournament

. In some regressions, we

include  xed effects for each wrestler a nd each

opponent; in other speci cations we include

wrestler-opponent interactions. In all cases, we

estimate linear probability models, with stan-

dard erro rs co rrected to take in to account the

fact that a match is included in the data set

twice—once for wrestler

and once for wrestler

Table 1 reports the excess win percentages

for wrestlers on the margin, by day, for the last

 ve days of the tournament. On day 15, only

wrestlers with exactly s even wins are o n the

margin; on day 14, wrestlers with either six or

seven wins are on the margin, etc. The six

columns correspond to different regression

speci cations. The even columns include the

differences in ranks for the two wrestlers enter-

ing this tournament. The  rst two columns have

no wrestler  xed effects; columns (3) an d (4)

include both wrestler and opponent  xed effects.

The  nal two columns add wrestler-opponent

interactions so that th e identi cation comes

only from deviations in this match relative to

other matches involving the same two wrestlers.

The results in Table 1 are q uite similar across

speci cations.

Wrestlers on the bubble on day

15 are victorious roughly 25 percent more often

than would be expected. Win percentages are

elevated about 15 percent on day 14, 11 percent

on day 13, and 5 percent on day 12 for wrestlers

on the margin. There is no statistically signi -

cant evidence of elevated win rates for wrestlers

on the bubble on day 11. The pattern of coef -

cients is consistent with the hypothesis that th e

frequency of match rigging will rise as the tour-

nament comes to a close. If all of the excess

wins are due to rigging, then the results imply

that on day 15 half of the bubble matches are

crooked. For days 14, 1 3, and 12 respectively,

the estimated percentage of rigged matches is

roughly 28, 22, and 10 percent respectively.

Adding the difference in current rank between wres-

tlers has little impact on the other coef cients in the regres-

sion. The difference in ranks is an important predictor of

match outcomes when wrestler  xed effects are excluded

from the model. The top-ranked wrestler facing an average

wrestler would be expected to win about 70 percent of the

time. Once we control for wrestler  xed effects, however,

the explanatory power of the difference in ranks disappears.

FIGURE 2. WINS IN A SUMO TOURNAMENT

(ACTUAL VS. BINOMIAL)

1597VOL. 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING

II. Distinguishing Between Match Rigging

and Effort

The empirical results presented thus far are

consistent with a model in which opponents

throw matches to allow wrestlers on t he margin

to achieve an eighth victory. The results, how-

ever, are also consistent with a scenario in

which effort is an important de terminant of the

match outcome, and wrestlers on the bubble,

having more to gain from a win, exert greater

effort.

In this section, we present a wide variety

of analyses that appear to con rm the corruption

story and rule out effort as the explanation.

What Characteristics In uence the

Likelihood of Winning When on the Bubble?

We begin by analyzing the personal and sit-

uational characteristics that in uence the suc-

cess rate of the wrestler on th e bubble. One

potentially important determinant of the fre-

quency of match rigging is the p robability that

the collusive behavior will be detected. During

our sample, there have been two periods in

The results are also consistent with a model in which

wrestlers show altruism for one another, sacri cing their

own outcomes to help an opponent who has more to gain .

Given the nature of athletics and the nontrivial cost to the

wrestler of losing the match (roughly $10,000), the altruism

story strikes us as an unlikely explanation.

TABLE 1—EXCESS WIN PERCENTAGES FOR WRESTLERS ON THE MARGIN FOR ACHIEVING AN EIGHTH WIN,

BY DAY OF THE MATCH

On the Margin on: (1) (2) (3) (4) (5) (6)

Day 15 0.244 0.249 0.249 0.255 0.260 0.264

(0.019) (0.019) (0.018) (0.019) (0.022) (0.022)

Day 14 0.150 0.155 0.152 0.157 0.168 0.171

(0.016) (0.016) (0.016) (0.016) (0.019) (0.019)

Day 13 0.096 0.107 0.110 0.118 0.116 0.125

(0.016) (0.016) (0.016) (0.016) (0.019) (0.019)

Day 12 0.038 0.061 0.064 0.082 0.073 0.076

(0.017) (0.018) (0.017) (0.018) (0.020) (0.021)

Day 11 0.000 0.018 0.015 0.025 0.010 0.012

(0.018) (0.018) (0.018) (0.018) (0.021) (0.021)

