Comparing the Revenue and Profit Effects Major League Baseball Team

Comparing the Revenue and Profit Effects
of Winning and Having a Star Player for a
Major League Baseball Team
Haverford College
Economics Department
Thesis Advisor: Anne Preston
2006
By Jon Kelman
1
Abstract
This thesis studies the revenue and profit effects of winning and having a star player for
Major League Baseball (MLB) teams over the period of 2000-2004. Regression analysis is used
to determine the revenue and expenditure effects of having a star player and winning; the two are
then compared to gauge profits. The analysis also attempts to find the value of stars and winning
for teams from different sized cities, as well as the marginal revenue product of star players as
the number of stars on a team increases. The findings are used to determine the best financial
strategies for MLB teams.
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Table of Contents
Introduction………………………………………………………………….....5
Previous Research……………………………………………………………...7
Dependent Variables……………………………………………………….....14
Independent Variables………………………………………………………..17
Revenue Findings……………………………………………………………..24
Effect of City Size on Revenue……………………………………………….32
Marginal Revenue Product of a Star………………………………………….36
Expenditures and Profits from Star Players and Winning…………………....41
City Population Effects on Expenditures for Star Players and Winning……..45
Marginal Expenditures for Star Players………………………………………51
Summary of Findings…………………………………………………………54
Team Strategy Implications…………………………………………………..56
Bibliography……………………………………………………………….....58
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I firstly want to thank my parents for their amazing support in all of life’s
endeavors. I also would like to acknowledge the kind people at ‘Baseball
Prospectus’ who helped me obtain most of my data, and my thesis
advisor Anne Preston, who is always helpful and graciously dealt with
my numerous last-minute meetings.
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Introduction
It is often forgotten that all major professional sports teams are businesses. Although
there are owners who use their team for leisure purposes, perquisites, political power, and tax
sheltering, the goal of most professional sports teams is to maximize profits. One would think
that the most obvious way to maximize revenues is to field a winning team, but winning teams
can be very costly, and thus do not necessarily maximize profits despite maximizing revenues.
A team can be unsuccessful in winning, but very successful as a business. An example is the Los
Angeles Clippers of the National Basketball Association (NBA); the Clippers are known as the
least successful franchise in major professional sports. The team has never won an NBA
championship, and is almost always near the bottom of the league in winning percentage. The
team’s lack of success is no accident, however, as the owner strives to make profits at the
expense of winning. By playing in a large market, the Clippers are able to attract fans despite
their lack of success. The owner of the team, Donald Sterling, recognizes the situation and thus
seeks to minimize payroll to reduce costs. The team is known to earn over $10 million in profits
annually, a substantial figure for an NBA franchise.
The financial success of the Clippers indicates that factors other than winning can drive
revenues. The primary sources of revenue for a professional sports team are game attendance,
media (television and radio) contracts, sponsorships, concessions (all purchases within a stadium,
including food, beverage, and parking), and merchandise (team memorabilia purchased outside
of the stadium). Concessions and attendance are inexorably linked, as are sponsorships, media
contracts, and attendance. These revenue sources depend on several factors, including team
success, geographic location, and team facilities such as a new stadium. For example, a large
part of the Clippers financial success stems from their location in Los Angeles. Teams from
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larger cities have a larger fan base to draw attendance from, and also have larger television
audiences. Interestingly, the Clippers are not the only NBA team in Los Angeles, yet are still
able to attract more fans than a smaller market team that wins more games. Teams with new
stadiums have also shown increased attendance for a few years after the stadium is built
(approximately five years in Major League Baseball). Teams from larger cities are more able to
field winning teams and build new stadiums, however, so it is difficult for teams from smaller
cities to compete.
Another source of revenue for a professional sports team may be having a ‘star’ player (a
star player being one with great skill or popularity). A star player can result in improved
competitive success; a winning team can market itself as successful, whereas a losing team has
much more limited marketing opportunities. A star player can also give the team a marketing
platform regardless of team success; that player will become ‘the face of the team’ and be
featured on every team publication and printed item, as well as all advertisements. Not only will
a star player draw more attention to a team, and thus cause higher attendance, greater concession
sales, larger media contracts, more sponsorships, and will significantly boost merchandise sales.
The value of a star that extends beyond his contribution to winning must be measurable, but what
is the value of a star player?
