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2017-04-07
Competitive Balance in Professional Sports
Leagues: What Causes it and Who Handles it
Best?
Marshall, Corey
http://hdl.handle.net/10456/42679
All materials in the Allegheny College DSpace Repository are subject to college policies and Title 17
of the U.S. Code.
ECONOMICS 620
Allegheny College
Meadville, PA
16335
Competitive Balance in Professional Sports Leagues: What Causes it and Who Handles it Best?
Corey Marshall
April 7th, 2017
Competitive Balance in Professional Sports Leagues: What Causes it and Who Handles it
Best?
By
Corey Marshall
Submitted to The Department of Economics
First Reader: Russell Ormiston
Second Reader: Janine Sickafuse
April 7th, 2017
I hereby recognize and pledge to fulfill my responsibilities as defined in the Honor Code and to
maintain the integrity of both myself and the college as a whole.
Corey Marshall
i
Acknowledgements
Professor Ormiston: I appreciate all the time that you have spent helping me complete this
project. Those emails containing 40 comments definitely took a long time, and without them this
paper would not have been what it is now. However it was not just the corrections, but the
process overall. You were there every step of the way willing to do everything you could to
assist me. Thank you.
Professor Sickafuse: This is a fitting end to my career here at Allegheny. I remember my first
semester and your FS business of sports class and now in my last semester I am once again in
one of your classes. I appreciate the guidance you have provided as both my professor and my
advisor.
Alexa: My path to this point would have been much more difficult without you. You always
were there to keep me on task even when I did not want to. Perhaps the biggest influence you
had was one that you did not even consciously attempt to provide. It was just being around your
success and your work ethic that inspires me to be better and for me to make you proud. You
never failed to raise the bar either whether it be graduating a semester early or working
downtown while studying every day. Anytime I did not want to study or did not want to work on
my comp I think that Alexa would do it with no complaints and so it motivates me. Aside from
motivating me you also provided me with so much fun and happiness over the years including
our movie dates and weekly breakfast dates. I look forward to the next chapter of our lives
together.
ii
Table of Contents
Acknowledgements……………………………………i
List of Figures…………………………………………iii
List of Tables………………………………………….iv
Abstract………………………………………………..v
Chapter 1: Introduction………………………………..1
Chapter 2: Literature Review………………………….2
Chapter 3: Theoretical Framework….………...……....22
Chapter 4: Empirical Analysis………………....….…..30
Chapter 5: Conclusion…………………………………41
References……………………………………………..45
iii
List of Figures
Figure 1 Win Curve……………………………………23
Figure 2 Lakers (Maximum Salary Cap)……...……….23
Figure 3 Pacers (Minimum Salary Cap)…………….…24
Figure 4 Indifference Curve………………..…………..28
iv
List of Tables
Table 1 Summary of Statistics……………………………30
Table 2 Major League Baseball Regressions……………..32
Table 3 National Football League Regressions…………...35
Table 4 National Basketball Association Regressions.........37
Table 5 National Hockey League Regressions…………….40
v
Abstract
This paper takes a closer look at competitive balance or evenness of the teams in United States
major professional sports leagues. Looking at some of the most common things associated with
competitive balance an equation is put together to test and see the impact of each variable it
contains. Each league had a different result with the same equation, but overall some of the
same variables appeared in several of the leagues. Using this information a league could make
moves in order to level out the competitiveness of the league and thus help its popularity.
1
I. Introduction
Sports have elevated from a mere recreational activity to legitimate economic giants. The
four major sports leagues in the United States are: the National Football League (NFL), National
Basketball Association (NBA), Major League Baseball (MLB), and National Hockey League
(NHL). Each one will be examined throughout this paper. It is easy to notice the massive fan
bases that these leagues possess as they are constantly on television. In this day and age not
being aware of professional sports has become nearly impossible because they seem to be
everywhere. Yet, the professional sports leagues are not just garnering the attention of the fans,
they are attracting the attention of economists as well. These leagues bring in billions of dollars
on a yearly basis, which is enough to gain the attention of the economic community. When
making money is a top priority, which is definitely true for professional sports leagues, paying
attention to economists can only help.
The primary focus for any business is to keep their customers happy and coming back.
The customers in this case are the fans of these sports leagues. Thus keeping the fans entertained
stands as a top priority because without fans, the leagues would fail. One way that fans stay
entertained is consistently put out a competitive product. Games that are competitive are much
more exciting than games were one team gets blown out. Because of this leagues have placed an
emphasis on maintaining good levels of competitive balance. A one size fits all system does not
exist for all four sports, but there are similar ideas that can be applied to each sport. Figuring out
what impacts the competitive balance and consequently which league is handling it the best gives
a solid starting point for determining how to reach an optimal level of competitive balance in all
leagues.
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However it is a process to achieve any type of clarity or make any type of observation
that alludes to something impacting the competitive balance. It is first important to understand
the research that has been done beforehand in order to build upon it. Then it is important to take
the previous ideas and conjure a new idea. In other words the next step is to prepare a theory of
what could possibly impact competitive balance that can be tested to observe the validity that it
holds. Finally once the theory is set, compiling data and running tests such as regressions is the
last step. It is then possible to make conclusions based on the results of the regressions and
conclude what holds the most influence for competitive balance in a league.
II. Literature Review
What exactly is competitive balance and what affects it are important questions that take
time to answer. Before answering the question, examining former research can be greatly
beneficial. This literature review chapter showcases other authors’ work on the topic of
competitive balance. The following articles used several different methods to determine
competitive balance. In addition, the measurement is applied to many different leagues. This
helps to set a foundation to answer the question of what determines competitive balance and
which league manages it best.
Larsen, Fenn, and Spenner (2006) look at the impact of free agency and salary cap on
competitive balance in the NFL. This article only examines the NFL and does not look at the
other American sports leagues. Competitive balance is defined as the distribution of wins in the
league. It mentions the competitiveness of a team’s games is an important determinant of gate
revenue. People want to see a competitive game over a blowout. Therefore, the profitability of a
league relates to the overall balance of a league. The competitive balance of the league over the
3
course of 30 years was examined by the authors, with a primary focus on the introduction of free
agency and the salary cap in 1993 in the NFL.
The topic of competitive balance has an abundance of research. Larsen, Fenn, and
Spenner (2006) note that much of the previous research focuses on MLB and how free agency
impacts competitive balance. Prior research shows that competitive balance stayed the same in
the American League, but slightly increased in the National League after the introduction of free
agency. While the NFL and MLB have different free agency and salary cap setups, this
information gives an idea of how it may work in the NFL. The Gini Coefficient and the
competitive balance ratio (CBR) are two methods that other papers employ to find the
competitive balance of a given league. The Gini coefficient is commonly used to examine
income or wealth distributions, however it can be retooled to measure overall competitive
balance in a league. The result of the Gini will always be between 0 and 1. 0 represents perfect
competition and 1 represents a single team winning all games. As noted by Fort (2002) one of
the problems with the Gini Coefficient is that no team is ever able to win all of the league games,
thus making a result of 1 impossible. The result is a maximum value of the Gini coefficient
when applied to sports leagues is less than 1. Larsen, Fenn, and Spenner suggest controlling the
upper bound for the schedule of the league. This results in a more accurate representation for the
competitive balance of a league. The CBR is the average time variation in won-loss percentage
for the teams by the average variation in won-loss percentages across seasons. It is examined in
full by Humphreys (2002) later in this paper.
Larsen, Fenn, and Spenner (2006) take a look at the deviation of the HerfindahlHirschman Index (HHI). The HHI index is a quadratic summation of all firm market shares in an
industry. It can be used to calculate how much of an industry one company occupies. A
4
common use for this would be to examine the soft drink industry. Using HHI it would be
possible to determine how much of the industry Coca-Cola holds compared to Pepsi. For the
purpose of measuring competitive balance instead of measuring “market share”, the article uses
the HHI to measure a team’s percentage of wins in a given season. So instead of overall market
share HHI can be applied to measure how much one team dominates a given sports season. The
authors make note that the value of the HHI decreases as the number of teams in the league
increases. This potential changes needs to be accounted for to get an accurate result over the
course of several years. Then the equation is the normal HHI result minus 1/N where N is the
number of teams in the league. This new result is labeled as dHHI. Using only the standard
deviation of winning percentages fails to account for expansion in a league because it does not
include a counter balance such as 1/N. This is a reason why Larsen, Fenn, and Spenner believe
the standard deviation is not a reliable way to measure league parity. However the article later
runs a model using the HHI and standard deviation for comparison purposes. The authors run
two different regressions, one with the standard deviation as the dependent variable, and the
other with dHHI as the dependent. This allows the authors to see how numerous factors impact
the competitive balance respectively.
