Journal of Sports Economics OnlineFirst, published on April 18, 2007 as doi:10.1177/1527002506296545
Competitive Balance and Game
Attendance in Major League Baseball
JAMES W. MEEHAN, JR.
RANDY A. NELSON
Colby College
THOMAS V. RICHARDSON
Colby College graduate, 2003
This article tests for the effects of a change in competitive balance on attendance at
Major League Baseball games using game-level attendance data for the 2000-2002
seasons. Employing the difference between the winning percentages of the home and
visiting teams as a measure of competitive balance, the authors find (a) the effects of a
change in competitive balance on attendance are not symmetric, (b) the effects of a
change in competitive balance increase as a team falls further behind the divisional
leader, and (c) the effects of a change in competitive balance decline throughout the
season if the home team has a better record than the visiting team but increase if the
home team has a worse record than the visiting team.
Keywords: competitive balance; attendance; Major League Baseball
S
ince the early days of professional baseball, team owners have recognized
that uncertainty about the outcome of a game, as well as the closeness of the
championship race during the season, are important ingredients in maintaining
fan interest. Major League Baseball (MLB) owners have used the relationship
between fan interest and competitive balance as their primary justification for
adopting rules that restrict league teams from competing against each other in
the market for fans and in the market for players. The owners argue that without
these restrictions there is the danger that the larger market teams will dominate
the on-field competition and the fans will lose interest in the sport, leading to a
loss in attendance and, perhaps, the demise of the league.
These concerns are not unreasonable. The very first professional baseball
league, the National Association, failed, in part, because a few teams dominated
the league, with the Boston Red Stockings winning the championship in 4 out of
JOURNAL OF SPORTS ECONOMICS, Vol. XX No. X, Month 2007
DOI: 10.1177/1527002506296545
Ó 2007 Sage Publications
1–18
1
Copyright 2007 by SAGE Publications.
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JOURNAL OF SPORTS ECONOMICS / Month 2007
the 5 years the league was in existence.1 When the National League (NL) was
formed as a successor to the National Association, it adopted rules that restricted
competition among its members in the hope of ensuring the league would be
financially stable. Initially, the NL restricted the number of teams in the league
to eight and limited each city to one team. In 1879, just 3 short years after the
NL was formed, the owners adopted the reserve rule, which restricted teams
from competing against one another for the top players within the league.
Although the owners originally did not argue that the reserve rule was necessary
to maintain competitive balance, it soon became their primary justification for
the rule (Eckard, 2001b). Over time, MLB adopted additional rules, such as the
amateur player draft, revenue sharing, and the luxury tax, which they also claim
are necessary to maintain competitive balance.2
The economic literature identifies three types of competitive balance (or
uncertainty of outcomes) that may affect the level of fan interest (see, e.g.,
Szymanski, 2003, pp. 1155-1156). The first is a measure of competitive balance
between seasons (championship uncertainty or across-season competitive balance). This measure captures the variety of teams that have won the championship throughout a period of time. The expectation is that if the same team wins
the championship year after year, or the same teams are in contention year after
year, the fans come to believe that the season outcome is a forgone conclusion and lose interest in attending games over time.3 The second is a measure
of competitive balance within a season (seasonal uncertainty or within-season
competitive balance). This measure captures the closeness of a championship
race within a given season. The expectation is that fans are more likely to maintain their interest and attend games if the pennant race is close throughout the
season.4 The third measure of competitive balance captures the uncertainty of
outcome of a particular game (game uncertainty or game competitive balance).
The expectation is that if the two teams playing a particular game are evenly
matched, the fans will be more likely to find the game interesting and attend
than if one team is expected to win the game with ease.
Because game competitive balance is at the root of the other measures of competitive balance (Miller, 2005), we will confine our analysis to that aspect of
competitive balance.5 We are aware of two studies that have examined the effect
of game competitive balance on game attendance for MLB.6 Knowles, Sherony,
and Haupert (1992) use pregame betting odds as a measure of game competitive
balance and find that attendance is positively related to the probability that
the home team wins, until the probability reaches a value of 0.6, after which
the attendance of the home team starts to decline. Rascher (1999) uses three measures of game competitive balance. Two measure pregame uncertainty: one is
pregame betting odds and the other is a measure, developed by Fort and Quirk
(1995), that converts the home team winning percentage and visiting team winning
percentage into the probability of the home team winning. The results for both of
these measures are consistent with the findings of Knowles et al. (1992), that is,
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
3
attendance is maximized when the probability of the home team winning falls
between .6 and .7. Rascher’s (1999) third measure of game competitive balance is
the square of the difference of the winning percentage of the home team and the
visiting team. Again, he finds that as competitive balance increases, attendance
increases. In short, the findings of both of these studies suggest that game competitive balance has a positive influence on attendance at MLB games. One possible
shortcoming of both of these studies is that their measures of competitive balance
do not allow for the possibility that competitive balance may have an asymmetric
effect on attendance. Will the effect on the home team’s game attendance be the
same when the home team is in first place and the last place team comes to town
as it is when the home team is in last place and the first place team comes to town,
assuming that the difference between the first and last place teams is the same in
each case? The hometown fans of the first-place team may not be as excited to see
the last-place team come to town as the fans of the last-place team are to see the
first-place team come to town. In the former case, attendance and competitive
balance may be positively related, whereas in the latter case, attendance and competitive balance may be inversely related. Moreover, is the effect of competitive
balance on attendance different at different points during the season? Early in the
season, the position of the hometown team relative to the visiting team may not be
as important to the fans as it is later in the season. Finally, do the effects of competitive balance on attendance depend on the team’s standing within its division; does
game competitive balance affect the attendance of the divisional leader in the same
way as it does for a team that is 20 games out of first place? None of these questions can be easily answered with the previous models. We develop two measures
of competitive balance that allow us to separate out the possible asymmetric effects
and provide answers to the above questions using data from three major league
seasons. After we describe our measures of competitive balance and our model,
we present our results and explore their implications.