The central problem with this specific question is that star players are generally on
winning teams. Not only do winning teams create star players by giving the player more fan and
media exposure, but star players are also better players, and thus help their teams win. In Major
League Baseball (MLB), there has been research performed within the past decade that has tried
to measure the exact athletic value of each player. Whereas the exact value of a player in a
dynamic team sport such as the NBA is seemingly impossible to measure, the value of an MLB
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player is estimable as is the degree of responsibility for the team’s success. The potential for star
players to have value beyond their contribution to team success leads to the question of what is
the value of a star player beyond contributions to team success in relation to the value of
winning? The study will have great implications for MLB, as it can be used to judge player
personnel decisions and overall front-office philosophies.
Previous Research
Previous research has generally neglected to value the revenue impacts of individual
players. The only author performing any work on the specific topic is Nate Silver, a writer for
Baseball Prospectus. Silver has written multiple articles trying to evaluate an individual player’s
revenue value by finding how many games he causes a team to win, and then translating those
wins into revenue gains. In his series of articles for Baseball Prosepectus “Lies Damned Lies”,
Silver (2005b) details the positive revenue effects of the Florida Marlins trading away most of
their highest paid players in an effort to increase profits during this past/current season.
Although fans are frustrated that their team is essentially committed to being a losing team next
season, Silver finds that selling talent was in the best interest of the Marlins organization. His
basic premise is that the marginal value of a few more wins that are brought by a star player are
not cost effective to a team that will not make have a significant chance of making the playoffs
or winning a championship. The Marlins situation is very similar to that of the Los Angeles
Clippers, who also do not stand to gain from building a more competitive team. Another piece
by Silver (2005a) from his series “Lies Damned Lies” studies the value of MLB free agents from
the 2005 off-season in relation to the contracts they received. Silver uses two measures
developed by ‘Baseball Prospectus’ (2006), Value Over Replacement Player (VORP) ratings,
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and a system called PECOTA, which projects future player performance. ‘Baseball Prospectus’
(2006) defines VORP as ‘a statistical measure of the number of runs contributed by a player
beyond what a replacement-level player at the same position would contribute if given the same
percentage of team plate appearances; VORP scores do not consider the quality of a player's
defense’. VORP ratings are similar to Wins Above Replacement Player (WARP), which
translates the runs into wins. The PECOTA rating system uses a number of factors to predict
player performance on a yearly basis, including VORP. Simply, player performance is predicted
by comparison to past players who had similar profiles. Silver’s article takes the first step
toward evaluating an individual player’s total value by determining the number of a wins a
player is worth and how much money a win is worth. Silver, however, does not discuss the fact
that wins can be worth different amounts to different teams, nor the marketing value of players
beyond contributions to team success. He notes at the end of the article that teams are paying
$2.14 million per win, which may mean that all players are being overpaid in that free agent
class.
Silver’s (2006) most recent article, “Is Alex Rodriguez Overpaid” is the most interesting.
Silver uses the revenue figures obtained from the Cleveland Indians 1997 season, when the team
went public for a year and thus released detailed financial records, as well as financial data from
all MLB teams during 1997-2004. Silver uses the data to find the revenue from marginal wins,
and in his ‘Linear Model’ finds one win to be worth $1.196 million. By using WARP, he is able
to find the revenue added by the wins created by the player. Silver also creates a ‘Market-Price
Model’ and ‘Two-Tiered Model’. The ‘Market Price Model’ finds the value of one win by using
the salary paid in the free agent market, and the ‘Two-Tiered Model’ improves upon the ‘Linear
Model’ by accounting for each additional win’s value in increasing the likelihood of a playoff
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appearance. As Silver points out, however, each win is not worth the same amount in reality. A
win is worth far less to the best and worst teams in the league; each win is far more valuable to
teams that are on the cusp of a playoff appearance. For example, the seventieth or one-hundredth
win for a team is worth about $600,000, whereas the ninetieth win is worth $3.5 million. One
area missed by Silver, however, is that star players can have economic value in more than just
creating wins, in terms of ‘star quality’ that attracts fan interest above and beyond competitive
success. Although the Los Angeles Clippers games nearly sell-out and the team easily receives
media attention, the Florida Marlins have very small attendance figures and media exposure and
thus may benefit from a star player. Silver’s analysis and regressions are, however, almost
identical to those used in this thesis. His work has been particularly helpful in deciding which
variables to include in the model.