Larsen and Spenner set up a regression model to examine the competitive balance in the
NFL. Their model was dHHIt = f(FA/SAL, Expansion, Strike1, Strike2, Strike3, Player Talent,
Schedule Length, Playoff Spots, Relocation, New Stadiums). The introduction of the salary cap
and free agency are hard to separate because they were introduced in the same year. This causes
their effect to be combined so they are joined into one variable fa/sal. Three different strike
variables were also included, because strikes can often change league balance due to a new
collective bargaining agreement. The NFL changed the number of games played over the last 30
5
years, so the schedule length variable accounts for that, while playoff spots accounts for the
change in the number of playoff spots. Relocation denotes the number of teams that relocated in
the past 5 years, and new stadiums is a proxy for the number of new stadiums in the past 5 years.
Obviously, player talent has a huge impact on league parity, so a variable was created to account
for that. Thus the authors attempted to formulate a variable that showed how unbalanced player
talent leads to unbalanced leagues. The variable for player talent was defined as, player talent
equals HHIPF plus HHIPA where HHIPF is the HHI of points scored by a team in year t, and
HHIPA is the HHI of points scored against a team in year t. The higher values of HHIPF
indicate that higher concentrations of offensive talent on fewer teams exemplify less parity for
the league as a whole. The same is true for HHIPA, because more concentrations of defensive
talent on fewer teams exemplify less parity. The article combines these two measures into the
player talent variable to account for special teams affecting the offenses and defenses. Schedule
length impacts the NFL because the league increased the season from 14 games to 16 games in
1977. It was assumed since NFL is a physical sport more games meant more injuries, which
could lead to more competitive balance. The number of playoff spots variable shows the
increasing number of teams that made the playoffs in the NFL. Eight teams made the playoffs
from 1970-1979, 10 teams from 1980-1989, and 12 teams from 1990 to present. The authors
included New Stadiums because they believed that a new stadium could lead to an increased
advantage for the home team. Lastly, relocation was included to account for any possible change
due to teams moving.
It was found that player talent distribution, all three strike years, the length of the
schedule, the number of playoff spots, and number of new stadiums were significant at the 5%
level. The introduction of free agency and the salary cap was found to be significant at the 10%
6
level. League expansion and team relocation were the only variables that were not found to be
significant. In terms of impact, free agency and salary cap, the strike in 1973, and the strike in
1987 were found to have negative coefficients. This means that these variables led to increased
competitive balance in the league. FA/SAL is negative because the dominant teams could no
longer hoard the best players, and other teams were able to sign them away. The strikes are not
as easy to interpret because that requires an examination of the specific strike, because each had
its own motivations. The player talent variable, 1982 strike, schedule length, number of playoff
spots, and number of new stadiums all had positive coefficients, which means they lead to less
competitive balance. It is expected that the higher the concentration of player talent, the less
competitively balanced the league would be, because if one team has more talent then it will win
more games. The regression also showed that a 14 game schedule led to more balance than a 16
game schedule. Additionally, it showed that more playoff spots and new stadiums led to more
league parity. Expansion and Relocation were both found to have negative coefficients, but as
previously mentioned, are not statistically significant.
Larsen, Fenn, and Spenner (2006) also used a second model which uses standard
deviations (SDs) instead of HHI of dHHI. All of the variables remained the same except Player
Talent. The SD of total points scored by a team in a given year is substituted for HHIPF and SD
of points allowed by a team in a given year is substituted for HHIPA. In this model distribution
of player talents, all three strikes, number of new stadiums, and length of the schedule were
significant at the 5% level. The strike in 1973 and new stadiums were found to have negative
coefficients and thus lead to more parity. Player Talent, the strike in 1982, and schedule length
had positive coefficients. Some differences between the models of HHI and SD were that
number of new stadiums was found to be positive for HHI, but negative for SD. FA/SAL and
7
playoff spots were no longer found to be significant. It was summarized that FA/SAL may not
be statistically significant because of multicollinearity on the right side of the regression. The
model was run again without including number of playoff spots, schedule length, league
expansion, and new stadiums and found FA/SAL to be negative and significant. The SD model
is not as effective as the HHI model, something stated previously, but it was included for
comparison purposes. A clear example of this is the New Stadiums variable. The paper does not
give a precise reason for this, but generally says that it is because the HHI is more accurate.
This paper provides an in depth look at the competitive balance of the NFL. The authors
conclude that the HHI or (dHHI) is an effective way to measure the competitive balance of a
league and using the regression is able to identify some of the major determinants of it. The
article can be used as a reference to examine the NFL to the current date. It also provides a
model that is applicable to other leagues such as Major League Baseball (MLB), and the
National Basketball Association (NBA).
Humphreys (2002) seeks to find alternate measures of competitive balance. Similarly to
the last article, Humphreys acknowledges that competitive balance in a given league is directly
related to fan interest. He notes that a prior article Neale (1964) referred to this as the League
Standing Effect.
The first method that Humphreys uses is one that was discussed in the previous article,
the standard deviation of winning percentages. He states that while it can be useful to measure
individual seasons, the standard deviation has it shortcomings when examining a large number of
seasons. It struggles to accurately capture the relative standings of teams in different seasons.
Since the author notices this problem, he believes that other methods are needed to supplement
the standard deviation of winning percentages.
8
The method that Humphreys suggests is the Competitive Balance Ratio (CBR). As stated
before it is the average time variation in won-loss percentage for the teams by the average
variation in won-loss percentages across seasons. This method compares multiple seasons to
each other to control for time. This solves the problem seen with the standard deviation of
winning percentages since the number of games played is no longer relevant. Expansion is
something that all major sports leagues have done as recently as 1998. So it is important to be
able to control for such an issue. Humphreys does make note that the CBR is not a replacement
of using the standard deviation and describes it as, “useful complement to σL because it also
reflects the average amount of team-specific variation in won-loss percentage that will not be
reflected in σL “, page 138. σL is a symbolic representation of the standard deviation of winning
percentages.
Humphreys (2002) applies the CBR to Major League Baseball (MLB). The time frame
is (1901-1999). He also includes the σL and HHI results with the CBR for comparison. He
separates the times into decades, 1900’s, 1910’s, etc. Because of this method he does not include
teams that joined midway throughout a decade. Seattle and Toronto joined in 1976 and as such
are not present in the 1970’s data. Also the Milwaukee Brewers are left out of the 1990’s data
because they switched leagues, spending 8 years in the American League (AL) and 2 in the
National League (NL). Examining the results shows that the standard deviations have generally
fallen and the CBRs have generally risen. This suggests that competitive balance has risen over
the years. The HHI also provides the same conclusion that the competitive balance has generally
risen. Yet, Humphreys states that the CBR is able to discover some things that the σL and HHI
are unable to. From the 1910’s-1920’s the standard deviation and HHI are very similar, but the
CBR shows a much higher result for the 1910’s than then 1920’s. Humphreys takes a closer
9
look at those two periods to find out why the results were so different. He found that in the
1910’s the standings were relatively balanced. However the 1920’s were a different story. The
New York Yankees dominated the AL and the Pittsburgh Pirates dominated the NL. There was
little turnover in relative standings during the two decades, but the league championships were
won among the same teams. The CBR is able to account for this, while the HHI and standard
deviation do not.
Humphreys believes that looking at the variation of the competitive balance and the
behavior of the fans is very useful to find the overall understanding. He decides to use
attendance as a measure of fan behavior. The author creates a regression using attendance as
dependent variable. The independent variables are population, war, strike, games played, teams
in the league, television, television time trend, and AL/NL time trends. War and Strike are
dummy variables that equal 1 when there was a war or strike that year respectively. Television is
a dummy variable that equals 1 after televised games began occurring. War, strike, games
played, number of teams, and television time trend were found to be significant. However,
television was not found to be significant meaning it does not affect attendance, but the time
trends are significant. This means that television has slowly taken away more from attendance
over the last century. Humphreys also included the CBR, HHI, and σL in the regression. Only
the CBR was found to be significant, meaning variation in the CBR is related to attendance of
baseball. Thus Humphreys concluded that attendance rises (falls) when there is more (less)
competitive balance in the league. One potential problem that Humphreys acknowledges is
omitted variable bias in his regression. One of the biggest variables that was omitted is price.
He did not account for price and that is definitely related to attendance. There also could be
potentially more omitted variables that Humphreys does not mention.
10
This paper provided more support for some of the theories that Larsen, Finn, Spenner
(2006) presented in their article. The idea that one method to measure the competitive balance of
a league is not adequate. Instead it is useful to use several methods and compare the results that
are found by each method individually. Humphreys focused primarily on CBR, while Larsen,
Finn, and Spenner primarily used HHI. Also Humphreys examined the role of fans and their
impact on competitive balance. This is further examined in an article studied later in this paper
Bowman, Lambrinos, and Ashman (2012). Grabbing the ideas of several articles and combining
them into one paper provides for the clearest explanation as to how competitive balanced is
managed in each league. The article by Humphreys gives this paper another aspect that allows it
to come to a much clearer conclusion at the end.