Rank difference — 0.0053 — 0.0020 — 20.0020

(0.0003) (0.0003) (0.0004)

Constant 0.500 0.500 — — — —

(0.000) (0.000)

0.008 0.018 0.030 0.031 0.0634 0.0653

Number of observations 64,272 62,708 64,272 62,708 64,272 62,708

Wrestler and opponent  xed effects No No Yes Yes Yes Yes

Wrestler-opponent interactions No No No No Yes Yes

Notes: The dependent variable in all regressions is an indicator variable corresponding to whether or not a wrestler wi ns the

match. The unit of observation is a wrestler-match. Values reported in the table are coef cients associated with an indicator

variable taking the value 1 if only the wrestler is on the margin for achieving eight wins, 21 if o nly the opponent is on the

margin for achieving eight wins, and 0 otherwise. On day 15, onl y wrestlers with seven wins are on the margin. On day 14,

wrestlers with six or seven wins are on the margin. On day 13, wrestlers with  ve, six, or seven wins are on the margin, and

so on. The omitted category in all regressions is all wrestlers who are not on the margin for achieving eight wins, as well as

wrestlers in matches in which both participants are on the margin for eight wins. When a full set of wrestler and opponent

 xed effects are included, the constant is omitted. In all cases, standard errors are corrected to account for the fact that there

are two observations per bout (one for each wrestler). The differences in the wrestler rank variable is the numerical rank order

of the wrestler minus that of his oppon ent, based on of cial rankings published prior to each tournament. This variable is

missing for part of our sample.

1598 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

which media attention has focused on match

rigging. The  rst of these was in April and May

of 1996. A former sumo wrestler who had be-

come a stable-master came forward with alle-

gations of match ri gging. At the same time,

another former wrestler also came forward to

decry rigged matches. Ironically, both of these

men died a few weeks later, just hours apart, in

the same hospital. T his fueled speculation

among the media of foul play, although a sub-

sequent police investigation revealed no evi-

dence for th is. The second period of media

scrutiny took place in late 1999– early 2000. A

former sumo wrestler named Itai rai sed allega-

tions of match rigging that were wid ely covered

by the media, even in the United States. The

three tournaments in our sample that are most

likely to be affected by the media attention are

those held in May 1996, November 1999, and

January 2000.

The literature on repeated-play games (e.g.,

Drew Fudenberg and Jean Tirole, 1991) sug-

gests that the ability to sustain collusion should

be positively related to the frequency with

which two wrestlers e xpect to meet in the future

since more future meetings imply the availabil-

ity of more severe punishments for wrestlers

who d o not cooperate. Empirically, we p roxy

the expected frequency of future m atches using

two variables: (1) the number of meetings be-

tween the two wrestlers that took place in the

preceding year, and (2) whether the wrestler is

in the last year of his career. Although the

precise ending of a wrestler’s career is not

known in advance to the participants, it is likely

that signals of retirement are available (e.g.,

declining performance, injuries, etc.).

If it

takes time t o establish a reputation as a wrestler

who is willing to collude and who can be

trusted, then one might predict that the longer a

wrestler has been active in the top ranks of

sumo, the better he will do when he is on the

bubble, and also, the worse he will perform

when the opponent is on t he bubble.

Because there are a series of monetary prizes

given to wrestlers who have good records in a

given tournament, wrestlers in the running for

such prizes are unlikely to be willing to throw

matches.

The overall tournament champion

wins $100,000; the

juryo

champion wins

$20,000. In addition, $20,000 awards for “ ght-

ing spirit” and “outstanding technique.” In order

to win those prizes, wrestlers must compile very

strong records. The potential value of a victory

for a wrestler in the running for such prizes is

likely to be at least as great as the value to a

wrestler on the margin for an eighth win.

A  n al determinant of match rigging that we

consider is the possibility of coordinated match

rigging among stables of wrestlers. The lives of

sumo wrestlers center around the stable with

which they are associated. Stable-masters exert

a tremendous in uence over both the wrestling

career of wrestlers and their lives more gener-

ally.

Given the important role of the stable,

and the fact that stable-masters bene t from

having highly ranked wrestlers, it would not be

surprising if corruption were coordinated at the

stable level. For example, stables might have

collective reputations, with stable-masters en-

forcing punishments on wrestlers who pursue

their individual best interests at the expense of

the stable. Some stable-masters, on the other

hand, may not co ndone match rigging because

of ethical concerns o r risk aversion.

