1. The Impact of Outcome Uncertainty on Attendance at Major League Soccer Games
Dustin N. Martin
Dr. Kris McWhite, Faculty Advisor
University of Georgia
Athens, Georgia
2015
2. The Impact of Outcome Uncertainty 2
ABSTRACT
The uncertainty-of-outcome hypothesis states that the more uncertainty there is about the
expected outcome of a sporting contest, the more appealing the contest will be to spectators.
Professional sports leagues implement policies designed to promote competitive balance among
league members in an effort to attract as many spectators as possible. Some of these policies
include reverse-order drafts, salary caps, and revenue sharing schemes. If these policies are
effective in increasing outcome uncertainty by promoting competitive balance, then league
policy makers may want to know if, and to what extent, outcome uncertainty affects attendance
demand for league contests. Numerous analyses have been conducted to test the impact of
outcome uncertainty on attendance demand at sporting events, including European soccer
matches and American football, baseball and basketball games. The results of these analyses
have been mixed. This is the first study to test the uncertainty-of-outcome hypothesis on
attendance at Major League Soccer matches in the United States. The study finds no evidence to
support the hypothesis that greater outcome uncertainty increases attendance at matches.
3. The Impact of Outcome Uncertainty 3
I. Introduction
The importance of competitive balance (CB) in sporting contests is a popular topic of
debate among sports enthusiasts. A classic example of the impact that a lack of CB can have on
fan interest is the steady decline in attendance at New York Yankees games from 1950-1958,
when the Yankees won 8 American League pennants and 6 World Series titles (Leeds and Von
Allmen, 2005). Four decades later, Major League Baseball was again concerned with a lack of
CB, as Commissioner Bud Selig convened a panel of experts to study the relationship between
financial inequality among teams and CB (Sanderson & Siegfried, 2003). In the final report,
Levin (2000) concludes that competition in Major League Baseball is not adequately balanced.
The report states that CB exists only when “every well-run club has a regularly recurring
reasonable hope of reaching postseason play” (Levin, 2000). Levin’s (2000) report recommends
several league policy changes to improve CB in MLB.
II. Literature Review
Whether league policies in MLB, or any other sports league, are effective in promoting
competitive balance is a matter of widespread debate among sports economists. This debate has
fueled research to measure CB and its impact on fan interest. According to Fort and Maxcy
(2003), there are two distinct categories of CB research in the academic literature. The first
category is the analysis of CB and the effects of league policies on CB. The second category
tests the impact of uncertainty-of-outcome (UO) on fan behavior. UO refers to the likelihood of
a competitor defeating an opponent in a sporting contest. The more evenly matched the
competitors are, the more uncertain the outcome of the contest will be. In his work on the labor
4. The Impact of Outcome Uncertainty 4
market for professional baseball players, Rottenberg (1956) introduced the uncertainty-of-
outcome hypothesis (UOH) by claiming that attendance at baseball games is (in part) a function
of the variation in winning percentages by the teams in the league. One of the most frequently
cited works on CB is Neale (1964), who uses the “Louis-Schmelling paradox” to explain the
importance of balance in a sporting contest. According to Neale, Joe Louis (former heavyweight
boxing champ) needs an opponent for a fight to take place. The more competitive the opponent,
the greater the fan interest in the fight, and the more income Louis can earn from participating in
the fight (Neale, 1964). Following Neale (1964), El-Hodiri and Quirk (1971) include UO in their
model of the economic structure of a professional sports league. They claim attendance at a
contest declines as the likelihood of one team winning increases (El-Hodiri & Quirk, 1971).
Over the past few decades, researchers have increased their focus on the relationship between
UO and attendance at sporting events. Szymanski (2003) provides a useful description of three
different types of UO: match uncertainty (outcome of a single match), seasonal uncertainty
(outcome of a single season), and championship uncertainty (outcome of multiple seasons). This
paper will focus on the impact of match uncertainty on attendance at individual soccer matches.
