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DOI: 10.1177/1527002514521429
published online 30 January 2014Journal of Sports EconomicsWen-Jhan JaneCompetitions
Peer Effects and Individual Performance: Evidence From Swimming
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Article
Peer Effects andIndividual Performance:Evidence FromSwimming Competitions
Wen-Jhan Jane1
AbstractThis article addresses the issue of peer effects on a swimmer’s performance. TheNational Database of Student Athletes in Taiwan from 2008 to 2010 is employed.The results show that a swimmer performs better when his or her competitors arefaster. The evidence shows that peer effects are positive. As to the relative quality ofswimmers in a competition, dispersed-quality competitors make a swimmer faster.The evidence also shows that older and taller boys swim faster. The regressions ofthe Heckman selection model support these conclusions.
KeywordsHeckman selection model, National Database of Student Athletes, peer effects onindividual performance
Introduction
There is growing literature that stresses the importance of the environment in deter-
mining the outcomes of individuals. Most of this literature is concerned with exam-
ining how peers and environmental factors affect youth behavior with regard to their
educational achievements, health, criminal involvement, work status, and other
1Department of Economics, Shih Hsin University, Taipei, Taiwan
Corresponding Author:
Wen-Jhan Jane, Department of Economics, Shih Hsin University, No. 111, Sec.1, Mujha Rd., Wunshan
District, Taipei 116, Taiwan.
Email: [email protected]
Journal of Sports Economics1-9
ª The Author(s) 2014Reprints and permission:
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economic variables. This article differs from previous studies by looking at the inter-
action of individual performance in swimming competitions.
It has long been recognized by psychologists that an individual’s performance
might be influenced by his peers. The first study to show evidence of such peer
effects was that of Triplett (1898), who noted that cyclists raced faster when they
were pitted against one another and slower when they raced only against a clock.
While Triplett’s study showed that the presence of others could facilitate perfor-
mance, others found that the presence of others inhibited performance. In particular,
Allport (1920) found that people in a group setting wrote more refutations of a logi-
cal argument, but that the quality of the work was lower than when they worked
alone. Zajonc (1965) resolved these paradoxical findings by pointing out that the
task in these experimental setups varied in a way that confounded the results. In par-
ticular, he argued that for well-learned or innate tasks, the presence of others
improves performance. For complex tasks, however, he argued that the presence
of others worsens performance.
The growing body of empirical studies on peer effects consistently find the pos-
itive impact of high-ability workers on their peers.1 Mas and Moretti (2009), for
example, showed that under hourly wages, high-ability grocery checkers increase
coworker efforts through social processes. Ichino and Maggi (2000) found that
absenteeism and episodes of misconduct are considerably more frequent in the
southern branches of the bank. They showed the impact of peers on negative produc-
tivity (absenteeism) in Italian bank workers and that an individual’s shirking level
increased with his coworkers’ average shirking level. However, their study was
based on cultural norms rather than ability. Azoulay, Zivin, and Wang (2010) found
that deaths of academic superstars lead to declines in coauthors’ publication rates.
Depken and Haglund (2011) found that team member quality improves team per-
formance, but at a decreasing rate in the National Collegiate Athletic Association
4 � 400 m men’s relay teams.
This article investigates whether positive or negative peer effects exist for swim-
mers in the National High School Athletic (NHSA) Games in Taiwan. To assess
whether swimmers experience peer effects, we estimated various empirical models
that relate an absolute and relative performance to the average quality of their com-
petitors in a race. The results suggest that as the average competitor quality
increases, that is, competitors’ average time decreases, individual performance
improves. However, as the standard deviation of the competitors’ quality increases,
that is, competitors’ standard deviation of time increases, individual performance
decreases. The former supports the positive peer effects. The latter indicates that a
disparity of quality in a competition reduces a swimmer’s performance.