MODEL SPECIFICATION
Data were collected for every regular season game during the 2000, 2001,
and 2002 seasons; the sample contains a total of 7,189 observations.7 The dependent variable is ATTENDANCE, which represents the total number of tickets
sold for a given game.
The independent variables used to explain variations in ATTENDANCE are
designed to control for when the game was played, weather conditions, ballpark
characteristics, characteristics of the city in which the home team is located, the
quality of the two teams, and the degree of competitive balance. Descriptive statistics for each of the variables included in the analysis are presented in Table 1.
To control for when the game is played, we include dummy variables for
the day of the week: SUNDAY, MONDAY, TUESDAY, WEDNESDAY,
THURSDAY, and FRIDAY. We anticipate that attendance is greatest for the
4
JOURNAL OF SPORTS ECONOMICS / Month 2007
TABLE 1: Descriptive Statistics
Variable
ATTENDANCE
SUNDAY
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
D2001
D2002
DAYGAME
AVETEMP
RAIN
INDOOR
NEWSTAD
INC
FCI
HPRVPO
HPRVWS
HPRVWSC
VPRVPO
VPRVWS
VPRVWSC
HALLSTAR
VALLSTAR
HBACK
VBACK
INTERLG
HWINPER%
AWINDIF%
WINDIFP%
WINDIFN%
N
M
SD
Minimum
Maximum
29,460.83
.1629
.0883
.1501
.1510
.1217
.1612
.3330
.3332
.2862
69.7709
.0773
.2674
.0450
33,439.44
139.5447
.2671
.0672
.0335
.2660
.0655
.0324
2.1460
2.1270
8.5590
8.6167
.1098
50.1024
10.8655
5.5378
5.3277
6,828
11,732.63
.3693
.2838
.3572
.3581
.3269
.3678
.4713
.4714
.4520
10.2676
.2767
.4427
.2072
6,374.0230
27.2043
.4425
.2504
.1801
.4419
.2474
.1770
1.5251
1.5161
8.5587
8.5710
.3127
9.2423
8.7096
8.3323
8.0898
2,134
0
0
0
0
0
0
0
0
0
30.5
0
0
0
21,160
76.77
0
0
0
0
0
0
0
0
0
0
0
8.3333
0
0
0
61,065
1
1
1
1
1
1
1
1
1
101
5.4
1
1
57,414
228.73
1
1
1
1
1
1
8
8
45
48
1
91.6667
63.6364
63.6364
55.4945
NOTE: ATTENDANCE = the total number of tickets sold for a given game; D2001 = dummy variable for the 2001
season; D2002 = dummy variable for the 2002 season; DAYGAME = a dummy variable for games played during
the day; AVETEMP = average of the daily low and high temperature for the day of the game measured in degrees;
RAIN = the number of inches of rain for a given day; INDOOR = games played indoors in either domed stadiums
or stadiums with retractable roofs; NEWSTAD = new stadiums; INC = an estimate of per capita income; FCI =
Fan Cost Index; HPRVPO = whether the home team appeared in the playoffs the previous season; HPRVWS =
whether the home team appeared in the World Series the previous season; HPRVWSC = whether the home team won
the World Series the previous season; VPRVPO = whether the visiting team appeared in the playoffs the previous season; VPRVWS = whether the visiting team appeared in the World Series the previous season; VPRVWSC =
whether the visiting team won the World Series the previous season; HALLSTAR = the number of players elected to
the All Star game for the home team; VALLSTAR = the number of players elected to the All Star game for the visiting team; HBACK = the number of games by which the home team trails the division leader; VBACK = the number
of games by which the visiting team trails the division leader; INTERLEG = a dummy variable included to capture
the effect of interleague games on attendance; HWINPER% = the team’s overall win percentage; AWINDIF% =
the absolute value of the difference between the winning percentages of the home team and visiting team; WINDIFP%
= the difference between the winning percentages of the home team and visiting team is ≥ 0; WINDIFN% = the
absolute value of the difference between the winning percentages of the home team and visiting team is < 0.
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
5
omitted day, Saturday, implying that the estimated coefficients for the day of
the week variables should all be negative. In addition, we expect that attendance
is lower for games played during the middle of the week, implying that the estimated coefficients for FRIDAY and SUNDAY are expected to be greater than
those for the remaining days.8 To allow for fluctuations in attendance from one
season to the next, dummy variables are included for the 2001 (D2001) and
2002 (D2002) seasons. A dummy variable also was included for games played
during the day (DAYGAME), the coefficient of which is expected to be
positive.9
To control for the effects of weather on daily attendance, we include AVETEMP,
which represents the average of the daily low and high temperature for the day
of the game measured in degrees, and RAIN, which represents the number of
inches of rain for a given day.10 A priori, we anticipate the estimated coefficients for AVETEMP and RAIN to be positive and negative, respectively. The
impact of adverse weather conditions may be mitigated for games played
indoors in either domed stadiums or stadiums with retractable roofs, both of
which are represented by the dummy variable INDOOR.11 Finally, during the
2000-2002 seasons, five teams opened new stadiums; we include a dummy variable NEWSTAD to control for the presumably positive impact the new stadiums
would have on attendance.