There are different ways to measure UO. One way uses some measure of point
differentials between competing teams in a contest, and is often used to measure match UO and
season UO. This is the measure used by Czarnitzki and Stadtmann (2002) in their study of the
top German football league, and by Scelles et al. (2013) in their study of the top French football
league. Another way of measuring UO uses outcome probabilities determined by bookmakers in
betting markets. This was first done by Peel and Thomas (1988, 1992) in their examination of
English Football League matches, and has become the most popular measure of match
uncertainty. Other researchers to use this measure include Forrest and Simmons (2002) and
5. The Impact of Outcome Uncertainty 5
Buraimo and Simmons (2008) in their studies of English soccer matches, and Pawlowski and
Anders (2012) in their study of the German Bundesliga.
Aside from UO, a variety of different control variables have been used to explain match
attendance. Researchers typically include variables that are relevant to their observations. For
example, Czarnitzki and Stadtmann (2002) and Pawlowski and Anders (2012) include variables
to indicate the reputation (or brand strength) of the away teams in each match, as an explanatory
factor in attendance demand. In studies of Major League Soccer (MLS) matches, DeSchriver
(2007) included a variable measuring the impact of a particular star player’s participation in the
match on attendance, and Parrish (2013) includes a variable for the number of Designated
Players (DP) participating in a match. Other variables that are frequently used include weather,
television broadcasts, distance between teams, and socioeconomic factors such as population and
income.
The literature on the impact of UO on match attendance produces mixed results. Among
the studies finding strong support for the UO hypothesis are Peel and Thomas (1988, 1992) and
Forrest and Simmons (2002). Those finding a weak relationship between UO and attendance
include Czarnitzki and Stadtmann (2002) and Scelles et al. (2013). A few studies even find the
opposite expected effect of UO on attendance (as UO increases, attendance decreases). They
include Buraimo and Simmons (2008), who explain that most of the spectators are home team
fans who prefer to see their team win (rather than casual fans with no particular allegiance to
either team), and Pawlowski and Anders (2012) who identify brand strength of the away team as
a powerful draw to a match.
The academic literature addressing the impact of UO on attendance in American sports
leagues focuses on baseball, football, basketball, and hockey. No previous attempts have been
6. The Impact of Outcome Uncertainty 6
made to examine the relationship between UO and attendance at MLS matches. Previous efforts
to identify determinants of attendance at MLS matches focus on the impact of non-UO
explanatory variables on average season attendance. This paper will follow the methods in
previous studies of European soccer leagues to examine the impact of UO on attendance at MLS
matches. MLS is a relatively new league (established in 1996), and serves as fertile ground for
testing the uncertainty-of-outcome hypothesis. I will use an ordinary least squares (OLS)
regression method to identify the impact of UO on attendance at individual matches, while
controlling for variables I have identified as most relevant to the characteristics of MLS. These
variables include: weekday dummy, rain dummy, rival dummy, umber of DPs participating, and
a playoff uncertainty (PU) measure. The variables I have identified as less relevant to MLS and
will not include are: distance between teams (the United States is much larger than the European
countries in other studies, and the distances between MLS teams are sufficiently great that away
teams do not bring a meaningful number of fans to matches), ticket price (prices typically do not
vary between matches), television broadcasts (all MLS matches are broadcast on either local,
regional, or national networks), and market characteristics such as population and income (these
are difficult to measure since identifying catchment areas for each team is problematic). A better
understanding of how UO impacts attendance at matches will enable MLS officials to craft
league policies that are more effective in achieving their stated goals. I test two hypotheses in
this paper. First, I expect games between competitively balanced teams (higher UO) to draw
larger attendances than those between imbalanced teams (lower UO), all else equal. Second, I
expect matches with greater implications for playoff qualification (higher PU) to draw larger
attendances than those with no implications for playoff qualification, all else equal.
7. The Impact of Outcome Uncertainty 7
III. Method
I use an ordinary least squares regression model to estimate the effect of outcome
uncertainty on match attendance for n = 314 observations during the 2014 MLS season. The
endogenous variable is the logarithm of match attendance (ATTm). Among the explanatory
variables are several control variables frequently used in the literature on the determinants of
attendance.