Chang and Sanders (2009) look specifically at revenue sharing among the teams in Major
League Baseball (MLB) and how that can impact competitive balance. Using this article
supplies another piece to this puzzle of determining what the causes of balance are. The authors
show that pool revenue sharing negatively affects total investment in the talent of a given team.
Using four different measures, the authors determined that this effect causes less competitive
balance. They observed that the MLB Players’ Association (MLBPA) has been consistently
against pool revenue sharing. This is an indication that revenue sharing may be beneficial to the
owners, but could be negatively impacting players.
Chang and Sanders (2009) realized that using the MLB may be too difficult because there
are so varying levels of teams. To simplify the study, they considered a simple league where
there are only two types of teams. The first (denoted as 1) is a high revenue team and is above
league average in revenue. Team 2 (denoted as 2) is a low revenue team that falls below league
average. A key assumption made by the authors is that MLB owners, and owners in every sport,
11
are profit maximizers. Chang and Sanders treat sports competition as a “contest” where a team’s
probability of success is directly linked to its investment in player talent. The article states that
both type 1 and type 2 teams, expected revenue are an increasing, but concave function for its
expected winning percentage (Chang and Sanders, 2009). They also take into consideration a
team’s level of attendance and label them “strong drawing” or “weak drawing”. MLB adopted a
“straight pool plan” which means each team contributes a certain percentage of its locally
generated revenue to the pool and then that is equally divided across all of the teams. What
occurs is team type 1 ends up sharing more revenue then they receive in return. The opposite is
true for type 2, they receive more revenue then they share. Chang and Sanders (2009) refer to
these terms as “luxury tax” and “luxury subsidy.” In the calculations the authors found that all
else being equal an increase in revenue pool sharing lowers talent investment by team 1.
The opposite is also true, a decrease in revenue sharing results in an increase in talent
investment by team 1. However if team 1 increases talent investment, team 2 may or may not
increase its player investment. Overall, team 2 operates in the exact same way as team 1. They
invest less when sharing is more, and they invest more when sharing is less. This is Proposition
1 in the article. An observation is made that increased revenue sharing invites moral hazard on
the part of the low revenue teams, but this is not the case for all low revenue teams. Based on
the idea of Proposition 1, pool revenue sharing affects the incentive structure for team owners.
Instead of “luxury tax” and “luxury subsidy” they now refer to them as “winning tax” and
“losing subsidy”. In a worst case scenario the type 2 team decides to pocket the losing subsidy
they receive, i.e. the moral hazard. Chang and Sanders confirmed Proposition 1 using different
methods. They also found that market size differential has a negative effect on competitive
balance.
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This leads to Proposition 2, which states an increase in pool revenue sharing not only
lowers talent investments made by the owners, but also reduces league competitive balance.
Market size differential has the same effect as the increased pool revenue sharing. The article
found that an increase in revenue sharing increases the expected winning percentage for team 1,
whereas it decreases the expected winning percentage of team 2. The authors utilize a method
used by Syzmanski and Kesenne (2004), which measures the ratio of the expected winning
percentages between the two teams. All else equal, an increase in expected winning percentage
ratio represents a lowering of competitive balance. Thus in the case of the MLB, an increase in
pool revenue sharing presents a decrease in competitive balance, because the winning percentage
ratio increased. Chang and Sanders then examined the difference in expected winning
percentages. They found that the expected winning percentage differential increased when the
pool revenue sharing increased, which signifies a decrease in competitive balance. When
examining Proposition 2 the authors were able to notice several implications. The first was that
pool revenue sharing is not an effective policy to improve a sports league’s performance. Next,
pool revenue sharing although supposedly proposed to improve the lower revenue teams,
actually may hinder them. Third, differences in the size of the market the team may also
contribute to reducing the league wide parity. This is especially true when team revenues are
pooled together. When examining Proposition 2 the authors found that pool revenue sharing is
not an effective policy and actually furthers the disparity between high revenue and low revenue
teams.
The last part of the article talks about what has been done and what can be done to solve
the issue raised in this paper. On page 112 of the current MLB Basic Agreement there is a
statement, ‘‘ . . . each club shall use its revenue-sharing receipts . . . in an effort to improve its
13
performance on the field. Each payee club, no later than April 1, shall report on the performancerelated uses to which it put its revenue-sharing receipts in the preceding revenue-sharing year.
Consistent with his authority under the Major League Constitution, the Commissioner may
impose penalties on any club that violates this obligation.’’ (Page 423 Chang and Sanders 2009).
Basically this encourages teams to use the revenue they receive towards player talent. Yet, since
there is not a minimum payroll, several teams still receive more than they spend on talent. The
authors proposed a minimum payroll as a solution to this problem. That leads into Proposition 3,
a policy that combines pool revenue sharing and a minimum payroll to increase the level of
competitive balance in the league. The minimum payroll is meant to act as a leveling
mechanism and the revenue sharing results in a financing mechanism. The authors still found
problems with this model because they were not sure how the revenue pooling share and the
amount of the minimum payroll were determined.
Generally this paper provides another insight into the competitive balance of a league.
Chang and Sanders (2009) found that revenue sharing in sports actually reduces the overall
competitive balance even though it is intended to be beneficial because of the lower revenue
teams investing less. Using this idea along with other articles may result in a better
understanding of how competitive balance works. Knowing that revenue sharing may not help
in the way that most people believe economists can examine if each sports league has something
like this, and if that could potentially hurt one league more than another.
Groot (2009) discusses competitive balance between European soccer and United States
(US) team sports (baseball, hockey, football, and basketball). The paper uses professional soccer
as its reference for comparison, so it is important to understand how their system works. Most
European soccer leagues have different levels, similarly to Major League Baseball has minor
14
league levels AAA, AA, A, etc. They utilize a system of promotion and relegation, which
means each season a select number of teams are demoted from the top league and the same
number are promoted from the lower league. This provides immense motivation to stay
competitive every season. It takes a different look at the determinants than the previous papers
have. This paper focuses on the number of goals/runs/points, the referees or umpires, and
overtime, and how they impact the overall competitive balance. Groot (2009) notices that sports
leagues in the US need to use other measures to maintain the level of competitive balance in their
respective leagues. For sports in the United States maintaining a certain level of competitive
balance is important, because this allows the league to get a special status under an antitrust law.
Some of these extra measures that Groot mentions are: rookie drafts where the worse teams get
better picks, revenue sharing among the teams, reserve clauses, luxury taxes, and salary caps
among others. Reserve clauses are when a player’s former team maintains his rights after the
contract expires and a luxury tax is a penalty a team plays for exceeding the salary cap. The
author argues that numerous factors that are largely absent in US sports, but present in Europe
raise the level of competitive balance without needing the “special measures” as he refers to
them.
The hypotheses of the paper are 1) Competitive balance is higher in sports with lower
scores, 2) impartial referees making a few large or several small mistakes has a beneficial effect
on competitive balance, and 3) Games ending in ties raises the level of competitive balance. If
true, these are all hypotheses that should benefit European soccer in terms of having a higher
competitive balance because they all tend to be seen in soccer. This makes the task of getting
special status under the antitrust law much easier for European teams since extra measures are
not as necessary.
15
Groot (2009) uses a Poisson distribution to calculate the effect of the number goals
scored. He does not use data from an actual sports league. The author refers to the weaker team
as team A and the stronger team as team B in the paper. Groot uses the term scoring context to
describe how may points or goals are to be expected in a sport. The article wants to determine if
the differing scoring context can impact the expected winning equivalent probabilities. The
author uses two diagrams to explain his point. The first one is of iso-winning curves, iso-scoring
lines, and relative team qualities. The graph illustrates that in order to stay on the same iso
winning line, or maintain the same CB, while increasing scoring context would require a steadily
increasing relative team qualities. This implies that higher scoring contexts (more points, runs,
or goals) require teams to be closer in ability, while the opposite is true for lower scoring
contexts. To showcase this point he compares Soccer and Baseball using winning equivalents,
relative team strength, and scoring context. Scoring context would be the expected number of
goals or runs. He states that if baseball has a context of 10 and soccer has a context of 3,
meaning that 10 runs would be scored in baseball and 3 goals in soccer. Using the same relative
team qualities for each sport, the winning equivalent is lower in soccer. The graph shows the
winning percentage of team A in this example for baseball is 14.6%, but is 28.8% for soccer. In
other words the lesser team has nearly twice the chance to win when playing soccer as opposed
to baseball. This is one of the reasons that American sports require more effort to artificially
produce competitive balance among the teams. One of the main points the article makes is that
in higher scoring context sports, even small differences in the qualities of teams can have large
effects on overall league parity. Watching sports it may be noticed that the weaker team would
employ tactics to “manage” the game and limit total points. These could be running the ball and
controlling the clock in football, good pitching and defense in baseball, and playing half court
16
slow basketball. Hypothesis one, competitive balance is higher in lower scoring sports, is found
to be correct in this model.