Consistent with previous studies, additional variables are included to control
for city-specific factors that may influence attendance. To control for differences in income across cities, we include an estimate of per capita income
(INC) measured in $1,000s.12 Based on the previous results reported by
Knowles et al. (1992), Borland and Lye (1992), Bruggink and Eaton (1996), and
Garcı́a and Rodrı́guez (2001), the estimated coefficient for INC is expected to
be positive. To control for differences in the cost of attending a game across stadiums, we include the Fan Cost Index (FCI), which represents the costs of two
adult and two child average cost tickets, four small soft drinks and hot dogs, two
small beers, programs, adult-sized caps, and parking.13 In theory, the estimated
coefficient for FCI should be negative, but previous studies by Bruggink and
Eaton (1996), Rascher (1999), Demmert (1973) and Clapp and Hakes (2005)
have reported estimates that are positive or insignificant.
Initially, we included a variable that measured the population of the Consolidated Metropolitan Statistical Area (CMSA) of the city in which the team was
located and a dummy variable to control for the existence of a competing MLB
team in the same city. Based on the results presented in Bruggink and Eaton
(1996), Coffin (1996), Noll (1974), Rascher (1999), Schmidt and Berri (2001),
and Knowles et al. (1992), we expected the coefficient for the population variable to be positive. In every one of our models, however, the variable was insignificant, which was consistent with the findings reported by Coates and
Humphreys (1996). The insignificance of the population variable may reflect
the fact that the larger CMSAs are very broadly defined (e.g., the Chicago
6
JOURNAL OF SPORTS ECONOMICS / Month 2007
CMSA includes residents of Illinois, Indiana, and Wisconsin). Another possible
explanation for the insignificance of the population variable is that it is positively correlated with FCI, INC, and the appearance of the home team in the
previous season’s World Series (r ¼ :236, .335, .316, and .454, respectively).
Consequently, we dropped this variable from the models we report on in the
article. We also dropped the variable that controls for the existence of a competing MLB team from our final models because it was never significant.
We employ a variety of measures to control for the quality of the teams
engaged in each game. First, the model contains dummy variables for whether
the home team or the visiting team appeared in the playoffs (HPRVPO,
VPRVPO), the World Series (HPRVWS, VPRVWS), or won the World Series
(HPRVWSC, VPRVWSC) during the previous season. To control for Rosen’s
(1981) ‘‘superstar’’ phenomenon, the model also includes the number of players
elected to the All Star game for the home team (HALLSTAR) and visiting team
(VALLSTAR);14 the estimated coefficients of all of the aforementioned variables are expected to be positive. To control for the quality of the home team,
we include the number of games by which it trails the division leader (HBACK)
as a measure of the team’s competitiveness within its division and the team’s
overall win percentage (HWINPER%) as a measure of team quality across both
divisions and leagues. To control for the quality of the visiting team we include
the number of games by which the team trails its divisional leader (VBACK).15
The variables HBACK, VBACK, and HWINPER% are updated on a daily basis.
Finally, a dummy variable (INTERLEG) is included to capture the presumably
positive effect of interleague games on attendance.
As our measure of game competitive balance, we employ WINDIF%, the difference between the winning percentages of the home team (HWIN%) and visiting team (VWIN%). We note that this variable is not monotonic with respect
to competitive balance in the sense that the degree of outcome uncertainty
declines as WINDIF% becomes more negative (visiting team has better record
than home team) or more positive (home team has better record than visiting
team). This issue may be addressed in one of two ways. First, by taking the
absolute value of WINDIF% (AWINDIF%) we are assured that the degree of outcome uncertainty increases or decreases as AWINDIF% decreases or increases, respectively. We thus employ AWINDIF% as our measure of competitive
balance in Model 1.16
Second, one drawback to the use of AWINDIF% is that it assumes fans
respond symmetrically to any change in competitive balance. For example, the
fans of a team mired in last place may prefer to see the first-place team rather
than the team in next-to-last place, implying that attendance would increase as
AWINDIF% increases. On the other hand, the fans of a team currently in first
place may prefer to attend a game in which the opponent is the second-place
team rather than the last-place team, implying that attendance would increase as
AWINDIF% decreases. To relax the assumption of symmetry, we define two
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
7
new measures of outcome uncertainty, WINDIFP% = WINDIF% if WINDIF%
≥ 0 and WINDIFN% = abs (WINDIF%) if WINDIF% < 0, where abs is
the absolute value operator. If the estimated coefficients of WINDIFP% and
WINDIFN% are equal, then fans respond symmetrically to any change in competitive balance, and AWINDIF% may be used in place of WINDIFP% and
WINDIFN%. A rejection of the null hypothesis that the estimated coefficients
for WINDIFP% and WINDIFN% are equal, however, would imply that fans do
not respond symmetrically to a change in competitive balance. If this is the case,
then the use of AWINDIF% may produce biased estimates of the response of
attendance to a change in competitive balance. We thus employ WINDIFP%
and WINDIFN% as our measures of competitive balance in Model 2.
ESTIMATION AND RESULTS
We address two issues pertaining to the estimation of the model prior to presenting our empirical results. First, the purpose of this study is to ascertain the
impact of competitive balance on the demand for MLB games. We employ attendance as our proxy for demand; if demand is not constrained by stadium capacity, then attendance will equal demand and censoring will not bias our results.