First, in line with Pawlowski and Anders (2012) and Buraimo and Simmons (2008), I
control for spectator persistence by including a variable for the attendance habit of the home
team (HABITH), which is the average home attendance for the previous season. Unlike the
aforementioned works, I do not include a variable for away team attendance habit because
attendance figures for away team spectators is not readily available for the observations in this
analysis. Next, I include a dummy variable that takes the value of 1 if the match was played on a
weekday, and 0 otherwise (WEEKDAYm). I also include a dummy variable that takes the value
of 1 if the match is played between rival clubs, and 0 otherwise (RIVALm). To determine if a
matchup constituted a rivalry I referred to the season guides found on the official website for
Major League Soccer (mlssoccer.com). Each team guide includes a section identifying rival
clubs. Previous research (Buraimo and Simmons, 2008; Garcia and Rodriguez, 2002) finds that
rivalries attract more spectators than non-rivalries, all else equal.
Finally, I include three variables to control for the expected quality of the match. The
first variable is the average number of goals the home team has scored at the start of each match
(GSPGH). Janssens and Kesenne (1987) find that spectators are particularly attracted to high-
scoring matches, with the home team average goals scored having a greater effect than the away
team average goals scored. Since the value of GSPG is zero for all teams at the start of the
8. The Impact of Outcome Uncertainty 8
season, I exclude the first match for each team from the observations. The second variable,
which is taken from Janssens and Kesenne (1987) and Czarnitzki and Stadtmann (2002),
measures the reputation of the away team (REPA). This variable is expected to capture the
attractiveness of recently successful visiting teams. I measure each team’s reputation with the
following index:
REP = ∑
𝑛
𝑥 𝑡√𝑡
𝑇
𝑡=1 , with T = 5
Xt is the team’s final position in the league standings t years ago and n is the number of teams in
the league. Multiplying the final league position x in year t by the square root of t weights the
index to reflect a decline in reputation over time (i.e. finishing in first place 5 years ago, and last
place in each year since, produces a lower reputation index than finishing first place in the
standings last year, and last place in the 4 previous years). The index is increasing with higher
final positions in the league standings. The last variable I include to control for match quality
captures the attractiveness of “star” players on the away team (STARSA). In recent years MLS
teams have signed several high-profile players that previously played in some of the most
reputable leagues in Europe, including the top leagues in England, France, Germany, Italy, and
Spain. These players are typically regarded as some of the best in the world. I compile a list of
all players on MLS teams in 2014 who previously starred in at least one of the five major
European leagues. This list includes a total of 10 players on 5 different teams. The variable
STARSA reflects how many of these players are on each team’s roster.
The last two variables in the model capture two separate measures of outcome
uncertainty. The first uses the Thiel measure to reflect match level UO (THIELm). The Thiel
measure was first used in the study of sports attendance determinants by Peel and Thomas
9. The Impact of Outcome Uncertainty 9
(1992), and has been used in several studies since then, including Czarnitzki and Stadtmann
(2002), Buraimo and Simmons (2008), and Pawlowski and Anders (2012). It is an index than
incorporates the probabilities of each possible outcome (home team win, away team win, and
draw), which are derived from betting odds. The index is increasing with increasing outcome
uncertainty, and is calculated using the following equation:
THEIL = ∑
𝑝 𝑖
∑ 𝑝 𝑖
3
𝑖=1
3
𝑖=1 log(
∑ 𝑝 𝑖
3
𝑖=1
𝑝 𝑖
),
Where pi represents the probabilities of a home team win, an away team win, and a draw. The
betting odds for this analysis are taken from the website betexplorer.com; a site that provides
current and historical betting odds from more than 100 bookmakers. The second variable for
outcome uncertainty is the uncertainty of the home team qualifying for the playoffs (PUH).