The second hypothesis is that referees impact the competitive balance of a league. Groot
(2009) summates that worse performance of referees results in higher competitive balance. On
page 391 of the article he states, “a referee making random errors produces noise that disturbs
the outcome of a match towards a more balanced outcome than would be the case where the
outcome is determined by relative team qualities.” The author creates two different types of
fallible, but impartial referees: discretionary (D) referees and nondiscretionary (N) referees. The
D referee grants an extra goal for one of the teams, and the N referee has biased decisions to one
team that leads to marginal change in scoring chances. Groot (2009) found that for either type D
or N of referee, the weaker team A benefits from it the most. He does state that in higher scoring
sports the impact of this effect is rather small, since a referee making one or a few bad calls does
not have as much of an impact. However, it is shown to also have a small effect on lower
scoring sports such as soccer. He found that the winning percentage for team A is 28.8% in a
soccer match. When adding the referee who gives a goal to team A or team B the winning
percentage increased by 2.9 points. So it is seen that the effect is minimal even in soccer. Groot
(2009) believes that in higher scoring sports the effect of the referees tends to balance out over
the course of a game. He states that lower scoring games require the need of television replay
more than higher scoring sports. Yet this is a contrast to what we see, as the American sports
employ TV replay in a much larger capacity then soccer. So overall this hypothesis is correct,
but to a lesser degree than anticipated.
The final hypothesis of the paper is the presence of an overtime period versus a tie. The
author supposes that the introduction of overtime decreases the competitive balance of the game.
17
American major sports all have some form of overtime, while European soccer does not have
overtime in league matches. Groot (2009) says that higher scoring games decrease the chance of
a tie, while lower scoring games increase the chance of a tie. Yet it can be seen that the
American sports all have some form of overtime, and soccer does not (in league play). The
negative effect of allowing overtime on competitive balance is higher in lower scoring sports
than higher scoring. Groot relates back to soccer and states that having overtime as opposed to a
tie is like having a seven game series or group stage as opposed to single knockout games.
Anytime chance is decreased, the stronger team has a better chance at winning. Thus, hypothesis
3 is confirmed because when the match has overtime the competitive balance does decrease.
The article showed that all three of the stated hypotheses were correct. More importantly
it introduced the idea that there are other ways of controlling the competitive balance, i.e.
introducing new rules. This article gives more insight into identifying what exactly controls
competitive balance. Although the paper was comparing European soccer to the four major
American sports and usually grouped the American sports together, these three ideas can still be
used to examine the American sports against each other as well. Groot mentioned examining
how rules such the shot clock in basketball, offside in hockey, etc, affected the scoring in those
sports and its consequential impact of competitive balance. Overall this paper provides an
additional and useful perspective on the topic of competitive balance.
Bowman, Lambrinos, and Ashman (2012) focused on the fan perspective of competitive
balance. The basic idea is that the quality of two teams playing is a key determinant of the level
of consumer interest. When a league has teams that are perennial losers a big issue arises.
Naturally the losing teams’ fans lose interest, but eventually so do the good teams’ fans since
watching blowouts even when your team wins is not enjoyable. In general, fans enjoy exciting
18
finishes that could go either way. This paper focuses on the use of point spreads to measure the
uncertainty of outcomes in the National Basketball Association (NBA) and the National Football
League (NFL). The authors theorize that if point spreads are unbiased estimators of the
outcomes, then the point spread for a particular game should be the best estimate of the actual
difference between the two teams. Thus the point spreads of games can give an indication to
how the competitive balanced is perceived from the outside. They state that higher spreads will
draw less fan interest because of the disparity between the teams. They do not believe that point
spreads should replace all other measures of competitive balance, but instead make a valuable
contribution to the topic. The idea is that the closer the point spread is to zero, the more
competitively balanced the two teams are according to the fans, the opposite it true for large
spreads. Their main hypothesis is that all else equal if the point spreads in a league’s games
increase (decrease) over time then the league has become less (more) competitively balanced.
There are several ways to use point spreads and the authors present them with the pros and cons
of each. Their sample size is the 384 games in NFL from 1985-2009 and 1526 games in the
NBA from 1990-2009.
The topic of competitive balance in sports is a well-documented issue among sports
economists. Many articles about competitive balance focus on the analysis of competitive
balance (ACB) or analysis of the uncertainty of outcome hypothesis (UOH) “Fort (2006)”.
Different authors take different approaches to analyzing both of those ideas. Three of the more
common ways to analyze competitive balance are talked about in the previous articles above:
Gini Coefficient, Herfindahl-Hirschman Index, and standard deviation.
One of the biggest differences between this paper and other articles pertaining to this
topic is prospective versus retrospective view on competitive balance. This is saying that most
19
articles are retrospective in that they look at final outcomes. Bowman, Lambrinos, and Ashman
(2012) focus on prospective or what is expected to occur. An important assumption is that the
authors believe that point spreads are a “useful guide” to how the fans feel about a game.
The six methods are mean absolute spread (MAS), mean absolute natural spread
(MANS), mean absolute predicted spread (MAPS), mean absolute predicted neutral spread
(MAPNS), balanced mean absolute predicted spread (BMAPS), and balanced mean absolute
predicted neutral spread (BMAPNS). Essentially, these build on one another. MAS is the most
simplistic measure. It is defined as
Where n is the number of games, S is the spread, h(k) is index of the home team, and a(k) is the
index of the away team. In other words MAS is 1 over the number of games times the
summation of the absolute value of the spread between two teams. MANS adjusts MAS by
eliminating the home field advantage bias that is included in the equation and only looks at the
differences between the teams. MAPS improves upon MAS and MAPNS improves of MANS,
by the individual game factor so that the spread and neutral spread reflect season long ratings and
not just specific games. These factors control for the problems associated with MAS and MANS
such as home field advantage, neutral advantage, and a few others. By corrected for these errors
the new variables MAPS and MAPNS provide a clearer and purer representation. In a
hypothetically balanced schedule the authors adapt MAPS and MAPNS as BMAPS and
BMAPNS respectively. A balanced schedule would be where each team plays every team at
home and on the road. They state that the measures with the predicted spreads “smooth out” the
ups and downs of teams, injuries, hot streaks, etc., and could be viewed as more favorable
measures. Then, the balanced schedule measures also smooth out as well as account for any
20
possible unbalanced schedules thus this would be the most ideal measure despite not being
applicable most of the time due to unbalanced schedules.
The article used the website covers.com for the point spreads of the NBA from 19902009. The authors obtained yearly values for MAPS, MAPNS, BMAPS, and BMAPNS. The
numbers showed an increase in competitive balance over the last 20 years. Then they ran a
regression with the measures as the dependent variables and time as the independent. Each of
the measures was found to have a negative coefficient and all were significant at the .10 level.
The same method was then used for the NFL from 1985-2009. The NFL did not show any
pattern in terms of competitive balance. The balance in the NFL fluctuated throughout the
sample period. The authors noticed some interesting things with the NFL measures. The
numbers peaked in 1992 and then decreased starting in 1993 (the year of a new collective
bargaining agreement). They decreased until 2003, where four of the six are at their lowest.
Then they began increasing until in 2009, where four of six are at a peak. They provide some
reasons for the erratic results of the NFL. The league expanded from 28 teams to 32 from 19952002. In each year when the expansion teams joined the ratings for the new teams were more
negative than any other team.
Bowman, Lambrinos, and Ashman (2012) make note that using only one of these
measures is not effective. It is important to take all of them together to achieve the necessary
assumptions. They make note of the 1987 strike in the NFL. The season was shortened to 15
games in which three of the games were played with replacement players. Inconsistencies such
as these caused the fan perception of the leagues competitive balance to fluctuate and thus
created unusual MANS and MAPNS results. Also the article makes note of the how the
scheduling affects the balance. In some ways the league can help control the fans perception of
21
balance by manipulating the schedule. Because of this, it is not beneficial to only use one
measure, but to use several to avoid these unfamiliar instances.