There have also been articles indicating that Value-Over Replacement-Player (VORP),
the measure of how valuable a player is towards a team’s on-field success, is undervalued. In an
article from 2004 titled “You Get What You Pay For: Are Major League Teams Overpaying for
Power?”, Ben Murphy and Jared Weiss (2004b) found that teams are paying more money for
players with high power statistics (high amounts of homeruns, triples, and doubles). Teams are
undervaluing players who single and walk more frequently, and are actually more valuable to a
team’s success. The authors, however, do not discuss the possibility that ‘powerful’ hitters are
more popular with fans and thus more valuable in a revenue sense than their VORP would imply.
Weiss and Murphy (2004a) have also written an article titled “Predicting Future Salaries: A
Simple Model”. In the article, the authors find the best model for predicting future salaries is to
take 94% of the previous year’s salary, and then modify that figure depending on last year’s
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VORP. The striking finding of the article is that once a player is paid a certain salary, he will
continue to receive that amount, as his on-field performance will only affect his salary slightly.
Although the economic value of specific players has not been well researched, there have
been many articles written on the revenue effects of winning in MLB. Most notably, recent
Haverford graduate Aaron Rabinowitz (2003) wrote about the value of an additional win to each
MLB team. Aaron’s findings suggest that wins are worth more to larger market teams than to
smaller market teams.
The effect of a new stadium on attendance has also been researched by several people;
the findings have been relatively consistent in that new stadiums produce an attendance boost for
a three-to-ten year period. Recent research by ‘Baseball Prospectus’, however, has indicated that
the attendance boosts are declining, and that the length of the attendance increase is five years or
less in the newest MLB stadiums; the attendance also decreases every year during that period,
until falling back to previous levels. As discussed, many revenue sources are interrelated in
professional sports. Thus, a University of Texas at Arlington professor, Craig Depken (2004),
has examined the effects of a new stadium on concession sales. His findings indicate that game
attendees at a new stadium spend $2.86 more per person than at the old stadium. Depken,
however, does not examine how concession sales vary as attendance in the new stadium declines.
Merchandise sales have been under researched. Rankings are given annually of the bestselling players’ jerseys, but these rankings come from a select few locations, and are not
representative of all retailers in the US. The actual number of jerseys sold for each player are not
given publicly, thus making it difficult to gauge how popular each player is in relation to others.
Although merchandise sales comprise a relatively small portion of total revenue for an MLB
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team, the lack of data and research proves problematic in creating a model that accounts for
player marketability.
Purpose
The goal of my thesis is to bridge the gaps between these previous research articles and
extend their analyses to compare the effects of winning and having a star player on total team
revenue. Most of my work will come from regression analysis. I will study all thirty MLB
teams over a five year period. I plan to use different dependent variables, all related to revenue,
including total revenue, gate revenue, local media revenue, and operating income. My
independent variables will include many of the factors mentioned in previous research: winning
percentage in the previous season, city population, city median per capita income, playoff
appearances in the past ten seasons, new stadium, and stadium quality. I will also account for
team history by including past championships won by the team.
The more novel part of my research is to discover the effects of the star player. I have
used two star player variables1; the first identifies the twenty position players and ten pitchers
with the highest VORPs in each season. Each team is then assigned a variable based on how
many stars they employ in a given season. The second measure of stars is All-Star game
appearances. All-Star game starters are voted by fans, and the rest of the roster is filled by the
manager’s choices of the best players in his league. All-Star game participants should thus be
viewed as the best and most popular players in MLB. Unfortunately, I have been unable to use
merchandise sales as a measure of stardom due to lack of data. Not all stars are great players; the
best example being players who were once stars, and although they are still popular, have
1
A third measure of a star player was also attempted by using the Highest VORP of a player on each team for each
season. The variable yielded statistically insignificant coefficients in all regressions, however, and thus has been
excluded from the analysis.
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suffered dramatic declines in their VORP. These players can still be used as marketing
platforms, and thus should be included as stars. There are also players who are popular in
specific regions, for example a Latino player in a predominantly Hispanic market, who are not
otherwise counted as stars. Another method considered to evaluate a star player was salary, as
the best and most popular players are generally given the highest salaries. Because lucrative
contracts are given in professional sports for varying reasons, salary may give a poor definition
of a star player, and thus is not used. A measure using total endorsement revenue for each player
was also considered, but not used due to lack of data.