The goal of this article is to employ the data of swimming competitions from
NHSA Games to investigate peer effects in a race. The remainder of this article is
organized as follows: The data and the empirical methodology are presented in the
second section. The results are discussed in the third section, and the article ends
with a summary of the main conclusions.
2 Journal of Sports Economics
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Empirical Methodology and Data Description
In Taiwan, the National Database of Student Athletes has accumulated approximately
1,582,000 athletes’ demographic data and performance records from 2007 to 2013,
forming a rare set of micro data that we use as the basis for this study. The database
includes all swimming, track and field, gymnastic, table tennis, badminton, tennis,
kickboxing, judo, archery, karate, and soft tennis athletes in the NHSA Games.2
For the NHSA swimming, individual races consist of freestyle, breaststroke,
backstroke, and butterfly races. Races cover 50, 100, 200, 400, 800, and 1,500 m.
The 800 m is for females and the 1,500 m is for males only. The butterfly, back-
stroke, and breaststroke races each cover 100 and 200 m. All four strokes are used
in the 200 m and 400 m individual medley events. The data cover 14 types of races
and were provided by the Ministry of Education for research purposes. Our data con-
tain extensive personal characteristics and yearly performance information on com-
petitors from 2008 to 2010. Demographic data include age, gender, height, and
weight. Competition dates and locations, as well as athlete’s schools, are also
included in the data set.
In order to consider peer effect on performance in a traditional labor market, two
challenges need to be overcome. One is the measure of individual performance and the
other is the definition of peers. This is the main reason why there are still few articles
discussing this issue. Swimming races present an ideal case where the performance of
each player, that is, the time, is easily measured in a uniform way. In addition, peers
for a player are easily defined in a game, that is, the rest of the competitors.
To test for a positive or negative peer effect, we control for both the average and
the standard deviation of participant quality in a race. The swimmer’s production
function estimated model can be specified as:
Timejt ¼ b0þ b1AvgTime�jt�1 þ b1SDTime�jt�1 þ FXit þ e; ð1Þ
where Timejt represents jth player’s seconds in a race. bs and F are estimated para-
meters, and e is an error term. The explanatory variables include the average seconds
of competitors which excluded player j in the previous race (AvgTime�jt�1); and the
standard deviation of competitors’ seconds which excluded player j in the previous
game (SDTime�jt�1).3 Control variables (Xjt) are the swimmer’s characteristics and
environmental factors. The former consists of swimmer’s height (Height), weight
(Weight), age (Age), and gender (Gender). The latter are dummies for the race types
(GameType), year dummy (Year), dummies for whether the race was a preliminary
(PRELIMS, yes ¼ 1, otherwise ¼ 0), and a final against a clock (CFINALS
yes ¼ 1, otherwise ¼ 0). Table 1 presents the descriptive statistics of the data.
The variable AvgTime�jt�1 is expected to have a positive relationship with
Timejt, if there exists a positive peer externality on a swimmer. Conversely, if the
peer externality on a swimmer’s performance is negative, the variable AvgTime�jt�1
is expected to be negative.
Jane 3
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The parameter of SDTimejt�1, on the other hand, could be either positive or neg-
ative since the dispersion degree of time for the competitors can result from any com-
bination of swimmers. For example, the participants in a race could consist of eight
average swimmers, or of three above-average swimmers, three below-average swim-
mers, and two average swimmers. However, when comparing two races with the same
potential (i.e., participants’ average time in a race), the sign of the parameter on
SDTimejt�1 provides evidence as to whether the average member in a race suffers
from positive peer effects, ceteris paribus. If the coefficient is positive, it means that
a dispersed human capital race induces more seconds. Therefore, a race with averagely
talented members has better individual performance. This represents that an average
human capital race suffers positive peer effects. Conversely, if the coefficient is neg-
ative, an average human capital race suffers negative peer effects.
Table 1. Descriptive Statistics of the Data.
Variable Description M SD Min. Max.