We empirically examine one particular form

of stable-level collusion: the presence of reci-

procity agreements across stables. If such deals

existed, one would expect both that wrestlers

from stable

will have very high win rates

when on the bubble facing wrestlers from stable

, and v ice versa.

It is dif cult to tell an

alternative story that would account for such a

pattern in t he data. For instance, if effort is the

In order to minimize endogeneity, we exclude the very

last tournament of a wrestler’s career. It is possible that a

loss on the bubble may drop the wrestler out of the top level

of wrestlers, inducing retirement. Including the last tourna-

ment of a wrestler’s career slightly increased the magnitude

and statistical signi cance of the coef cient.

Although we do not directly observe which wrestlers

might be under consideration for these prizes, having one of

the  ve best records (plus ties) up until that point in the

tournament is an excellent predictor. Wrestlers with one of

the  ve best records in the tournament entering days 13, 14,

or 15 win a prize 50 percent of the time. Less than  ve

percent of wrestlers with reco rds outside the top  ve on

days 13–15 eventually win a prize.

For instance, it is expected that the foremost sumo wres-

tler in a stable will marry the daughter of the stable-master.

The variable we use to test this empirically is the

overall win rate for wrestlers on t he bubble in matches

involving both a wrestler from stable A and a wrestler from

stable B (excluding the current match). This variable re ects

both stable A’s success on the bubble against stable B and

stable B’s success against stable A.

1599VOL. 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING

story, then stables with wrestlers capable of

exerting particularly high effort when they need

a win might also be expected to have wrestlers

who rise to the occasion when faced with the

opportunity to beat a very motivated opponent,

leading to a zero or negative correlation. Simi-

larly, if one stable has developed speci c tech-

niques that provide it with an a dvantage over a

particular stable, success rates on the bubble

will again be negatively related.

These various hypotheses are tested in Table 2.

Because our interest is in how these factors

in uence success on the bubble, the table re-

ports only the coef cients on the

interactions

between these various factors and the outcome

of bubble matches, i.e., any incremental impact

that the se factors have on bubble matches above

and beyond their impact in nonbubble matches.

Also included in the speci cations, but not

shown in the table, are t he main effects. Column

(1) is the baseline speci cation. Column (2)

adds both wrestler and opponent  xed effects.

Column (3) also includes wrestler-opponent in-

teractions. The results are generally quite simi-

lar across the three columns of the table.

The top row of the table is the main e ffect of

a wrestler being on the bubble, which leads to

an excess win likelihood of roughly 12–16 per-

centage points. In those tournaments with a high

level of media scrutiny, however, these excess

wins completely disappear.

In two of the three

speci cations, th e performance of wrestlers on

the bubble in high and low media scrutiny tour-

naments is statistically signi cant at the 0.05

level. In none of the three columns can one

reject the null h ypothesis that wrestlers on the

bubble in high-scrutiny tournaments do any bet-

ter than chance. In the words of Supreme Court

Justice Louis D. Brandeis, “Sunlight is said to

be th e best disinfectant.”

When the opponent is in the running for

winning one of the special prizes awarded, any

bene t of being on the bubble also disappears.

This result is consistent with opponents in the

running for prizes being unwilling to throw a

match.

The variables designed to capture factors in-

To calculate the overall excess win percent for a

wrestler on th e bubble in a p eriod of high media scr utiny,

the coef cients in rows 1 and 2 are added together.

We thank an anonymous referee for bringing this very

appropriate quote to our attention.

TABLE 2—DETERMINANTS OF EXCESS WIN L IKELIHOODS

FOR WRESTLERS ON THE BUBBLE

Variable (1) (2) (3)

Wrestler on bubble 0.126 0.117 0.155

(0.026) (0.026) (0.029)

Wrestler on bubble

interacted with:

High media 20.188 20.177 20.146

scrutiny (0.071) (0.071) (0.080)

Opponent in 20.149 20.129 20.156

running for a

prize this

tournament

(0.047) (0.046) (0.052)

Number of 20.0048 20.0031 20.0024

meetings

between two

opponents in

the last year

(0.0082) (0.0081) (0.0096)

Wrestler on

bubble

20.0361 20.0195 20.0346

in his last year

of competing

(0.0398) (0.0395) (0.0493)

Years in sumo for 0.0077 0.0077 0.0091

wrestler on

bubble

(0.0036) (0.0036) (0.0043)

Winning 0.272 0.293 —

percentage in

other bubble

matches

between these

two stables

(0.059) (0.058)

0.016 0.074 0.246

Wrestler and

opponent  xed

effects?