I have used the star player variables as independent variables, trying to determine their
effects on revenue holding constant for all of the other aforementioned variables. Most
importantly, I can separate the revenue effects of increased team winning percentage from all
other revenue effects of a star. Understanding which aspects of a franchise affect which aspects
of revenue has great implications for MLB teams and players.
As there has been much research on the effects of winning on attendance, the goal of my
research will be to specifically investigate the overall effects of a star player. I will not only
attempt to find which revenue inputs are affected by star players, but also how much these inputs
are affected. The analysis has been extended to a star’s effect on operating income by comparing
revenue to expenditure. The marginal value of a star may be different as the number of stars
changes, thus the analysis has also sought the marginal value of a star as number of stars
increases. Different teams are also likely to have different responses to star players, as was the
case with winning in Rabinowitz’s (2003) thesis, thus the analysis will be extended to compare
teams from different market sizes in terms of revenue and expenditures.
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The revenue effects of star players will be compared to the revenue effects of winning.
The revenue effect of winning is manifested in several ways. As Nate Silver (2006) notes, each
extra game won brings a team closer to the playoffs, which he estimates to have a $30 million
impact on current revenues; therefore, the relationship between winning and revenue is not
necessarily linear. As with current and lagged winning, a current playoff appearance also helps
future revenues. Similar to the analysis of star players, the effects of winning on revenue and
expenditures will be estimated and compared to gauge operating income and finally used to
compare revenue and expenditures for teams from different sized markets. A comparison of the
results between star players and winning will show what type of strategy different teams should
pursue.
I will first determine the revenue effects of winning and having a star player. I will then
explain whether the revenue effects change for different sized markets. Then, I will attempt to
determine the marginal value of a star as the number of stars increases. I will then perform the
same analysis on expenditures by firstly determining the expenditures associated with winning
and having a star player, then examine the expenditures for different sized markets, and finally
determining the marginal expenditure associated with a star as number of stars increases. The
revenue effects will be compared to the expenditure effects in the expenditure section to gauge
profitability.
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Table 1: Summary of all Dependent Variables Examined (all in millions of dollars)
Total Revenue
Gate Revenue
Other Revenue
Local Media Revenue
Total Expenditures
Player Expenditures
Other Expenditures
Operating Income
Observations
150
150
150
89
150
150
150
150
Mean
123.740
45.816
77.924
20.990
121.796
76.646
45.151
2.012
Standard Deviation
35.784
25.559
17.188
14.413
37.562
30.075
13.522
12.963
Minimum
53.9
2
44.4
0
52.2
18.2
-21.3
-37.1
Maximum
264
143
127
63
301.1
197
104.1
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Dependent Variables
Total Revenue1
The most basic dependent variable measured is total revenue for each team. Total
revenue includes all forms of revenue, including gate receipts, concession sales, sponsorship
revenue, merchandise sales, and local media revenue. The values for the variable, as well as all
the other revenue related variables, have been derived before taxes, interest, depreciation, and
amortization. One of these taxes is MLB revenue sharing, which essentially takes money from
wealthier teams and gives money to the lower revenue teams. The revenue sharing is accounted
for in later analysis, but not in the regressions. As seen in table 1, the mean revenue figure is
$123.74 million, but varies greatly from $53.9 million to $264 million. Although teams do not
generally release financial data, the total revenue figures were obtained from Forbes via Rodney
Fort’s “Sports Business Data Pages” website. The MLB commissioner’s office did release
financial figures in 2001 as part of the “Blue Ribbon Panel”, but these figures are generally
viewed as incorrect in comparison with the Forbes estimates.
1
All revenue, expenditure, and winning data from “Rodney Fort’s Sports Business Pages” (Fort 2006)
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Gate Revenue
Gate revenue includes all revenue received from game attendance. The gate revenue thus
includes not only game day ticket sales, but also season ticket sales and luxury box/suite sales.
As seen in table 1, the mean is $45.816 million, but has a large standard deviation of $25.559
million. Unlike many other revenue sources, gate revenue is not strongly related to contracts and
can thus change very quickly in response to changing environment around the team. In other
words, if the team suddenly starts winning more games, gate revenue should immediately
increase.