Time Player’s seconds in a game 163.8458 177.6139 24.43 1,220.95Proxies of peer effects
AvgTime Average seconds ofcompetitors
161.2749 174.0081 25.2075 1,126.244
SDTime Standard deviation ofcompetitors’ seconds
18.6576 27.3796 .3707 257.8379
AvgTimeP Average seconds ofcompetitors inpreliminaries
124.7666 75.8428 25.2475 333.0688
SDTimeP Standard deviation ofcompetitors’ seconds inpreliminaries
5.8531 4.2992 .3500 21.5017
AvgTime(t � 1)
Average seconds ofcompetitors last year
181.9861 234.1711 27.3015 1,119.079
SDTime(t � 1)
Standard deviation ofcompetitors’ seconds lastyear
139.3349 767.0914 1.40498 4,678.039
Control variablesAge Swimmer’s age 19.8242 1.8767 16 24Height (cm) Swimmer’s height 167.9784 8.4398 116 201Weight (kg) Swimmer’s weight 60.4344 9.9606 33 100Gender Swimmer’s gender (male¼
1, otherwise ¼ 0).5366 .4987 0 1
CFINALS Dummy of final raced onlyagainst a clock (yes ¼ 1,otherwise ¼ 0)
.0701 .2553 0 1
PRELIMS Dummy of preliminary(yes ¼1, otherwise ¼ 0)
.6580 .4745 0 1
Note. n ¼ 4,210.
4 Journal of Sports Economics
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According to the literature concerning the relationship between a swimmer’s soma-
totype and performance, the coefficients of Height and Gender are expected to be neg-
ative, the coefficient of Age is expected to be negative, and the coefficient of Weight is
insignificant.4 Cyclists raced faster when they were pitted against one another and
slower when they raced only against a clock (Triplett, 1898). The comparison base for
PRELIMS and CFINALS is the finals, so both coefficients are expected to be positive.
Empirical Results
The empirical results of Equation 1 for pooled ordinary least squares (OLS) regressions
are regressed. The w2 values of the Breusch–Pagan (B-P) test (¼9303.39) rejects the null
hypothesis of homoscedasticity. Therefore, a robust regression using iteratively
reweighted least squares is employed in the following estimations. Moreover, unob-
served individual-specific heterogeneity and sample selection biases induced by the non-
random process for competitors in a race are considered in the regressions. The Breusch
and Pagan Lagrangian multiplier test (¼622.92) rejects the null hypothesis of the absence
of an unobserved effect, and the Hausman (1978) test cannot reject the null hypothesis
that the difference in coefficients is not systematic. The random effects (RE) model is
supported. In a test of the selectivity effect, however, Mills’ ratio (l) does not support the
results in the Heckman selection model. The results are presented in Table 2.
The parameters on the measures of peer effects are of most interest in this article.
Both coefficients of AvgTimet�1 and SDTimet�1 are significant. The former is con-
sistently and positively related to a swimmer’s seconds, and the latter is consistently
and negatively related to a swimmer’s seconds in OLS, weighted least squares
(WLS), and Heckman selection regressions.
The evidence here indicates that a swimmer’s speed is influenced by the compet-
itors’ average and relative quality. The evidence of AvgTimet�1 supports a positive
peer effect on individual performance. A one-unit decrease in the average time of
the participants represents better competitors in a game and it will result in shorter
seconds (e.g., 0.31 s in the Heckman selection model with clustering race) for a
swimmer in a race. This part of the results corresponds to Depken and Haglund
(2011). Moreover, the evidence of SDTime indicates that a dispersed human capital
race induces a shorter time. A race with average quality members leads to a swim-
mer achieving longer seconds. A one-unit decrease in SDTime increases a swim-
mer’s time by 0.056 s in the Heckman selection model with clustering race,
ceteris paribus. This is in contrast to Brown’s (2011) findings that ‘‘large ability dif-
ferences in golfers is associated with lower performance.’’