No Yes Yes

Wrestler-opponent

interactions?

No No Yes

Notes: The dependent variable in all three regressions is an

indicator variable corresponding to whether or not a wres-

tler wins the match. In addition to the listed interaction

terms, all main effects are also included in the speci ca-

tions. Wrestler on bubble is an indicator variable that equals

1 (21) if the wrestler (opponent) is on the bubble on days

13, 14, or 15 (record of 7-7, 7-6, 6-7, 7-5, 6-6, or 5-7) but

the opponent (wrestler) is not, and 0 otherwise. Matches

from 1989, the  rst year of our sample, are excluded be-

cause the variable for the number of matches between the

two wrestlers in the previous year cannot be computed .

Observations where stables are unknown or no two wres-

tlers from the stables ever meet on the bubble in our data set

are also excluded from the sample. The number of obser-

vations is consequently 42,788. Standard errors are cor-

rected to account for the fact that there are two observations

per bout (one for each wrestler).

1600 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

 uencing implicit collusion achieve mixed re-

sults. The number of matches between two

wrestlers in the preceding year has an unex-

pected negative impact on a wrestler’s likeli-

hood of winning a match on the bubble,

although the coef cient is substantively small

and carries a

-statistic of far less than 1 in all of

the speci cations. W restlers in the last year of

their career do slightly worse than e xpected on

the bubble, although again the result is not

statistically signi cant. With the exception of

the last year, ho wever, success on the bubble

increases over the career. A  ve-year veteran is

about 4 percentage points (off a baseline of 13

percentage points) more likely to win on the

bubble than a rookie. This last result is consis-

tent with the importance of developing a

reputation.

Finally, the bottom row of coef cients in

Table 2 measures the extent to which a wres-

tler’s success on the bubble today is in uenced

by overall success rates (excluding this match)

when wrestlers from that stable meet wrestlers

from the opponent’s stable and one of the wres-

tlers is on the bubble.

The coef cient is

strongly positive and statistically signi cant. As

noted above, that result that is dif cult t o rec-

oncile with any hypothesis other than stable-

coordinated collusion. Moreover, the size of the

coef cient is large: for each 10-percentage-

point increase in success in other bubble

matches between these two stables, the wrestler

on the bu bble is 3 percentage p oints more likely

to win today, controlling for other factors.

What Happens When Wrestlers M eet

Again in the Future?

If collusion is the reason that wrestlers on the

bubble p erform well, then the opponent must be

compensated in some way for losing the match.

It is possible that such payments are made in

cash, or in promises to return the favor in the

future. The likelihood that two wrestlers will

meet again soon is high: in our data 74 percent

of the wrestlers who meet when one is on the

margin for eight wins will face one another

again within a year.

Table 3 explores the pattern of match out-

comes ov er time for wrestlers who meet when

one is on the margin. The even columns include

wrestler-opponent interactions so identi cation

of the parameters comes only from variation in

outcomes involving the same two opponents;

the odd columns do not. The regression speci-

 cations include in dicator variables categoriz-

ing the timing of the meetings between two

wrestlers relative to the match where one wres-

tler is on the bubble. The omitted category is

matches preceding a bubble meeting by at least

three matches.

Focusing  rst on columns (1) and (2), which

correspond to all meetings on the bubble, there

are no systematic differences in outcomes in the

two matches preceding the match on the bubble,

as re ected in the statistically insigni cant c o-

ef cients in the top row. When the wrestler is

on the bubble (second row), he is much more

likely to win, consistent with the earlier tables.

The p arameter of greatest interest is the nega-

tive co ef cient for the  rst meeting between the

two wrestlers after the match in which the wres-

tler is on the bubble. The wrestler who was on

the margin in the last meeting is approximately

seven percent

less

likely to win than would

otherwise be predicted. This  nding is consis-

tent with part of the compensation for throwing

a match being t he promise of the opponent

returning the favor in the next meeting. There is

no evidence that any return of favors extends

beyond the next match, as two and three

matches out the winning percentages return to

normal.

The  nal four columns of Table 3 replicate

the  rst two columns, except that the sample is

divided into cases where the wrestler wins when

on the margin versus instances when the wres-

tler loses when on the margin.