Other Revenue
Other revenue is all revenue that is not gate revenue; the figures for the measure were
obtained by subtracting gate revenue from total revenue. Other revenue thus includes
sponsorship revenue, concession sales, local media revenue and merchandise sales. The measure
is somewhat vague, as it covers several types of revenue, but is useful when used in comparison
with local media revenue figures. The measure includes forms of revenue that are able to
respond quickly to changes in the team, but also includes revenue sources that are unable to
respond quickly. Concession and merchandise sales are able to quickly respond, but sponsorship
and local media revenue are derived from multi-year contracts, and thus do not generally respond
to sudden or brief changes to the team. The measure should thus show slight responses to
sudden team changes, but will not react as dramatically as gate revenue.
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Local Media Revenue1
Media revenue includes all revenue from local media, namely television and radio
contracts. In lower revenue professional sports leagues, such as the NHL, television and radio
contracts are such that the teams are given a certain amount of airtime and receive revenue by
selling advertisements (while giving some of the money back to the network). MLB teams,
however, are popular enough that local media outlets pay for the rights to broadcast their games.
The networks then maintain the rights to all revenue received through advertisements. The local
media revenue figures were obtained from Broadcast and Cable Magazine. The figures were
given as a sum of television and radio contracts, and thus cannot be separated for more in-depth
analysis. The figures were not released for 2002, and were unavailable for 2004, leaving only 3
years of observations2. As the figures were also obtained from a different source than the other
revenue variables, they differed slightly from Forbes estimates (Forbes estimates were generally
lower). The data was thus not subtracted from ‘other revenue’, as the figures could be
misleading. As seen in table 1, the mean value is $20.99 million, but local media revenue varies
greatly from $0 to $63 million3. Similar to gate revenue, the local media revenue data indicate
how a specific revenue source is affected by the independent variables. The local media data can
also be compared with ‘other revenue’, as an indicator of which portion of ‘other revenue’ is
affected by the independent variables (the local media revenue portion, or the sponsorship sales,
merchandise sales, and concession sales portion). Unlike gate revenue, local media revenue is
derived from contracts and is thus slow to react to changes in a franchise; therefore, should a
team suddenly start winning more games, the local media revenue will not increase unless the
1
Local media revenue data received from Nate Silver, who compiled the data from “Broadcast & Cable Magazine”
The Montreal Expos did not report their local media revenue in 2001, thus leaving 89 total observations over the
five year period.
3
The Montreal Expos did not have any local media contracts in 2003, and thus did not have any local media revenue
for the year.
2
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current season is the last in a given contract, then the contract value may increase for the
following season.
Operating Income
The revenue measures do not account for the costs to achieve such revenue levels. A
variable has thus been included that measures operating income. Operating income is simply the
measure of a team’s total revenue minus total expenditures, or more simply, profit. As seen in
table 1, the mean operating profit is $2.012 million, indicating that MLB teams were profitable
as a whole over the five year period examined.
Independent Variables
Table 2: Summary of all Independent Variables Examined
Stars
All-Stars (past two seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Lagged Winning Percentage
Playoffs (past 10 seasons)
Observations
Mean
Standard Deviation
Minimum
Maximum
150
150
150
150
150
150
145
150
150
1
4.353
1.578
20.680
2.733
0.24
75.805
50.002
2.133
0.983
2.363
2.058
4.366
4.806
0.429
11.496
7.804
2.113
0
2
0.303
14.291
0
0
49
26.5
0
4
13
8.008
34.556
26
1
95
71.6
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Market Characteristics
City Population1
1
City population and median income data is from US census reports in 2000. The figures for 2000 are repeated for
each year in the five year period, thus there is no variation in city population for each city
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An important factor in determining individual team revenue is the market/city in which
the individual team plays. The New York Yankees and Mets play in a vastly different market
than the Kansas City Royals of Kansas City, Missouri. The variable chosen to account for
market differences is city population. As shown in table 2, the mean city population (measured
in millions of people) is 1.578, but the market sizes vary from 303,000 to 8.08 million. Previous
research indicates that teams from larger cities maintain a greater revenue flow than teams from
smaller markets.