If, however, the game is sold out, then demand will exceed attendance and our
independent variable will be censored. An examination of the data indicated that
344 games, representing 4.76% of our sample, were sellouts. Failure to control
for censoring results in estimates that are inconsistent and almost always smaller
in absolute value than the maximum likelihood estimates.17 To correct for this
problem, the model was estimated using the censored-normal regression procedure in STATA (version 8) that allows for a variable censoring point, which in
our case is stadium capacity. The maximum likelihood estimates of the parameters, together with their asymptotic t statistics, are presented in Table 2.
Second, early in the season, a team’s winning percentage may be extremely
volatile, implying that AWINDIF% or WINDIFP% and WINDIFN% may be
poor proxies for the degree of competitive balance at this stage of the season.
Rascher (1999) attempted to correct for this problem by multiplying a team’s
winning percentage by the percentage of games played in the season in an attempt
to create a measure of competitive balance that was linear in wins. Algebraically,
this is equivalent to (Wins/Games Played)∗ (Games Played/162) = (Wins/162).
The problem with this approach is that it may indicate competitive imbalance for
two teams with identical winning percentages if they have not played the same
number of games. As an alternative, we estimated the model deleting the observations for the first 10 games of each season in an effort to eliminate any outliers in
our measure of competitive balance.18
The majority of the estimated coefficients for Models 1, 2, and 3 presented in
Table 2 are similar in sign, magnitude, and level of statistical significance. As
expected, the estimated coefficients for the weekday dummy variables are all
8
Constant
SUNDAY
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
D2001
D2002
DAYGAME
AVETEMP
RAIN
INDOOR
NEWSTAD
INC
FCI
INTERLEG
HPRVPO
HPRVWS
HPRVWSC
APRVPO
APRVWS
APRVWSC
HALLSTAR
VALLSTAR
Variable
Asymptotic
t Statistic
−8.58
−10.02
−18.78
−22.28
−21.60
−19.87
−8.01
−1.26
−9.12
6.87
9.75
−2.55
−8.79
13.54
13.78
23.59
6.81
7.42
−3.53
4.53
0.99
6.55
−3.49
12.88
10.05
Estimated
Coefficient
−12,618.94
−3,979.879
−8,361.863
−8,664.936
−8,283.431
−7,946.434
−3,064.703
−336.428
−2,524.107
2,060.724
110.237
−966.329
−2,291.334
8,098.000
0.3328
125.976
2,337.915
2,180.184
−2,245.000
3,681.414
275.636
4,211.911
−2932.85
1,084.53
793.921
Model 1
TABLE 2: Censored Regression Results
−17,458.96
−3,988.040
−8,364.273
−8,667.239
−8,282.777
−7,960.291
−3,073.982
−408.579
−2,618.135
2,072.74
104.220
−967.899
−2,280.939
8,110.742
0.3252
125.420
2,403.281
2,163.551
−2,165.800
3,408.000
122.051
3,993.855
−3,002.532
1,040.965
699.346
Estimated
Coefficient
Model 2
−10.72
−10.07
−18.85
−22.36
−21.68
−19.97
−8.06
−1.53
−9.48
6.93
9.22
−2.56
−8.78
13.60
13.50
23.57
7.03
7.39
−3.42
4.21
0.44
6.20
−3.60
12.37
8.75
Asymptotic
t Statistic
−13,425.27
−3,996.347
−8,434.711
−8,708.540
−8,326.052
−8,001.359
−3,066.760
−365.113
−2,543.000
2,066.233
91.910
−1,001.999
−2,399.437
8,194.794
0.3172
123.830
2,447.001
2,194.751
−2,311.611
3,458.912
29.693
3,951.940
−2,804.694
1,016.105
671.197
Estimated
Coefficient
Model 3
(Continued)
−7.59
−10.12
−19.05
−22.52
−21.84
−20.12
−8.06
−1.37
−9.21
6.92
8.01
−2.66
−9.11
13.72
13.18
23.11
7.17
7.48
−3.65
4.27
0.11
6.15
−3.37
11.86
8.31
Asymptotic
t Statistic
9
6828
−68,083.17
−88.669
−68.250
188.804
−94.076
Estimated
Coefficient
Model 1
−4.97
−4.83
11.39
−7.47
Asymptotic
t Statistic
−10.04
1.15
−199.829
24.721
6828
−68,059.83
−6.32
0.57
12.97
Asymptotic
t Statistic
−114.893
10.353
298.486
Estimated
Coefficient
Model 2
−43.622
177.595
−6.097
−1.706
−1.105
−1.452
6828
−68,042.65
−145.288
−17.044
252.286
Estimated
Coefficient
Model 3
−0.77
2.39
−1.85
−0.75
−3.02
−3.19
−4.71
−0.60
10.35
Asymptotic
t Statistic
NOTE: D2001 = dummy variable for the 2001 season; D2002 = dummy variable for the 2002 season; DAYGAME = a dummy variable for games played during the day; AVETEMP = average of the daily low and high temperature for the day of the game measured in degrees; RAIN = the number of inches of rain
for a given day; INDOOR = games played indoors in either domed stadiums or stadiums with retractable roofs; NEWSTAD = new stadiums; INC = an estimate of per capita income; FCI = Fan Cost Index; INTERLEG = a dummy variable included to capture the positive effect of interleague games on attendance;
HPRVPO = whether the home team appeared in the playoffs the previous season; HPRVWS = whether the home team appeared in the World Series the previous season; HPRVWSC = whether the home team won the World Series the previous season; APRVPO = the absolute value of whether the visiting team
appeared in the playoffs the previous season; APRVWS = the absolute value of whether the visiting team appeared in the World Series the previous season;
APRVWSC = the absolute value of whether the visiting team won the World Series the previous season; HALLSTAR = the number of players elected to the
All Star game for the home team; VALLSTAR = the number of players elected to the All Star game for the visiting team; HBACK = the number of games by
which the home team trails the division leader; VBACK = the number of games by which the visiting team trails the division leader; HWINPER% = the team’s
overall win percentage; AWINDIF% = the absolute value of the difference between the winning percentages of the home team and visiting team; WINDIFP%
= the difference between the winning percentages of the home team and visiting team is ≥ 0; WINDIFN% = the absolute value of the difference between the
winning percentages of the home team and visiting team is < 0; HBACK = the number of games by which the home team trails the division leader; GMSLEFT
= the number of games left in the season.