The authors state that this paper provides another valuable dimension into the topic of
competitive balance in professional sports leagues. They do not intend for the article to be used
by itself, but in a supplementary fashion to other articles. If fans perceive a league to be more
balanced it helps the overall health of the league. The reason being, when a league is balanced it
begins to gain more interest among the fans. They also concluded that point spreads do reflect
the competitiveness between two teams. This article exhibited that the NBA has improved
balance, but the NFL has neither increased nor decreased balance to a large degree. However,
they did not seek out a definitive answer for this and instead said it might have to do with
expansion. Using this article along with other methods will provide a much clearer idea of how
each league handles competitive balance.
Overall there were four main ideas made through the five articles. The first being the
regression approach found in Larsen, Fenn, and Spenner (2006) and Humphreys (2002). The
authors in these two articles used HHI, Gini Coefficients, CBR, and standard deviation to
calculate the competitive balance and then see how certain factors impact those numbers. The
next two ideas are effective in describing how some variables affect competitive balance because
they provide a basis to make an argument. Chang and Sanders (2009) focused on revenue
sharing and Groot (2009) studied the impact of the sport itself on the competitive balance. The
last focus was on the fan’s perception of competitive balance and is found in Bowman,
Lambrinos, and Ashman (2012) and Humphreys (2002). This idea is useful to provide a
different insight and another angle to examine competitive balance. Using these four main ideas
together will provide the most complete examination into each league’s competitive balance.
22
III. Theoretical Framework
The same question remains, what is competitive balance and which league handles it the
best? The previous articles provide a point of reference that is able to provide a solid foundation
that can be built upon. The most important aspect when looking into competitive balance is
acknowledging what can affect the balance in sports, and this section will take a closer look at
some of the most important factors when studying the competitive balance. Once the factors of
competitive balance are better understood it is then possible to examine them to see the results.
The calculation of competitive balance essentially comes down to how a number of variables
impact it. This equation would looks like Competitive balance = f(free agency, salary cap,
number of teams, league revenue, playoff spots, length of season, revenue sharing, rule changes).
These are the factors that impact the competitive balance and need to be addressed.
One of the first factors people think of is free agency in the sport. Each sport has some
form of free agency, this variable can be examined across all American sports leagues. Free
agency can be examined a little more closely with the Coase Theorem. The Coase Theorem is
defined as, resources flow to their most valued use regardless of who owns them to begin with.
The book uses a specific example that involves the Indiana Pacers and Los Angeles Lakers of the
NBA. They state that the Pacers may value the player at a marginal revenue product of $5
million, but the Lakers might value the same player at a marginal revenue product of $7 million.
There are three main reasons for this disparity in player evaluation. They are size and loyalty of
the team’s market, the level of the team’s competitiveness, and the revenue a team receives for
making the playoffs. Because of these three reasons each team values an extra win at a different
amount. In this example, the Lakers value an extra win higher than the Pacers and as such are
willing to pay more for the player.
This concept is depicted by a win curve, which shows how
23
much marginal revenue a team gains for each win (Gennaro 2007). Figure 1 depicts a potential
win curve for both the Lakers and Pacers. The curves represent the marginal revenue the team
values each additional win. It can be seen that at the beginning or when wins are low the
marginal revenue for an additional win
Figure 1
is not great. Eventually the two curves
Win Curve
Marginal Revenue
Lakers
meet and the marginal revenue for that
win is equal. However after this point
Pacers
the win curves break apart drastically.
The reason for this is because the
Laker’s fans expect the team to
contend for a title and those wins are
Number of
Wins
more valuable for that franchise. In a
free market, or free agency, the team that values the player higher will be able to acquire the
player. The book also believes that being able to trade picks and players allows for the same
result (Leeds 2002). Looking into this one can
Figure 2
believe that free agency would lead to a
competitive imbalance because the teams similar to
Lakers
$
the Lakers would buy most of the player while
teams such as the Pacers would be unable to
acquire them.
Max Salary Cap
The leagues recognized this potential
problem and they implemented salary caps in order
Players
to control the situation. The salary cap is a limit to
24
how much each team is allowed to spend on their players. To use the same example as before, if
the Lakers are already at the salary cap the value they place on the player from the Pacers is
irrelevant. The cap does not allow them to pay the $7 million for him and then the player ends
up on a different team who can afford him (Leeds 2002). The cap functions similarly to a price
ceiling or price floor. Everyone desires to be at the equilibrium point, or where the supply and
demand meet, but a ceiling or floor restricts how close the person, or market can get. This can be
seen on Figure 2 on the previous page. A team such as the Lakers wish to spend at the
equilibrium point, but a maximum salary cap shown on the previous page restricts the amount
they are able to spend. Conversely this can work
Figure 3
in the opposite fashion with a salary floor.
Suppose a small market team such as the Pacers
$
Pacers
wish to spend as little as possible. A minimum
salary car forces them to spend more than they
Min Salary Floor
would desire. This is shown in Figure 3 by the
min salary floor line. This forces both the Lakers
and Pacers to spend amounts that are a lot closer
than a free market would have allowed. This is
Players
why free agency and the salary cap go hand and hand, in fact the NFL actually introduced both
the same year.
The purpose of this paper is to evaluate the competitive balance in each sports league. So
how do the salary cap and free agency impact the competitive balance of a league? The salary
cap would be expected to increase competitive balance since it limits how much talent a team
can stockpile. Free agency cannot be as easily projected. It can work in both directions, a good
25
player can go to a bad team and a good player can go to a good team. These cases would cause
an increase and a decrease in competitive balance respectively. It can be expected that leagues
that have a cap and free agency would have higher balance then ones that do not. When they are
used in tandem, the salary cap is capable of holding free agency in check, which is why the
positive effect is predicted.
Another consideration in the competitive balance of a league is the number of teams in
the league. This does not seem as straight forward as free agency/salary cap, thus a closer look is
needed. There are currently 30 teams in the NBA, so the talent in the league is dispersed
between the 30 teams. However if they decide to add an expansion team then they need to
accommodate for an extra team. In each sport the way this occurs can be different, but it is
generally implemented similarly. The existing teams are able to protect a certain number of their
players and the expansion team drafts from the unprotected. In the case of the NBA, each of the
initial 30 teams would protect up to eight players on their respective teams. Then the expansion
team, drafts a team from a pool of all the unprotected players. In other words the new team
steals players from the other 30. This creates a further spread of the talent in the league. This
system would lead some to believe the league has an instant increase in competitive balance, but
that is not the case. In the NBA a typical roster consists of 12 or 13 players. If the current 30
teams are able to protect their top 8 players then the players available to be drafted by the
expansion team are the bottom third of the roster. In the majority of the cases the expansion
team is not very good as a result and this actually decreases competitive balance because they
lose the majority of their games. Consequently the number of teams should be expected to have
a negative impact on competitive balance.
26
Competitive balance and revenue are sometimes seen to be two sides of the same coin.
The argument can be made that more competitive balance creates higher revenue league wide,
but it can also work in the opposite direction. In some cases more revenue for the teams can
create more competitive balance because teams have more money to spend on players. One way
of encompassing how revenue impacts competitive balance is to look at attendance. If a team
experiences higher attendance throughout the course of a season, the team has significantly more
money than it would have had with the lesser attendance. In result, they might be more likely to
be active in free agency the next offseason since they have more money. It is important to note
that in many cases the larger market teams generate the most revenue which can give them a
competitive advantage. Ideally the attendance variable will examine changes in the attendance
instead of focusing purely on each number independently. This can help to focus on the change
in competitive balance when teams experience higher than normal attendance. If the effect were
able to be isolated as previously stated, then the attendance variable would be expected to have a
positive impact on competitive balance.
The number of playoff spots could also impact the competitive balance in the league. It
is first important to examine how the playoffs in general impact the competitive balance. The
win curve described earlier can provide a better understanding as to why the number of playoff
spots matters. When teams are in contention they are more likely to be active in spending for
better talent because they believe they have a chance to win a championship. The team who
contends begins to value an extra win a lot more than they would if they were not in contention.
MLB recently expanded their playoffs from eight to ten teams. Before the teams that were 10-14
may not view the playoffs as a realistic goal and could begin to prepare for next year. This
would lead to them being less competitive and thus decreasing competitive balance. However,
27
with the extension of the number of teams, those same teams may strive to make the playoffs.
Thus they spend more on talent and the overall competitive balance increases. Therefore the
expansion of league playoffs would be expected to increase competitive balance in a sports
league.
The length of the season in the league could also impact the competitive balance in a
given league. Groot (2009) wrote about how competitive balance in soccer is generally lower
than American sports. One of his main points was having overtime had a negative effect on the
competitive balance. He argued that having extra time in a game allowed the better team more
time to win the game. By using the same logic having a longer season should have a lower
competitive balance than having fewer games. To put it simply, an underdog’s odds decrease at
an increasing rate as the amount of time is added. When a league adds games to its schedule the
competitive balance would be expected to decrease in the years following.