As for the control variables, the coefficients of age, height, and gender are nega-
tively significant. For these students, older and taller boys induce faster times. Boys
are faster than girls. According to the RE Model, a 1-year increase in age decreases a
swimmer’s time by 1.76 s, and a 1-cm increase in height decreases a swimmer’s time
by 0.176 s, ceteris paribus.
Jane 5
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Tab
le2.
Tim
ean
dPee
rEffec
tsR
egre
ssio
nR
esults
(Dep
enden
tV
aria
ble
:T
ime
inSe
conds)
.
Poole
dO
LSPoole
dW
LSR
EM
odel
Hec
kman
Sele
ctio
nM
odel
Hec
kman
Sele
ctio
nM
odel
(Clu
ster
ing
Rac
e)
Var
iable
sse
conds
seco
nds
seco
nds
Seco
nd
stag
eSe
lect
Seco
nd
stag
eSe
lect
Avg
Tim
e(t�
1)
.360**
*.7
13**
*.1
26
.311**
*.3
10**
*(.048)
(.026)
(.155)
(.058)
(.059)
SDT
ime(
t�
1)
�.0
64**
*�
.128**
*�
.023
�.0
56**
*�
.056**
*(.009)
(.005)
(.028)
(.011)
(.011)
Age
�1.3
33**
*�
.760**
*�
1.7
6**
*.0
43**
*.0
43
(.146)
(.079)
(.208)
(.012)
(.031)
Hei
ght
�.1
45**
�.1
49**
*�
.176**
*�
.135**
.004
�.1
33**
*.0
04
(.047)
(.025)
(.060)
(.067)
(.004)
(.042)
(.007)
Wei
ght
�.0
30
.002
�.0
54
�.0
15
.004
�.0
11
.004
(.038)
(.021)
(.059)
(.060)
(.003)
(.048)
(.005)
Gen
der
�10.6
56**
*�
8.8
87**
*�
9.9
73**
*�
11.9
69**
*�
.22**
*�
12.1
05**
*�
.217**
(.607)
(.328)
(.825)
(1.3
58)
(.055)
(1.9
38)
(.084)
CFI
NA
LS5.6
23**
1.3
11**
*�
.991
4.0
49*
4.0
60
(1.7
06)
(.922)
(1.8
26)
(2.1
31)
(3.5
39)
PR
ELI
MS
5.4
20**
*3.1
55**
*2.1
57**
*4.5
21**
*4.5
25**
*(.585)
(.316)
(.673)
(.694)
(.739)
Gam
eTyp
eY
esY
esY
esY
esY
esY
ear
Yes
Yes
Yes
Yes
Yes
Const
ant
99.1
25**
64.0
44**
*133.8
47**
*74.7
75**
*�
2.2
6**
*73.3
64**
*�
2.2
61*
(7.8
37)
(4.2
35)
(13.3
32)
(14.9
83)
(0.6
1)
(8.9
05)
(1.2
68)
Obse
rvat
ions
3,0
26
3,0
26
3,0
26
4,2
10
4,2
10
Cen
sore
dobs
2,9
08
2,9
08
Num
ber
ofid
924
(Pse
udo)
R2
.995
.9948
B-P
test
(w2)
9303.3
9**
*H
ausm
ante
st11.0
4LM
test
622.9
2**
*M
ills’
ratio
(l)
�1.0
43
�.2
21
(6.5
35)
(1.0
22)
Not
e.O
LS¼
ord
inar
yle
astsq
uar
es;L
M¼
Lagr
angi
anm
ultip
lier;
RE¼
random
effe
ct;W
LS¼
wei
ghte
dle
ast
squar
es.V
alues
inpar
enth
eses
are
the
stan
dar
der
rors
.**
*Den
ote
ssi
gnifi
cance
atth
e1%
leve
l.**
Den
ote
ssi
gnifi
cance
atth
e5%
leve
l.an
d*D
enote
ssi
gnifi
cance
atth
e10%
leve
l.