HBACK
VBACK
HWINPER%
AWINDIF%
WINDIFP%
WINDIFN%
WINDIFP%∗ HBACK
WINDIFN%∗ HBACK
WINDIFP%∗ GMSLEFT
WINDIFN%∗ GMSLEFT
N
Log likelihood
Variable
TABLE 2: (Continued)
10
JOURNAL OF SPORTS ECONOMICS / Month 2007
negative and significant at the 1% level or better, indicating that attendance is
greatest on SATURDAY and greater on FRIDAY and SUNDAY than the
remainder of the week. There was no significant difference in average attendance between 2000 and 2001, but depending on the model, attendance during
the 2002 season fell by between 2,524 to 2,618 fans per game. This latter result
may reflect the impact of an increase in the unemployment rate from 4.7% in
2001 to 5.8% in 2002, or possibly the reluctance of some fans to attend large
public gatherings following the terrorist attacks on September 11. Based on the
estimated coefficients from Models 1-3, games played during the day drew
between 2,061 and 2,073 more fans than night games. Each one-degree increase
in temperature boosted attendance by between 91.9 and 110 fans, whereas each
inch of rain reduced attendance by between 966 and 1,002 people.
Playing in a new stadium increases attendance by between 8,098 and 8,195
fans, whereas playing indoors reduced attendance by between 2,281 and 2,399
attendees; the latter result may simply reflect the fact that fans prefer attending
games played outdoors. Interleague games played between teams from the
National and American Leagues increased attendance by between 2,338 and
2,447 fans relative to intraleague games. An increase in per capita income and
the cost of attending a game (as measured by the fan cost index) both have a
positive impact on attendance. The latter finding is consistent with the evidence
presented in Bruggink and Eaton (1996), Rascher (1999), and Clapp and Hakes
(2005) and may possibly indicate that the FCI variable is not exogenous.19
Improving the quality of the home team, as measured by an increase in the
number of all stars, a reduction in the number of games by which the team
trailed the division leader, or an increase in the team’s winning percentage, had
a positive and significant impact on attendance in all three models. In addition,
attendance increased if the home team appeared in the playoffs or won the
World Series in the previous year but surprisingly declined if they played in but
lost in the World Series.20 Improving the quality of the visiting team has a smaller impact on attendance than an increase in the quality of the home team in
almost every case. Increasing the number of all stars on the visiting team has a
positive and significant impact on attendance in all three models, but Model 1
was the only equation in which reducing the number of games by which the visiting team trails the division leader had a positive and significant impact on
attendance. Visiting teams that made the playoffs in the previous year had no
statistically significant impact on attendance, whereas playing in the previous
year’s World Series had a positive and significant impact on attendance in every
case. Contrary to expectations, attendance declined if the visiting team won the
World Series in the previous season.21
The estimated coefficient for the competitive balance variable is negative and
significant at the 1% level in Model 1; a 10-percentage point increase in the
difference between the winning percentages of the home and visiting teams
reduces attendance by 940.76 fans. In Model 2, the impact of a change in
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
11
competitive balance depends on whether the home team has a better record than
the visiting team. In games in which the home team has the better record, a 10percentage point increase in the difference between the winning percentages of
the home and visiting teams (WINDIFP%) reduces attendance by 1,998.3 fans.
The estimated coefficient of WINDIFN% is insignificant, implying that a
change in competitive balance has no impact on attendance if the visiting team
has a better record than the home team. The null hypothesis that the coefficients
of WINDIFP% and WINDIFN% are equal may be rejected at the 1% level using
a Wald test, implying that fan response to a change in competitive balance is
asymmetric with respect to whether the home team has a better record than the
visiting team.
The results obtained from Models 1 and 2 both assume that the effects of outcome uncertainty are constant throughout the season and independent of the
team’s standing within its division. The number of games remaining in the season may affect the effects of competitive balance on attendance in one of two
ways. First, early in the season, a team’s record may be a noisy signal of team
quality because a short winning or losing streak may significantly alter its
record; in this case, the effect of competitive balance on attendance may be
minimal at the start of the season but increase as the season progresses and the
signal implied by a team’s winning percentage improves in quality. Alternatively, as the season draws to a close, the impact of a change in competitive balance may diminish as fans get caught up in pennant races and try to obtain
tickets before the season ends regardless of the winning percentages of the home
and visiting teams. We anticipate that the effects of competitive balance on
attendance will be inversely related to a team’s standing within its division for
two reasons. First, the teams that are ranked at the top of the division are likely
to be of such high quality that their fans are less likely to respond to changes in
competitive balance than the teams that are ranked near the bottom of the division. Second, when teams ranked at the bottom of the division face opponents
with worse records, the opponents are likely to be of such poor quality that fans
prefer not to attend. To test these hypotheses, we estimated Model 3, which
includes interaction terms obtained by multiplying both WINDIFP% and
WINDIFN% by GMSLEFT and HBACK, where the former represents the number of games remaining in the season and the latter represents the number of
games by which the home team trails the divisional leader. The parameter estimates and asymptotic t statistics for Model 3 are presented in the last two columns of Table 2.