Revenue sharing is commonly debated for its effectiveness. The main idea behind it is
simple, divvy up the money so the lower revenue teams make money and the upper teams cannot
hoard it. It seems like a simple concept that should work, but that is not always the case. Chang
and Sanders (2009) as mentioned in the literature review attempted to examine this exact
situation. They found that in general revenue sharing practices tend to decrease competitive
balance in the league. The main reason for this is the debate about whether the owner of a team
should desire to make money or win. In many cases winning and making money are
accomplished, but some teams become complacent with making a steady profit and do not wish
to mess up a good thing. Major League Baseball has a revenue sharing system in place.
Nonetheless it seems as though the same teams can be found at the top and at the bottom of
overall team salary. Take the 2015 Atlanta Braves for example. Forbes lists their 2015 revenue
28
as $266 million dollars, good for 13th out of 30 teams in
the league ("Baseball's Most Valuable Teams."), and yet
Figure 4
their payroll was 23rd in the league at a little over $87.6
Indifference Curve
million dollars ("MLB Salaries."). Now they were not
winning either as they finished 28th in the league
Reference.com). So the Braves were a horrible team that
Money
standings with a record of 67-95 (Baseball-
Braves
did not spend much money on players and yet were in the
Yankees
top half of the league in total revenue. Even as a sports
fan it is easy to understand how making that much money
Wins
might make them reconsider spending for players. Some
teams are happy to be making a consistent profit and they sometimes value it over winning
games. Look at the Indifference Curve to the right. It has money on the y-axis and wins on the
x-axis. This graph is a possible explanation for why some general managers are content making
money. The budget constraint is also on the graph. A budget constraint represents all the points
that are available for a team to produce at. In other words each team must be on the same budget
constraint. A key assumption made is that the owners revenue is fixed and as such will always
fall on this budget constraint. In the real MLB a fixed budget constraint would not be possible,
but for the purpose of the graph the assumption must be made. Perhaps a team like the Atlanta
Braves operates on the part of the budget constraint that is closer to the top of the budget
constraint. The indifference curve represents a line where the owner is equally happy with all
points on the line. So the team would choose the point where the indifference curve and the
budget constraint meet. However an owner more focused on winning, perhaps the New York
29
Yankees, would have an indifference curve that is much closer to the bottom of the budget
constraint. For this reason revenue would be expected to have a negative effect on competitive
balance.
Each professional sports league constantly makes changes to their respective games in
order to maintain fan interest and therefore revenue. The majority of these are rule changes. It is
impossible to give an over arching expectation for how rule changes effect the balance because
each one is a different case. Instead each rule change that is included would have to be evaluated
on its own. Three examples of significant rule changes can be found in recent years from the
MLB, NFL, and NHL (National Hockey League). In the MLB they instituted instant replay in
recent years. It would be expected that instant replay decreases competitive balance because it
decreases chance, which hurts the lesser team. The NFL extended the extra point field goal back
13 yards. It makes sense that this decreased balanced slightly because the teams with better
kickers missed less extra points. The NHL changed their overtime rules a few years ago.
Normal hockey is played with 5 skaters and 1 goalie on each team. It used to be that overtime
was played with 4 players instead of 5, but now it has been decreased to 3 on 3. It is difficult to
decide who benefits from this rule change, but teams with more top end players could benefit
from this rule change. These are just three examples, but they show how each league makes
changes that can potentially have consequences to the competitive balance of the league.
All of these variables provide a part of the bigger puzzle that is the competitive balance
of the league. By diagnosing as many main contributors as possible, the theory becomes more
complete. These theories can then be utilized in order to provide a solid footing on which the
data is built. Using the aforementioned variables and applying the data for the past 36 seasons
the results should provide some insight into the most important factors for competitive balance.
30
Based on prior research and the theories above, attendance and length of the season should have
some of the biggest impacts on the competitive balance. Also using HHI the data will provide an
a measuring tool for how balanced each league is.
IV. Empirical Analysis
Variable
Observations
Attendance
MLB
Attendance NFL
36
Table 1
Summary Statistics
Mean
Standard
Deviation
27,453.85
3,745.92
32
63,943.02
3,921.80
Minimum
Maximum
19,115.73
32,696.13
57,065.62
68,775.95
31
36
15,584.27
2,536.28
9,923
17,867.2
Attendance NBA
35
15,954.49
1,325.65
12,993
18,233
Attendance NHL
36
.0344
.0037
.0167
.0384
HHI MLB
36
.0345
.0023
.0310
.0391
HHI NFL
36
.0379
.0034
.0339
.0445
HHI NBA
35
.0362
.0037
.01669
.0384
HHI NHL
36
10.9271
1.5824
7.5980
14.7533
SD MLB
36
2.9444
.2323
2
3
SD NFL
36
12.6971
1.5428
7.9642
15.6593
SD NBA
35
16.1714
2.8231
11
24
SD NHL
As mentioned previously in the paper, the next step is to apply data to the proposed
theories established in chapter 3. The equation, competitive balance = f(free agency, salary cap,
number of teams, league revenue, playoff spots, length of season, revenue sharing, rule changes)
is implemented across all four professional sports leagues. Each league will be examined with
HHI as the dependent variable for one regression and with standard deviation of winning
percentages as the dependent in another regression.
When looking at the competitive balance of an individual sports league, it is important to
take a large enough sample size so that the results are accurate. Therefore, the sample size for
this data is the 1980-1981 season through the 2015-2016 season, which is a total of 36 seasons
worth of data for each of the major sports leagues in the United States. There are a few
exceptions to this for a variety of reasons with one being the NFL attendance numbers for the
1985-1986 through the 1989-1990 seasons were unavailable, so there are only 32 observations.
Also the NHL had the entire season cancelled due to a lockout in 2004-2005, so there are only 35
observations for the NHL variables. Table 1 is a summary for some of the major data variables.
The data compiled was obtained from Sports-Reference LLC and four of its websites BaseballReference.com, Basketball-Reference.com, Hockey-Refeence.com, and Pro-Football.com as
well as from ESPN.com and NFL.com.
32
Each attendance variable is the average attendance per game. While the HHI and SD
variables are the Herfindahl-Hirschman Index as used by Larsen, Fenn, Spenner (2006) and
Standard Deviation of team wins. These variables are the means to measure the overall
competitive balance. The HHI of a perfectly competitive league is zero so the lowest number
would imply that league is the most balanced. The mean calculates the average HHI number
throughout the 36 seasons. Examining Table 1 shows that the MLB has been the most
competitive league while the NFL is a close second in regards to the HHI measure. It is
important to look at the standard deviation of the HHI numbers as well because it shows how
consistently competitive season to season the leagues have been. This is not the same variable as
the SD variable in the first column of Table 1. This standard deviation is calculating the
deviation between the HHI numbers. This shows that while the MLB on average has been the
most competitive it is also tied for the least consistent with the NHL. The NFL has the smallest
amount of deviation and has generally kept a similar level of HHI.
The standard deviation can also be a way to study the competitive balance of a league.
Similarly to HHI, the lower the number, the higher the competitive balance in that particular
leagues. These numbers are not able to be compared from league to league because the leagues
play a different number of games. The NFL has a very low standard deviation of 2.9444, but
they only play 16 games while the NBA and NHL play 82, and the MLB plays 162. While the
NBA and NHL play the same number of games, their standard deviations still cannot be
compared without some inaccuracy because of a few seasons in which the length of the season
was not 82 due to a strike.
Attendance is included in Table 1 for a better understanding how much of an impact this
variable could hold when interpreting the regressions. The NFL has the largest average
33
attendance which is logical because their stadiums are larger and MLB’s tend to be the second
largest. Also the NBA and NHL have similar numbers, which is expected since they play in
arenas that are about the same size.
Major League Baseball is the most competitively balanced league according to the HHI
measure. However, it helps to have a deeper understanding of how it got there and how it could
potentially change. In Table 2 the results for two different regressions are included. One
regression with dHHI as the dependent variable and the other with the standard deviation of team
wins as the dependent variable. The dHHI is the HHI value minus one over the number of teams
in the league. This is a technique used by Larsen, Fenn, Spenner (2006) that adjusts for league
expansion. Salary cap, free agency, revenue sharing, and replay are all 0/1 variables, since they
Table 2
Major League Baseball
dHHI
Standard Deviation
.2153
.4069
36
36
Coefficient
t-value
Coefficient
t-value
Omitted
Omitted
Omitted
Omitted
-.0008
-0.68
1.1186*
2.65
.0004
0.52
-.3727
-1.37
-.0004
-0.19
-.1630
-0.20
.00002
0.21
.0692*
2.37
R-Squared
# of Observations
Variable
Salary Cap
Free Agency
# of Teams
# of Playoff Teams
Revenue Sharing
Length of the
Season
-.0010
-0.48
-.3775
-0.48
Replay
.0000007*
2.14
-.0002
-1.42
Attendance
-.0025
-24.5921
Constant
all measure whether or not the MLB has that particular attribute. They are assigned a 1 in the
seasons in which that particular variable was present. For instance, replay would be a 1 for each
year after and including the year the MLB instituted a replay system. Replay is included because
of the argument made by Groot (2009) which is that perfect refereeing could impact the game
34
itself. The correct call is going to be made more frequently if replay is used by the officials. The
other variables represent the number of teams, number of playoff teams, length of the season,
and average attendance. The constant represents the level of dHHI or standard deviation that
would occur if all of the variables were at zero.