One would not

expect a wrestler to intentionally lose in future

meetings to an opponentwho does not throw the

match on the margin. Thus, breaking down the

Because wrestlers do not change stables over the

course of their careers, there is no usable variation in this

variable when wrestler-opponent interactions are included

in column (3).

We have experimented with other groupings of

matches, f or instance allowing a different coef cient for

matches preceding/following the bubble match by mo re

than t hree meetings. The parameters of interest are not

sensitive to alternative speci cations.

In columns (3)–(6), the actual matches taking place on

the bubble are excluded from the regression si nce there is no

variation. In columns (3) and (4), all bubble matches are

won by the wrestler on the bubble; in columns (5) and (6),

no matches are won by the wrestler on the bubble.

1601VOL. 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING

data in this way provides a natural test of the

hypothesis that the poo r performance in the next

match is due to a deferred payoff to an opponent

who threw a match. The data provide clear

support for the collusion hypothesis. Wrestlers

who win on the bubble tend to do slightly better

than expected leading up to the bubble match,

then do much worse in the next meeting with

the same opponent. Relative to the surrounding

matches, the  rst post-bubble match sees the

wrestler losing approximately 10 percentage

points more frequently than would be expected

(i.e., row 3 minus row 1).

The pattern for wrestlers who lose to the oppo-

nent when on the margin for achieving eight wins

is very different. In the matches just prior to the

bubble match, the wrestler is slightly underper-

forming. This continues unaffected through the

post-bubble matches as well. Unlike columns (1)–

(4), there is no downward spike in wins following

the bubble match. The  nding that winners on the

bubble fare badly the next time they face the same

opponent, but losers do not, is consistent with the

match-rigging hypothesis, but not with an effort

story. If increased effort is responsible for strong

performances in matches on the margin, there is

no reason to expect systematic underperformance

the next time the two wrestlers meet, and certainly

When two wrestlers meet and both are on the bubble,

there is similarly no evidence that the wrestler who wins

fares more poorly the next time the two wrestlers meet. Thi s

is consistent with no match rig ging occurring when both

wrestlers are on the bubble, as predicted by the model.

More generally, there is no evidence of negative serial

correlation in match outcomes. When multiple lags of past

match outcomes between the two wrestlers are added to the

speci cations, the coef cients are positive.

TABLE 3—WIN PERCENTAGES IN PRECEDING AND SUBSEQUENT MATCHES

(For Two Wrestlers Who Meet When One is on the Margin in the Final Three Days of a Tournament)

Variable

All Matches on the

Margin

Only Matches in

Which the Wrestler on

the Margin Wins

Only Matches in

Which the Wrestler on

the Margin Loses

(1) (2) (3) (4) (5) (6)

One or two matches prior to the 20.002 0.005 0.0 20 0.0 19 20.041 20.035

bubble match (0.009) (0.012) (0.011) (0.017) (0.016) (0.022)

Bubble match 0.151 0.164 — — — —

(0.010) (0.014)

First meeting after bubble match 20.073 20.062 20.082 20.079 20.056 20.040

(0.011) (0.015) (0.015) (0.020) (0.0 20) (0.0 27)

Second meeting after bubble match 20.002 0.005 0.031 0.028 20.061 20.039

(0.013) (0.016) (0.017) (0.022) (0.0 23) (0.0 30)

Three or more meetings after 20.010 0.012 0.013 0.022 20.045 20.013

bubble match (0.006) (0.011) (0.007) (0.014) (0.0 08) (0.0 17)

Constant 0.500 — 0.50 0 — 0 .500 —

(0.000) (0.000) (0.000)

Wrestler-opponent interactions? No Yes No Yes No Yes

0.008 0.271 0.002 0.279 0.002 0.279

Notes: Entries in the table are regression estimates of the outcomes of matches between, after, and co ntemporaneous with

these two wrestlers meeting when one wrestler is on the margin for achieving eight wins on the last three days of the

tournament. T he dependent variable in all regressions is an indicator variable for whether the wrestler wins a match. The unit

of observation is a wrestler match. The  rst two columns correspond to all wrestlers who meet when one is on the margin.