The estimated parameters for the noncompetitive balance variables in Model
3 are of similar sign, magnitude, and level of significance as those obtained
in Models 1 and 2. The estimated coefficients of WINDIFP% and WINDIFN%
are negative and positive, respectively, although only the latter is significant
at the 5% level. The estimated coefficients of WINDIFP%∗ GMSLEFT and
WINDIFN%∗ GMSLEFT are both negative and significant at the 1% level,
12
JOURNAL OF SPORTS ECONOMICS / Month 2007
TABLE 3: Estimated Impact of a 10-Percentage Point Change in WINDIFP% and WINDIFN%
on Attendance
Number of Games
Left in Season
150
130
110
90
70
50
30
10
WINDIFP% Games out of First
WINDIFN%
0
10
20
30
10 Games Out
−2,094.41
(−9.65)
−1,874.33
(−8.48)
−1,652.24
(−6.68)
−1,301.30
(−4.13)
−1,210.05
(−3.52)
−988.96
(−2.45)
−767.86
(−1.64)
−546.77
(−1.03)
−2,704.09
(−7.86)
−2,483.00
(−7.45)
−2,261.90
(−6.68)
−1,913.52
(−5.13)
−1,819.71
(−4.64)
−1,598.62
(−3.67)
−1,377.53
(−2.83)
−1,156.43
(−2.13)
NA
(−1.84)
−3,092.66
(−4.95)
−2,871.56
(−4.63)
−2,525.74
(−4.02)
−2,429.38
(−3.81)
−2,208.28
(−3.35)
−1,987.19
(−2.90)
−1,766.09
(−2.45)
NA
−572.17
−3,702.32
(−3.93)
−3,481.23
(−3.73)
−3,137.97
(−3.37)
−3,039.04
(−3.25)
−2,817.94
(−2.98)
−2,596.85
(−2.70)
−2,375.75
(−2.42)
−281.83
(−1.19)
8.89
(0.04)
298.83
(1.08)
589.17
(1.76)
879.50
(2.18)
1,169.84
(2.43)
1,460.17
(2.60)
NOTE: Values in bold are significant at the 5% level or better. Values in parentheses are asymptotic
t statistics. WINDIFP% = the difference between the winning percentages of the home team and
visiting team is ≥ 0; WINDIFN% = the absolute value operator of the difference between the
winning percentages of the home team and visiting team is < 0; NA = not applicable.
implying that the effects of a change in competitive balance decline as the season
progresses. The estimated coefficients of WINDIFP%∗ HBACK and WINDIFN∗
HBACK are both negative, although only the former is significant at the 10%
level or better. The results from Table 3 thus offer weak support for the hypothesis that the effects of competitive balance on attendance are greater for weaker
teams whose winning percentage exceeds that of their opponents.
In Model 3, the impact of a change in competitive balance on attendance is
a function of the number of games left in the season and the number of games
by which the home team trails the divisional leader. Define bWP , bWP∗GM , and
bWP∗HB as the estimated coefficients for WINDIFP%, WINDIFP%∗ GMSLEFT,
and WINDIFP%∗ HBACK, respectively; the estimated impact of a 10-percentage point change in WINDIFP% may be written as follows:
qATTEND=qWINDIFP% ¼ ½bWP þ bWP∗GM ∗GMSLEFT
þ bWP∗HB ∗HBACK∗ 10:
ð1Þ
Define bWN , bWN∗GM , and bWN∗HB as the estimated coefficients for WINDIFN%, WINDIFN%∗ GMSLEFT, and WINDIFN%∗ HBACK, respectively; the
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
13
estimated impact of a 10-percentage point change in WINDIFN% may be
written as follows:
qATTEND=qWINDIFN% ¼ ½bWN þ bWN∗GM ∗GMSLEFT
þ bWN∗HB ∗HBACK∗ 10:
ð2Þ
We derive estimates of the impact of a 10-percentage point increase in
WINDIFP% for different values of both GMSLEFT and HBACK; for WINDIFN%, we vary only GMSLEFT because the estimates for different values of
HBACK are not significantly different from one another due to the insignificance of the estimated coefficient for the WINDIFN%∗ HBACK interaction
term. The estimated values of equations 1 and 2, together with their asymptotic t
statistics, are presented in Table 3.22
The results in Table 3 clearly indicate that when the home team has a better
record than the visiting team, the effects of a change in competitive balance are
greatest early in the season and decline as the season progresses. For example, a
10-percentage point increase in WINDIFP% reduces attendance by 2,483 fans
with 130 games remaining for a team that is 10 games out of first place but by
only 1,156 fans with 10 games remaining at the end of the season. If the home
team has a lower winning percentage than the visiting team, then the impact of a
change in competitive balance on attendance is insignificant until the last third
of the season, after which the impact is positive and significant; a 10-percentage
point increase in WINDIFN% adds an additional 879.5 fans with 50 games left
in the season but by an additional 1,460 at season’s end. This last result is consistent with the hypothesis that the fans of teams with poor records would prefer
to attend games with stronger opponents, even if the result is a decrease in the
degree of competitive balance. The results also indicate that if the home team
has a better winning record than the visiting team at a given point in the season,
then the impact of an increase in competitive balance increases as the team falls
further behind in the standings. For example, with 50 games remaining in the
season, a 10-percentage point increase in competitive balance would reduce
attendance by 989 fans for the division leader but by 2,818 fans for a team that
is 30 games out of first place.