Janssens and Kesenne (1987) include a measure of championship uncertainty in their modeling
of Belgian soccer attendances, in which they create an index that reflects how close a team is to
winning the league championship (finishing in first place), based on the number of points the
team has accumulated at each stage of the season. I include a similar index that reflects the level
of uncertainty with regard to qualifying for the MLS playoffs. This index takes the following
values:
𝑃𝑈 = {
100
𝑐 − 𝑏
, 𝑖𝑓 0 ≤ 𝑐 − 𝑏 ≤ 𝑚 − 3𝑡
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
Where c is the points a team needs to accrue to qualify for the playoffs (based on the previous
season’s point totals), b is the number of points a team has already accrued, m is the maximum
number of points a team can accrue during the season, and t is the number of games a team has
10. The Impact of Outcome Uncertainty 10
already played. The difference between c and b represents the number of points a team still
needs to qualify for the playoff after t games played. The difference between m and 3t represents
the maximum number of points a team can still accrue after t games played. If c-b is less than or
equal to m-3t, then it is still mathematically possible for a team to qualify for the playoffs.
However, if c-b is greater than m-3t, then a team is mathematically eliminated from playoff
contention. Also, if c-b is less than zero, a team has already accrued enough points to qualify for
the playoffs, in which case there is no uncertainty about playoff qualification. This index differs
from Janssens and Kessene (1987) in that c-b can take a negative value in this analysis, since c is
the minimum number of points needed to qualify for the playoffs, rather than finish first in the
league. The index is increasing with increasing uncertainty. We can expect the value of this
index to be small early in the season (when all teams are still mathematically in contention for
playoff qualification) because there are enough games left to be played that each game has less
of an impact on playoff berths. As the season progresses the value of this index increases as the
impact of each game on playoff berths increases with fewer games left to be played.
The complete model takes the following form:
log(ATTm) = β0 + β1 log(HABITh) + β2 WEEKDAYm + β3 RIVALm + β4
GSPGh + β5 REPa + β6 STARSa + β7 THIELm + β8 PUm + ε
IV. Results
There were 323 matches played during the 2014 MLS regular season. I excluded the first
9 matches of the season since the GSPG variable was zero for all teams at the start of their first
match. This leaves me with a total of 314 observations. I have two questions concerning the
impact of outcome uncertainty on match attendance. First, does match level UO affect match
11. The Impact of Outcome Uncertainty 11
attendance? Second, does playoff UO affect match attendance? The model explains
approximately 68% of the variation in attendance (Adjusted R2 = 0.677829). Table 1 provides
descriptive statistics for all of the model variables except the dummy variables (RIVAL,
WEEKDAY) and the STARS variable (since 14 of the 19 teams have a value of zero for this
variable).
Table 1. Descriptive Statistics
Mean SD Min Max
log(ATT) 4.25 0.18 3.57 4.81
log(HABIT) 4.25 0.13 3.92 4.64
GSPG 1.42 0.40 0 4
REP 25.79 19.57 3.97 87.11
THIEL 0.45 0.03 0.31 0.48
PU 6.57 11.02 0 100
Table 2 provides the reputation indexes for all 19 MLS teams. Total Rep shows each team’s
reputation for the 2014 season, and is the sum of each individual season’s reputation for the
previous five seasons. The index is increasing with increasing reputation.
13. The Impact of Outcome Uncertainty 13
Table 3 provides the estimated coefficients and p-values for the explanatory variables in the
model. Regarding the UO variables, neither match level uncertainty (THIEL) nor playoff
uncertainty (PU) have statistically significant results at the 5% level (p = 0.6494 and p = 0.1289,
respectively). The estimated coefficient for THIEL is also negative, indicating the opposite
expected effect. HABIT is significant and positive, as expected, while WEEKDAY is significant
and negative, also as expected. GSPG, RIVAL, and STARS are also significant at the 5% level
with slightly positive effects on attendance. Chart 1 shows match attendance versus home team
goals scored per game, and indicates a slightly positive relationship between GSPG and ATT.
Finally, REP has a slightly positive effect on attendance but is not statistically significant at the
5% level (p = 0.1068).