6 at TEXAS SOUTHERN UNIVERSITY on October 26, 2014jse.sagepub.comDownloaded from
The coefficients of PRELIMS and CFINALS are positively and significantly
related to a swimmer’s performance. Compared with finals, preliminaries and finals
against a clock increase a swimmer’s race time by 4.52 and 4.05 s on average in the
estimation of the Heckman selection model. This indicates that swimmers raced
faster when they swum against one another and slower when they raced only against
a clock. The results reinforce the evidence for peer effects, and it corresponds to the
findings of Triplett (1898) and Depken and Haglund (2011).
Conclusion
While most research examining how peers affect youth behavior are concerned with
educational achievements, health, and economic variables, this article looks at the inter-
action of individual performance in swimming competitions. The results of this study
confirm that the peer effect from the average quality of competitors on a swimmer’s per-
formance in a NHSA race is positive. The peer effect from the relative quality of com-
petitors on a swimmer’s performance in an NHSA race is negative. Large differences in
the ability of swimmers are associated with higher performance. Moreover, the results
of regressions in the Heckman selection model reinforce the evidence of peer effects.
These findings suggested three important implications. First, peer performance is
an important factor for a swimmer’s performance. This means that if the swimmers
in a race are faster, and if they are racing against one another (as opposed to against a
clock), better performances will be stimulated. Understanding peer effect is the first
step toward learning how to best structure situations in which competition exists
among players of heterogeneous ability. Second, the evidence of peer effects from
the relative quality of competitors suggests a positive learning effect from the top
swimmer in a race. While it is a substantial leap to transfer the findings on swim-
mers’ race performances to children’s school behavior, our results suggest that there
may be a potential upside to introducing a learning effect into the classroom by hav-
ing a superstar pupil. Finally, physical characteristics are important. The signifi-
cance of the Height coefficients confirms and reinforces the relationship between
a swimmer’s height and performance. These estimations of marginal effects can pro-
vide valuable information for swimmers and coaches.
Acknowledgements
Jane would like to thank the editor and the anonymous referees for their helpful comments on
the manuscript. All remaining errors are my own.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, author-
ship, and/or publication of this article.
Jane 7
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Funding
The author(s) disclosed receipt of the following financial support for the research, authorship,
and/or publication of this article: Jane is grateful to the National Science Council for its finan-
cial support (NSC101-2410-H-128-006-MY2).
Notes
1. To the best of our knowledge, the only exceptions are two studies using data from profes-
sional golf tournaments in which players’ compensation is tournament based. Guryan,
Kroft, and Notowidigdo (2009) find no evidence that a player’s performance is affected
by the existence of star players, while Brown (2011) documents that the presence of a
superstar (Tiger Woods) is associated with reduced performance from peers. On average,
higher skill PGA golfers first-round scores are approximately 0.2 strokes higher when
Tiger Woods participates, relative to when Woods is absent. The overall superstar effect
for tournaments is approximately 0.8 strokes.
2. The National High School Athletic Games is the largest multisport event for junior and
senior high school players in Taiwan. The Games started in 1952, under the name of
Taiwan Provincial High School Games. It is now hosted by the Ministry of Education and
the National Sports Council, Executive Yuan. The host city changes every year.
3. Both square terms of AvgTime�jt�1 and SDTime�jt�1 are also included in the regressions,
and the conclusions are similar. The results of estimation are provided by the author if
needed.
4. For discussion of the relationship between a swimmer’s somatotype and swimming perfor-
mance, see Helmuth (1980), Blanksby, Bloomfield, Ponchard, and Ackland (1986), Mei
(1989), Chollet, Pelayo, Delaplace, Tourny, and Sidney (1997), and Geladas, Nassis, and
Pavlicevic (2005).
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Author Biography
Wen-Jhan Jane, PhD, is an associate professor in the Department of Economics. His current
research focuses on the applied microeconometrics, especially the topics of peer effects,
superstar effects, and discrimination in professional sports.
Jane 9
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