In columns (3) and (4), the coef cients reported corr espond only to those cases where the wrestler on the bubble wins the

match. Columns (5) and (6) report coef cients only for those wrestlers on the bubble who lose the match. Columns (3) and

(5) are estimated jointly, as are columns (4) and (6). Except for columns (1) and (2 ), bubble matches are excluded from the

regressions. The excluded category in all regressions are matches occurring more than two matches prior to a bubble match

and not falling into any of the other categories named. When a full set of wrestler and opponent  xed effects are included,

the constant is omitted. In all cases, standard errors ar e corrected to account for the fact that th ere are two observations per

bout (one for each wrestler). Number of observations is equal to 64,273.

1602 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

not exclusively among those who won on the

bubble.

The payment-in-kind story suggested by the

results above is unlikely to be the only form of

compensation for wrestlers who throw matches.

Based on Table 3, roughly two-thirds of the

excess wins garnered on the b ubble are returned

the next ti me the two wrestlers meet. This

price—t wo-thirds of a match down the road in

return for throwing a match today—is too low

to represent the only form of payment. When

rumors circulate about match rigging in sumo,

they often suggest the presence of cash trans-

fers, although we are able to provide no evi-

dence about this channel.

Do the Data Con rm Public Allegations of

Cheating by Sumo Insiders?

Two former sumo wrestlers have made pub-

lic the names of 29 wrestlers who they allege to

be corrupt and 14 wrestlers who they claim

refuse to rig matches (Keisuke Itai, 2000; Ona-

ruto, 2000;

Shukan Post

, 2000).

In this sec-

tion, we investigate whether the performance on

the bubble of these two groups of wrestlers

systematically di ffers. If strong performance on

the bubble is due to match rigging and t he

allegations are true, then one would expect the

corrupt wrestlers to do extremely well on the

bubble, whereas the honest wrestlers would do

no better in bubble matches than on any other

match.

To test this hypothesis, we estimate a re-

gression identical to equation (1), but includ-

ing a full set of interactions between whether

a match is on the bubble and the classi cation

of each wrestler and his opponent as either

“corrupt,” “clean,” or “status unknown.” Only

43 of the 281 wrestlers (15 percent) in our

sample are speci cally identi ed as either

corrupt or clean. The remainder are classi ed

as status unknown. The whistle-blowers were

more likely to identify prominent wrestlers

with l ong c areers, however, so over 60 per-

cent of the matches in our sample involve at

least one wrestler identi ed by name as either

clean or corrupt.

Table 4 reports the results of the estimation.

All of the coef cients in the table come from a

single regression. The values in the table repre-

sent excess win percentages on the bubble, i.e.,

how much better a wrestler does when on the

bubble relative to matches in which neither

wrestler is on the b ubble. The columns of the

table identify the status of the wrestler on the

bubble—the wrestler who wants to buy a vic-

tory. The rows correspond to the status of the

opponent of the wrestler on the bubble—the

wrestler who might want to sell a win. Wh en

two wrestlers identi ed as corru pt me et on the

bubble, the one who needs the victory is 2 6

percentage points more likely to win the ma tch

than if those two wrestlers met with neither on

the bubble. This excess win percentage is highly

statistically signi cant. When a corrupt wrestler

meets a wrestler classi ed as “status unknown,”

the results are very similar. Win percentages for

the wrestler needing the victory when both

wrestlers are classi ed a s “status unknown” are

also highly elevated (18.1 percentage points

higher), but not quite as extreme. In stark con-

trast, none of the  ve coef cients involving

wrestlers identi ed as clean are statistically sig-

ni cant from zero. This implies t hat the out-

comes o f bubble matches involving a clean

wrestler are no different than the results when

the same two wrestlers meet, but neither is on

the bubble. This result holds true regardless of

whether the cl ean wrestler is himself on the

bubble or facing a wrestler who is on the bub-

ble. Thus, Table 4 provides strong con rmation

not only of the claim that elevated win percent-

ages on the bubble are due to m atch rigging, but

also that the allegations made by the two sumo

insiders appear to be truthful. Moreover, it ap-

pears that most of th e wrestlers not sp eci cally

named by the whistle-blowers are corrupt, since

their outcomes differ only slightly from those

wrestlers named as corrupt.

III. Conclus ion

This paper provides strong statistical analysis

documenting match rigging in sumo wrestling.

The incentive structure of promotion leads to

gains from trade between wrestlers on the mar-

gin for achieving a winning record and their

opponents. We show that wrestlers win a dis-

proportionate share of the matches when they

are on the margin. Increased effort cannot

The books that we cite are published only in Japanese.