CONCLUSIONS
Professional sport leagues in general have long been interested in the issue of
competitive balance. In professional baseball, for example, the belief that fan
attendance is positively related to outcome uncertainty has lead to the adoption
of rules including the amateur player draft, revenue sharing, and the luxury tax
in an effort to prevent large-market teams from consistently dominating their
smaller-market rivals. Knowles et al. (1992) and Rascher (1999) provide empirical support for the hypothesis that attendance at individual baseball games is
14
JOURNAL OF SPORTS ECONOMICS / Month 2007
positively related to the degree of outcome uncertainty. Both studies indicate
that attendance is maximized when the probability of the home team winning
falls between .6 and .7.
Previous research into the effects of outcome uncertainty on individual game
attendance has implicitly assumed that the effects of a change in competitive
balance are symmetric. This study tests the hypothesis that fans react in an
asymmetric manner to a change in competitive balance. For example, the fans
of a last-place team may prefer to see the first-place team rather than the team
in next-to-last place, implying that attendance would increase as the degree of
competitive balance declines. On the other hand, the fans of a team currently
in first place may prefer to attend a game in which the opponent is the secondplace team rather than the last-place team, implying that attendance would
increase as the degree of competitive balance increases. In addition, we test to
determine if the effects of a change in competitive balance are constant throughout the season and are invariant to the number of games by which the home
team trails the divisional leader.
Using attendance data for almost every individual game played during the
2000-2002 seasons, we estimate three different censored regression models to
explore the effects of competitive balance on attendance. In each case, the
degree of competitive balance is measured as the difference between the winning percentages of the home and visiting teams. In Model 1, where the effects
of a change in competitive balance are constrained to be symmetric, we find that
a 10-percentage point change in the winning percentages of the two teams
reduces attendance by approximately 940 people, a result that is significant at
the 1% confidence level. In Model 2, where the effects of a change in competitive balance are allowed to differ depending on whether the home team has a
better record than the visiting team, statistical tests indicate that the estimated
effects are not equal, implying that the effects of a change in competitive balance are not symmetric. Consistent with a priori expectations, a 10-percentage
point increase in the difference between the winning percentages of the two
teams reduces attendance by 1,999 fans if the home team has a better record
than the visiting team. Somewhat surprisingly, however, a change in competitive balance does not have a significant impact on attendance if the visiting team
has a better record. This latter result implies that the negative impact of a reduction in outcome uncertainty is essentially canceled out by the presumably positive impact of getting to see a better team for the fans of clubs with inferior
records.
In Models 1 and 2, the effects of a change in competitive balance are constrained to be constant throughout the season and the same for all teams regardless of their standings within their divisions. When these constraints are relaxed
by introducing the appropriate interaction terms in Model 3, the results indicate
that if the home team has a better record than the visiting team, then the effects
of a change in competitive balance are greater earlier in the season and increase
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
15
as the gap between the home team and the divisional leader expands. If the visiting team has a better record than the home team, then the impact of a change in
competitive balance on attendance is (a) independent of the number of games by
which the home team trails the divisional leader, (b) insignificant early in the
season, and (c) positive during the last quarter of the season. This final result
implies that the negative impact of a reduction in outcome uncertainty is outweighed by the positive impact of getting to see a better team for the fans of
clubs with inferior records.
The results of this study support the hypothesis that baseball fans respond to
a change in competitive balance, generally preferring to attend games in which
the outcome is in doubt. Our findings, however, indicate that the effects of game
competitive balance on attendance may be more complex than previously
thought. Failure to account for factors such as the number of games remaining
in the season, the standing of a team within its division, and whether the home
team has a better record than the visiting team may bias one’s conclusions as to
how a change in competitive balance affects fan behavior.
NOTES
1. The National Association started play in 1871 and was dissolved after the 1875 season when
the owners of the stronger clubs in the league left to form the National League. For an excellent history of the National Association, see Ryczek (1992). For an excellent history of the early years of
professional baseball, see Seymour (1960).
2. See the Blue Ribbon Panel Report (Levin, Mitchell, Volcker, & Will, 2000), which argued
that the biggest problem facing Major League Baseball (MLB) was the growing imbalance during
the 1990s between the haves (the large-market teams) and the have-nots (the small-market teams).
As a solution to the competitive balance problem, the panel recommended still more revenue sharing, a competitive balance tax, a competitive balance draft, and reform of the amateur draft to further
restrict competition for amateur players.
3. Eckard (2001a) provides some evidence to support this claim. Regressing the season attendance of individual MLB teams on a measure that captures the number of consecutive years a team
is in contention for the league championship, he finds that team attendance declines with each additional year that the team is in contention for the pennant.
4. Schmidt and Berri (2001) provide some support for this claim using both time series data and
panel data for MLB.
5. For the remainder of our analysis and discussion, the term ‘‘competitive balance’’ refers to
game competitive balance.
6. Several studies examine the relationship between game attendance and game competitive balance for other sports. Generally, they find weak support for the claim that game competitive balance
does lead to greater attendance. For a summary of these studies, as well as the studies that look at
seasonal and championship uncertainty, see Szymanski (2003, Table 2, pp. 1157-1158).