Chart 1. ATT ~ GSPG
14. The Impact of Outcome Uncertainty 14
Table 3. Estimates of the attendance model
Estimate Std Error p-value
Intercept -0.190734 0.244178 0.4353
HABIT 1.0383406 0.047372 <0.0001
WEEKDAY -0.054845 0.013887 <0.0001
RIVAL 0.0347633 0.015334 0.0241
GSPG 0.0356605 0.015196 0.0196
REP 0.000528 0.000326 0.1068
STARS 0.0188108 0.006768 0.0058
THIEL -0.101697 0.223465 0.6494
PU 0.0007965 0.000523 0.1289
A note of caution is necessary to address variability in the observed attendances. This model
does not include a variable for population, because defining the area of influence for each team is
problematic. However, I do not assume that population has no impact on match attendance. The
observed attendances in this study have a wide range of variability across teams, which suggests
population differences have an impact on match attendances. A possible reason for this is that
teams in larger cities have a larger potential fan base to draw spectators from. All else equal, a
large market team will have a wider range of possible attendances than a small market team, in
which case we should expect teams from smaller cities to have a smaller variation in attendances
15. The Impact of Outcome Uncertainty 15
than teams from larger cities. In this study, there appears to be a slight upward trend in
attendance variation as city size increases. Chart 2 shows the relationship between MSA
population and attendance variation for each team.
Chart 2. Attendance Variation vs MSA Population
V. Conclusion
Evenly matched competitors in sporting contests has long been considered a necessary
condition for the stability and financial success of these contests. Accordingly, professional
sports leagues often institute policies designed to promote competitive balance. Leagues hope to
increase spectator appeal by increasing the outcome uncertainty of matchups. One expression of
spectator appeal is attendance at individual games. However, studies of the relationship between
attendance and UO have produced mixed results. While some have found support for the
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[CELLRANGE]
[CELLRANGE]
0
2000
4000
6000
8000
10000
12000
0 5 10 15 20 25
StdDev,Attendance
MSA Population (millions)
AttendanceVariation vs MSA Population
16. The Impact of Outcome Uncertainty 16
hypothesis that matches with greater UO indeed draw more spectators, others have not. This
study examined the impact of two types of UO on MLS attendance, match-level UO and playoff
UO. In addition to these UO variables, I included several control variables frequently used in the
literature to model attendance demand. I found no support for the uncertainty-of-outcome
hypothesis in MLS matches. This suggests that league policies to promote competitive balance
in MLS may not be as important for the financial success of the league as other policies that
promote the factors that this study did find to be significantly impactful on attendance. For
example, league efforts to foster rivalries among teams through scheduling and promotions could
increase spectator interest in numerous matches each year. Also, continued efforts to attract
high-profile players from overseas could increase the interest of casual fans who are more likely
to attend matches in which these players participate. Since weekday matches tend to attract
fewer spectators, MLS could either reduce the number of weekday matches or provide greater
incentive to attend these matches through promotions. Finally, the league could implement
policies that encourage more goal scoring, since the average goals scored per game of the home
team positively impacts attendance. This might be accomplished by increasing the number of
points awarded for a win, which would likely encourage teams to invest more resources in
offensive talent, and adopt a game strategy designed to win, rather than to not lose.
While this study found no evidence to support the uncertainty-of-outcome hypothesis,
promoting competitive balance may still be a necessary component of a league’s strategy to
attract spectators. It is possible that UO has a greater impact on television audiences than it does
stadium audiences. Since many more people can watch games on television than can watch from
inside a stadium, there’s potential for greater variation in the number of spectators watching any
17. The Impact of Outcome Uncertainty 17
given contest. Further analysis that includes a variable for TV ratings for each game is needed to
determine any effect UO may have on fan interest beyond the confines of the stadium.
Since previous studies of the effects of UO on attendance in other sports have found
support for the UOH, there may be some differences between sports that explain why MLS
match attendance is less sensitive to changes in UO. For example, Major League Baseball teams
play 81 home games each season, compared to 17 home games for MLS teams. The relatively
large number of home games played by baseball teams gives fans more opportunities to attend
games, which allows fans to be more selective in which game(s) they attend. Also, since higher
scoring matches are more appealing to fans, sports that have a larger range of possible scoring
outcomes may have attendances that are more sensitive to UO than MLS. If different
characteristics between sports affect the impact that UO has on match attendance, then studies
finding no support for the UOH (such as this one) do not necessarily disprove the hypothesis as it
applies to sporting contests in general. Instead, the results of such studies can only be applied to
the sport observed, rather than generalized across sports.
18. The Impact of Outcome Uncertainty 18
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