We thank Serguey Braguinsky both for bringing the exis-

tence of this information to our attention and for translating

the relevant material for us.

1603VOL. 92 NO. 5 DUGGAN AND LEVITT: CORRUPTION IN SUMO WRESTLING

explain the  ndings. Match rigging disappears

in times of increased media scrutiny. Wrestlers

who are victorious when on the bubble lose more

frequently than would be expected the next time

they meet that opponent, suggesting that part of

the payment for throwing a match is future pay-

ment in-kind. Reciprocity agreements between

stables of wrestlers appear to exist, suggesting that

collusive behavior is not carried out solely by

individualactors. Allegationsby sumo insiders are

demonstrated to be veri ed in our data.

While sumo wrestling per se is not of direct

interest to economists, the case st udy that it

provides is po tentially of usefulness to the eco-

nomic analysis of corruption. Anecdotal allega-

tions of corrupt practices among sumo wrestlers

have occasionally surfaced, but have been dis-

missed as impossible to substantiate. In this

paper, we d emonstrate that the combination of a

clear understanding of the incentives facing par-

ticipants combined with creative uses of d ata

can reveal overwhelming statistical evidence of

corruption. Details of the corrupt practices, the

data sources, and the telltale patterns in the data

will all vary from one application to the next.

Nonetheless, the success of our study in docu-

menting the predicted patterns of corruption in

one context raises the hope that parallel studies

with more substantive economic focus may

yield similar results.

Moreover, our analysis provides insight into

how to combat corruption. First, the match rig-

ging we identify can be directly linked to the

arti cially imposed n onlinearity in incentives

for wrestlers wh o achieve a winning record.

Removing this distortion to incentives would

eliminate the bene ts of corruption. Second,

match rigging appears to be sensitive to th e

costs of detection. Increased media scrutiny

alone is suf cient to eliminate the collusive

behavior. Presumably, other approaches to rais-

ing the expected punishment would likewise be

effective. Third, at least in the sumo context,

insiders appear to have good information about

who is corrupt. Providing strong incentives for

whistle-blowers, particularly when suc h accusa-

tions ca n be corroborated by objective data

analysis, may prove effective in restraining cor-

rupt behavior.

While perhaps beyond the scope of this pa-

per, a question of interest is why those in charge

of the sumo wrestling have not attempted to

eliminate corruption, either by eliminating the

nonlinearity or by increasing expected punish-

ments. A partial answer is that there are barriers

to entry for a second sumo league, so the com-

petitive pressure exerted on th e current sumo

association is limited.

A second possibility is

Nonlinearities of this sort have been shown to distort

behavior in many other contexts as well, including Robert

Topel (1983) and Judith Chevalier and Glenn Ellison

(1997).

It is worth noting that the popularity of sumo wrestling

has declined substantially over the last two decades, sug-

gesting that other forms of recreation are substitutes.

TABLE 4—EXCESS WIN PERCENTAGES ON THE BUBBLE FOR WRESTLERS LABELED BY SUMO

INSIDERS AS “CORRUPT” OR “CLEAN”

Wrestler on the Bubble Is Identi ed as:

Corrupt Status Unknown Clean

Opponent of

wrestler on the

bubble is

identi ed as:

Corrupt 0.260 0.270 20.010

(0.037) (0.021) (0.038)

Status 0.271 0.181 0.041

unknown (0.021) (0.019) (0.031)

Clean 0.036 20.033 0.022

(0.027) (0.035) (0.074)

Notes: Entries in the table are coef cien ts from a regression with full set of interactions

between whether a match is on the bubble and the classi cation of a wrestler and his opponent

as clean, corrupt, or status unknown by two sumo insiders (Itai, 2000; Onaruto, 2000; Shukan

Post, 2000). The regression is identical to equation (1) in the text, except for the inclusion of

the aforementioned interactions. Twenty-nine wrestlers are categorized as corrupt, 14 are

classi ed as clean. Th e remainder of wrestlers are not speci cally named and are categorized

as status unknown. Stan dard errors are corrected to take into accou nt that there are two

observations per bout (one for each wrestler). Number of observations is equal to 64,273.

1604 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

that the nonlinear payoff structure generates

interest in otherwise unimportant matches on the

 nal days of the tournament. For the same rea-

son that wrestlers want to rig the matches on the

bubble, the fans are interested in the outcome.

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