7. There were 7,234 games played during this period. We were unable to obtain attendance data
for 45 games, reducing the final sample to 7,189 observations. Attendance data for the last 5 years
are available online from http://sports.espn.go.com/mlb/teams under the schedule tab. Alternatively,
attendance data beginning with the 1951 season are available at http://www.retrosheet.org/ under the
game logs tab.
16
JOURNAL OF SPORTS ECONOMICS / Month 2007
8. Previous studies by Hill, Madura, and Zuber (1982); Knowles, Sherony, and Haupert (1992);
Bruggink and Eaton (1996); and Garcı́a and Rodrı́guez (2001) employ a single dummy variable for
games played midweek, implying that the estimated coefficients for MONDAY, TUESDAY, WEDNESDAY, and THURSDAY are all equal. This hypothesis was tested and rejected at the 1% confidence level using an F test; as a result, we employ separate dummy variables for each day during the
middle of the week.
9. A dummy variable for the second game played as part of a split day/night doubleheader also
was included; the estimated coefficient was never significant so this variable was dropped from the
final model.
10. Data for both variables were obtained from the National Oceanic and Atmospheric Administration’s National Climatic Data Center Web site at www.ncdc.noaa.gov.
11. Data pertaining to stadium capacity, age, and the type of stadium (dome, retractable roof, or
open) are available from www.baseball-almanac.com.
12. The data for the United States are based on the 2000 census and are reported in the 2002 edition of the Survey of Current Business available online at www.bea.doc.gov. The data for Canada
are based on the 2001 census and are available online from www.statcan.ca. The Canadian data were
converted to U.S. dollars using the U.S./Canadian exchange rate on January 1, 2001.
13. Data on the Fan Cost Index (FCI) are available at www.teammarketing.com.
14. For games played prior to the All Star game in a given season, we use the number of players
elected to the All Star game for the previous season; for games played after the All Star game, we
use the number of players elected for that season. In some cases it is possible for the number of all
stars on a given team to equal zero if a player left a team at the end of the season as a result of a
trade, retirement, or free agency.
15. It is not possible to include the winning percentage of the visiting team (VWINPER%) in the
model because this would create perfect multicollinearity between HWINPER%, VWINPER%, and
the measures of competitive balance discussed below.
16. As an alternative to WINDIF%, we employed the probability that the home team would win
(PHTW), computed using data on the winning percentages of the home and visiting teams and the
formula presented in Fort and Quirk (1995). Following Rascher (1999), we interacted the probability
of a win with the percentage of games played in the season. Including PHTW and PHTW2 in the
model, we obtained results that were similar to those obtained by Rascher (1999) in terms of sign,
magnitude, and statistical significance. This approach does not, however, allow us to explore the
asymmetric effect of a change in competitive balance.
17. See Greene (2000, pp. 905-912) for a discussion of censored models and the consequences of
failing to correct for censoring.
18. The model was estimated using the full sample of 162 games and then reestimated deleting
the first 5, 10, 15, and 20 games of each season. For regressions that include the full sample, we also
include a dummy variable for the first game of the season. The estimated coefficients for the competitive balance variables were relatively stable across samples in terms of sign, magnitude, and statistical significance. To conserve space, we present the estimates for the full sample minus the first
10 games; copies of the remaining estimates are available from the authors on request.
19. Alexander (2001) employs two-stage least squares to estimate a demand function for attendance at MLB games. His results indicate a negative relationship between price and attendance,
providing support for the hypothesis that the positive coefficient for FCI may be the result of
endogeneity.
20. The previous season World Series loser was the Atlanta Braves in the 2000 season, the New
York Mets in the 2001 season, and the New York Yankees in the 2002 season. Although the Atlanta
Braves were a dominant team in the 1990s and early 2000s, their home attendance began a steady
decline, from a high of 3.3 million, right on through the 2004 season, when attendance was a little
Meehan et al. / COMPETITIVE BALANCE AND ATTENDANCE IN MLB
17
more than 2.3 million. Perhaps their fans were disappointed because their team failed to win the
World Series again. Although the New York Mets were the loser in the 2000 World Series, they were
barely a .500 team in 2001. By 2002, the New York Yankees had already appeared in four straight
World Series, winning three, so their fans may have reached the point of diminishing returns in seeing them play in 2002. Eckard (2001a) finds evidence that attendance tends to decline with each
additional year that a team is on a run of dominance. Thus, the possible loss of fan interest in the
Braves and Yankees because of their continued dominance during this period and the precipitous
decline in the quality of the Mets may explain the anomalous results for whether the home team won
the World Series (HPRVWSC). However, we recognize that any attempt to explain this result is at
best an educated guess.
21. This result is even more puzzling than the negative effect on attendance when the home team
was a World Series loser. The previous season World Series winners were the New York Yankees
for 2000 and 2001 and the Arizona Diamondbacks for 2002. The Yankees had won the World Series
3 years in a row, starting in 1998. In 1998, they beat the San Diego Padres 4-0; in 1999, they beat the
Atlanta Braves 4-0; and in 2000, they beat the New York Mets 4-1. Again, this result is consistent
with Eckard’s (2001a) finding that attendance tends to decline with each additional year that a team
is on a run of dominance.
22. The standard errors were computed by the nlcom (nonlinear combination of estimators)
command in Stata (Version 8; for a discussion of this procedure, see Greene, 2000, pp. 272-276).
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James W. Meehan, Jr. is the Herbert E. Wadsworth Professor, Department of Economics, Colby
College.
Randy A. Nelson is the Douglas Professor, Department of Economics and the Department of
Administrative Science, Colby College.
Thomas V. Richardson is a 2003 graduate of Colby College.