Now that all of the variables are identified it is possible to examine the results. The first
thing to notice is that in both regressions from Table 2 free agency and salary cap were omitted
because of multicollinearity. In other words, these two variables are highly correlated with other
variables in the regression. This can be a problem with 0/1 variables because often times they
can run together and not give the clearest results. Taking a look at the dHHI model first it is
important to diagnose any significant variables, or variables that have a t-value above 1.68 or
below -1.68. Being significant signifies that the variable does impact the dependent variable.
The only variable that is significant from the dHHI regression is attendance. The coefficient of
0.0000007 indicates that the dHHI value will increase by that much for each additional person
that attends the game. Thus, attendance has a negative effect on MLB competitive balance in
this regression. However there is not an exact theory that would explain this particular result.
In the SD model in Table 2 the number of teams and length of the season are statistically
significant. Thus for each team added to the MLB, SD of winning percentages would increase
by 1.1186, and for each additional game the SD would increase by .0692. Each of these would
increase the standard deviation of winning percentages for the MLB and cause less competitive
balance. This observation makes sense, because the introduction of an expansion team can often
decrease balance because that new team could struggle. Also, adding more games would be
expected to decrease balance following the theory from Groot (2009) that states that giving the
better team more chances decreases balance.
35
Lastly, the R-Squared values from the MLB regressions of .2153 and .4069 are far apart.
These numbers represent how much of the variation is explained by the regression so the dHHI
regression explains 22% of the variation and the SD regressions explains 41%. Therefore the
standard deviation is a much better model compared to dHHI in the case of the MLB.
The league with the second lowest HHI level was the National Football League. It had a
mean HHI of .0345 and it also had lowest amount of deviation from year to year at .0023. This
following regressions in Table 3 use many of the same variables as the previous regression in
order to maintain a level of comparison. All of the variables are the same except for a rule
change for the NFL. The rule change which was implemented for the 2015-2016 season is when
the NFL moved the point after attempt field goal back 15 yards to make it more difficult. This
could lead to a competitive advantage for teams with a consistent kicker and it is included to see
if this rule could have had any impact on the balance of the league. The number of observations
is only 32 despite most of the information being collected for 36 years, because of the four
missing years of attendance in the late 1980’s seen from Table 1.
These two regressions on Table 3 also suffer from multicollinearity as each regression
has two omitted variables. Looking at the dHHI regression the free agency and revenue sharing
variables have been omitted. The only significant variable is attendance from the dHHI model.
In this case the coefficient for attendance is negative implying that more people at each game
would increase the competitive balance which stands in opposition to the result shown in the
dHHI regression for MLB. The coefficient is very small, but it is important to remember that the
R-Squared
# of Observations
Variable
Table 3
National Football League
dHHI
Standard Deviation
.3078
.6052
32
32
Coefficient
t-value
Coefficient
t-value
36
Salary Cap
Free Agency
# of Teams
# of Playoff Teams
Revenue Sharing
Length of the
Season
Replay
Further PAT
Attendance
Constant
-.0002
Omitted
-.0004
.0004
Omitted
-.0002
-0.16
-.0007
-.001806
-.0000004*
-.0136
-0.38
-1.29
2.01
-0.68
0.82
-0.92
Omitted
-.0336
-.0948
-.0058
Omitted
.1366*
.2117
-.0230
.00003
1.8950
-0.19
-1.22
-0.10
4.84
0.90
-0.12
1.01
NFL had the largest average attendance out of the four major sports leagues with a number
around 64,000. So while the coefficient is small, the NFL is likely to see larger impact from this
variable than the other three sports. This is not necessarily backed but logic, but it can be made
clearer when using the theory from Bowman, Lambrinos, and Ashman (2012). One of the main
takeaways from that paper is that if fans perceive a league to be more balanced it would generate
more interest among the fans. Thus by connecting the dots on these two ideas, the thought
becomes clearer. Knowing that fans will attend the games more if the perceived balance is
increased, and also knowing that attendance increases balance it can be reasoned that they are
intertwined effects and would increase together
The SD model omits the salary cap and revenue sharing variables. It is a bit unusual for
the omitted variables to be different, but in this case there is a reason for it. The NFL introduced
free agency and a salary cap in the same season which would mean the variables would have the
same 0/1 data. Thus to the eyes of the regression they are portraying the same data and thus
either one could be omitted. In the standard deviation of wins regression length of season is seen
as very significant with a high t-value of 4.84. While MLB also saw this variable be significant
the impact on the regression is much more severe with a coefficient of .1366. For each
additional game played the standard deviation increases by that amount and therefore the
37
competitive balance decreases. The length of the NFL season has been set at 16 since the first
season in the sample of 1980, however there were two occasions when the league played a slate
of games that was under 16 due to a strike. According to the regression, those seasons were more
competitive than the full length seasons. Once again this follows the logic of Groot (2009)
which states that the better teams will separate themselves when given more time to do so. Groot
commonly relates this to the scoring of an individual game, but the idea can be applied to the
overall season and number of games as well.
Once again an examination of the R-Squared values is useful for evaluating each model.
The results for these two regressions are better than the ones seen with MLB. The dHHI
regression has an R-Squared value of .3078 and the SD has a value of .6052. Once again, the
standard deviation regression shows as a more reliable source of examining the competitive
balance in this league. Also the value of .6052 is a much higher than the other three regressions
seen thus far.
The National Basketball Association is a particularly interesting case because it is
the least competitive in regards to the HHI measure. Looking at this league’s champions for the
sample size helps to explain why this has the least balance. Since 1980-1981, the Los Angeles
Lakers won ten championships, the Chicago Bulls won six, the San Antonio Spurs won five,
Boston Celtics four, Detroit Pistons three, and Miami Heat three. When six teams have won 31
of the 36 championships this does not signal league wide balance. However, the recent history
of NBA champions could show a new trend. Looking at the NBA from the 2010-2011 season
until now, six of the seven champions have featured a different franchise. Although it is worth
noting that Lebron James has won three, two with Miami and one with Cleveland. Once again
looking at a regression provides more insight into the inner workings of how he NBA got to this
38
point and what could change it in the future. The variables from Table 4 are the same as MLB
with the only rule change being the introduction of a replay system. These results once again
feature the full 36 seasons. The NBA regression shows a few insights that were not seen by the
previous two leagues. Also for the first time there are not any omitted variables due to
multicollinearity.
R-Squared
# of Observations
Variable
Salary Cap
Free Agency
# of Teams
# of Playoff Teams
Revenue Sharing
Length of the
Season
Replay
Attendance
Constant
Table 4
National Basketball Association
dHHI
Standard Deviation
.5276
.5565
36
36
Coefficient
t-value
Coefficient
t-value
-.0021*
-2.03
8.082
-0.62
-.0012
-1.63
-.5322
-0.55
-.00008
-0.21
.7736
1.53
-.0002
-0.61
.5034
1.32
.0005
1.01
.4475
0.67
-.00001
-0.50
.1871*
5.21
-.0004
.0000009
-.0033
-0.80
1.67
-1.4464*
.0008
-19.0771
-2.30
-1.20
In the dHHI model the only significant variable is the introduction of a salary cap. The
coefficient is negative which implies it would decrease the dHHI and in turn increases
competitive balance. The coefficient is not large and only minimally increases competitive
balance. This falls in line with Coase theorem talked about in the theory section. When a salary
cap is implemented the better teams cannot afford to sign all of the best players, so it levels
league wide talent to an extent. Despite the fact that it is not significant, the free agency variable
is worth looking at. A t-value of greater than 1.69 or less than -1.69 signifies a significant
variable. The t-value of -1.63 on the free agency variable shows that this was nearly significant
as well as attendance with a t-value of 1.67.
39
Looking at the standard deviation of wins regressions tells a different story for the league.
Length of the season is once again significant along with replay. The length of season
coefficient is largely positive and implies that more games would significantly decrease
competitive balance. Length of the season has a similar explanation to the National Football
League. While the season length has been 82 games since before the 1980-1981 season there
were two seasons shortened by a strike. This regression is the first time that replay has been
found to be significant, and it has a negative coefficient which increases competitive balance.
This is the expected result because replay would lead to more perfect refereeing. The coefficient
of -1.4464 is a massive coefficient and implies that the introduction of replay dramatically
increased the competitive balance in the National Basketball Association.
The final step is to examine the regressions to one another and once again we use the RSquared result to do so. The HHI regression has a value of .5276 and the standard deviation of
wins has a value of .5565. Therefore, the HHI covers 53% and the standard deviation covers
56% of the variation. While the standard deviation is higher the difference is not large enough to
clearly show which regression model should be the most utilized model.
The National Hockey League is perhaps the most interesting league to study. Out
of the four leagues studied in this paper it has had the least amount of consistency from the first
year until the most recent. This is not in terms of HHI or SD, but in terms of the actual data for
the league. It had the largest number of expansion teams increasing from 21 in 1980-1981 to the
current 30 that it has now. Despite only having 21 teams in 1980 the league has never changed
the number of playoff teams which is consistent at 16. While the regression later will show that
the number of playoff teams is omitted, it is still astounding to allow about 76% of the league
into the playoffs. The league also changed their number of regular season games twice (not
40
including strike shortened seasons) from 80 to 84 and then down to 82. Perhaps the most unique
thing about the NHL is the 2004-2005 season when the entire season was lost due to a lockout.
This is why the number of observations for the following regression table is 35 and not 36.
Considering all of these events it makes sense that the NHL is tied with the highest standard
deviation of HHI values. The regressions in Table 5 for the NHL provides some of the best and
most useful signals in understanding the competitive balance.
The regressions also include the most rule changes out of all the regressions ran in this
study with a total of four. These include sudden death overtime, overtime point, shootout, and
three on three overtime. The NHL does not operate on a system of wins for playoff seeding, but
instead uses points which are awarded 2 for a win and later on 1 for losing in overtime or a
shootout. Eventually the NHL made the regular season overtime five minutes and if no
one scores in the period, the game goes to a shootout game similar to penalty kicks in soccer.
Lastly the NHL decreased the number of skaters in overtime from four on four to three on three
to increase the fast paced action. These two regressions and in particular the dHHI model
provides the largest number of significant variables compared to the previous regressions. There
are also three variables that are omitted in each regression, which are number of playoff teams,
revenue sharing, and shootout.
In the dHHI regression from Table 5 on the next page salary cap, length of season,
overtime point, and attendance are all significant. Salary cap and overtime point are both
positive, and as such, decrease competitive balance in the league by .0051 and .0036
respectively. This goes against the logic of a salary cap, because it is a measure that is meant to
even out the league. Perhaps this
Table 5
41
R-Squared
# of Observations
Variable
Salary Cap
Free Agency
# of Teams
# of Playoff Teams
Revenue Sharing
Length of the
Season
Sudden Death
Overtime Point
Shootout
3on3 Overtime
Attendance
Constant
National Hockey League
dHHI
Standard Deviation
.8728
.4211
35
35
Coefficient
t-value
Coefficient
t-value
.0051*
5.40
.9928
0.74
.0011
0.78
1.9189
0.92
.0003
1.50
.3360
1.05
Omitted
Omitted
Omitted
Omitted
-.0001*
-3.26
.0398
0.77
.0001
.0036*
Omitted
.0022
-.00000186*
.0232
0.08
2.99
1.36
-2.68
3.0708
-.9168
Omitted
1.9448
-.0034*
54.6979
1.52
-0.53
0.82
-3.40
is a result of it being a 0/1 variable and it is picking up other factors other than just the salary
cap, hoever without further examination of this issue it is impossible to know exactly why this
could possibly be the case. Rewarding a team for an overtime loss with a point also decreases
balance. This makes sense because a better team would win or go to overtime more often than a
bad team, and this would allow them to accumulate more points than the worse teams. The two
variables that improve the competitive balance are length of the season with a coefficient of .0001 and attendance at -.00000186. These two variables have been significant in previous
leagues and the same logic holds true in this case. Length of the season in the NHL has more
impact due to the two times the league changed the overall number of games as well as having
two shortened seasons of 48 games, but the length of the season variable would hold only minor
impact in non-strike years because of the small value in this regression. Attendance could
42
showcase a significant impact in periods of large attendance swings even with the small
coefficient.
The standard deviation of wins regression shows only attendance being significant, but it
has a much stronger coefficient than the dHHI regression. It is once leads to an improved
competitive balance, but has a coefficient of -.0034.
When looking at the R-Squared values for these two models the results are not even
close. The dHHI model has a value of .8728 and the standard deviation sits at .4211. The dHHI
R-Squared value is significantly higher than any of the other leagues showed as it covers 87% of
the variation. Not only is it the best model in the case of the NHL, but it is the most accurate
model that was used in this paper.
V. Conclusion
The professional sports leagues themselves can look into research such as this and make
important decisions to improve the overall health of their league. It is a vital thing that all
leagues must do to avoid being surpassed in popularity by another sports league. This could be a
reason why the NHL has made so many changes since 1980. It is largely viewed as the fourth
most popular sport in the United States, and therefore feels pressure to change to attract or even
maintain fans. Conversely the other three leagues have had minimal if any major rule changes
that were included in this paper. It would be expected that if one of these other three would
desire more interest they may adopt a new rule.
Using two different models in measuring the competitive balance is useful, but it might
be preferable to identify the most efficient way. Overall in the four sports leagues, using the RSquared as a judging tool, standard deviation was seen to give more accurate results as it was
more efficient for MLB, NFL, and NBA regressions. The HHI model was vastly more efficient
43
in regards to the NHL and it was marginally close in the NBA as well. However this is merely a
small sample size of this type of research, and does not portray the final answer so to speak.
This paper features a few things that could be built upon, but also some things that need a
total overhaul. One of the easiest changes could be to expand the sample size to include more
than 36 seasons to give a more complete view of each league. Another addition could be the
inclusion of more variables that could pertain to competitive balance. Along those same lines,
the rule change variables present a unique problem to future research. These can be relative to
the author or authors conducting the research, because one person might view a rule change as a
major variable and another could view it as insignificant. Using different methods of
determining the competitive balance is a technique that Larsen, Fenn, and Spenner (2006) did as
well and was mirrored in this paper. Implementing more than the HHI and standard deviation of
wins would only provide clearer results and should be considered. Lastly most articles focus on
one league in particular, but providing multiple leagues to use as reference provide some insight
not able to be noticed otherwise. This paper indicates that MLB has had the most balance since
1980-1981 and that the NBA has been the worst. Not only does it provide comparison between
the leagues it also emphasizes which factors would be seen as the most important having
appeared numerous times across several leagues. Length of the season and attendance appeared
several times and should be viewed as two of the major factors in the overall balance of the
league being studied.
One of the largest flaws with this paper and for all papers like it is the use of 0/1
variables. 0/1 variables can sometimes portray broad or even unrelated factors because
something else could have occurred during those years that effected balance, not necessarily the
variable included. An example would be maybe you have a 0/1 variable for the NBA that starts
44
in 1984 and it shows that it hurt competitive balance. This could be misleading because in 1984
Michael Jordan entered the NBA that 0/1 variable could be influenced by his entrance and not
only the intended variable. There is also the problem of multiple 0/1 variables picking up on one
another and showing the same information, which was seen by the numerous cases of
multicollinearity found in this paper. There is not a way to avoid this without leaving out one of
the variables from the regression. Especially in the case of the NFL where the salary cap and
free agency were introduced during the same season. This problem is one that may not have a
better solution.
The overall purpose of the paper was to identify which league has been the best at
handling competitive balance and recognize what impacts it. As previously mentioned length of
the season, attendance, a few rule changes, salary cap, and number of teams have all been seen to
impact the balance, but the length and attendance were the most consistent. Therefore it would
be logic to believe that these are two of the most important factors of competitive balance.
As for the question of which league handles it best, that answer is not as clear. As
previously stated the SD of wins is not able to be compared across leagues because of the
different number of games each league plays. Then the HHI was extremely close between the
NFL and MLB. MLB had a lower mean HHI across the 36 seasons that was .0001 lower than
the NFL. While the NFL had the lowest deviation of the HHI values across those same 36 years.
It is too close to come to a solid conclusion using only the data in this paper, but the results are
not useless. While the difference between the NFL and MLB was minor, the difference between
the NFL and the NHL (the second and third lowest HHI values from Table 1) is larger. The NFL
is .0017 lower than the NHL and .0034 lower than the least balanced NBA. Thus it is safer to
conclude that while it is not possible to determine the league that handles it best, it is possible to
45
rule out the NHL and NBA so to speak. To find the full answer more research into this topic
would be required.
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