Income
A variable has also been included for median per capita income; the variable is similar to
the one used by Nate Silver (2006) in his regressions. The values given are in thousands of
dollars. Table 2 shows a mean value of 20.680, and a standard deviation of 4.366. A wealthier
market may not only buy more tickets, but may also buy more expensive tickets and more
merchandise. A higher median per capita income should thus lead to higher revenues.
Team Characteristics
Championships1
Another factor that plays into team revenues is team history and previous success. For
example, the Boston Red Sox play in a market that is not relatively large, but are team with a
rich history and a strong following because of their history. To account for team history, a
variable for past championships is included. The championships variable includes all World
Series won in team history, with equal weight given to all championships. There are several
teams that won championships and then relocated. The championship variable only counts
1
Championship and playoff data was obtained from “HickokSports.com” (Hickok 2005)
18
championships won by the current franchise in the current city, since team success in another
city should not affect the fan base in a new city. Table 2 reveals the mean number of
championships to be 2.733, and a standard deviation of 4.806. The large variance is likely due to
the New York Yankees having won twenty-six championships, seventeen more than any other
team.
Playoff Appearances in the past ten years1
Team success is another important factor in determining revenue. On-field success can
be manifested in several ways in terms of revenue, but potentially the most lucrative is achieved
by a playoff berth. According to estimates by Nate Silver (2006), a playoff appearance is worth
approximately $25 million. The eight teams that reach the playoffs in a given year should thus
be expected to earn at least $25 million more than the other twenty-two teams. Consistent with
Nate Silver’s (2006) findings, a variable for number of playoff appearances in the past ten
seasons has also been included. The variable is intended to measure recent team success. As
seen in table 2, the number of playoff appearances in the past ten seasons varies between zero
and nine2. The variable can be compared to the winning percentage and past championships won
variables to indicate how current performance compares with recent past and distant past
performance. Unlike the variable for playoff appearance in the current season, this variable
should increase all of the revenue inputs.
Lagged Winning Percentage
1
Variables for playoff appearance in the current season and winning percentage in the current season were also
examined. Neither of the variables provided statistically significant coefficients, however, thus lagged winning
percentage and past playoff appearances were used instead.
2
The MLB strike in 1994 caused the season to end before the playoffs, thus, the highest number of playoff
appearances possible in the ten year period is nine.
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Team success also has the effect of increasing team popularity, which, in turn, lures more
fans to the ballpark, as well as increases merchandise, concession, and sponsorship sales. To
measure team success, a variable for lagged winning percentage has been included, which
measures the winning percentage from the previous season. Table 2 indicates lagged winning
percentage varies between 26.5 and 71.6. MLB teams play a 162 game schedule, thus a one
percent increase in winning percentage is the equivalent of about 1.5 more games won.
New Stadium
Another tool used by teams to increase revenues is having a new stadium. Many teams in
recent years have lobbied extensively for public funding to help build a new stadium. There
have been numerous studies on the revenue effects of a new stadium, with the prevailing idea
being that new stadiums have a ‘honeymoon effect’ of temporarily increasing revenues. The
effect wears-off gradually, and is generally negligible after five years. The profitability of such
short-term revenue gains is thus highly debatable. A 0,1 variable has been included to indicate
whether the given team has built a new stadium within the past five years1. As seen in table 2,
the mean value of the variable is 0.24, and the standard deviation 0.429. A new stadium should
have the effect of increasing attendance, as well as concession, merchandise, and sponsorship
sales.
Stadium Quality
A variable has also been included that measures stadium quality. The stadium quality
ratings were created in 2003 by several columnists for espn.com (2004). This variable is the
same as the one used by Nate Silver (2006) in his regressions. Five data points are missing
1
Stadium opening dates were obtained from “MLB Baseball Stadium” (MLB Teams 2006)
20
because espn.com compiled the survey in 2003, and ratings are not available for the old stadiums
of teams that built new stadiums between 2001 and 2003. The rating system is on a one-hundred
point scale, but table 2 indicates a high mean value of 75.805. High stadium quality should have
a similar effect on attendance as having a new stadium, in increasing attendance and concession,
sponsorship and merchandise sales.
Stars1
The central focus of this thesis is to analyze the effects of a ‘star’ player on revenue. Star
players can effect revenue by several means. Not only do star players boost a team’s winning
percentage, but holding constant for these winning percentage effects, they also increase the
team’s marketability. A star player should thus increase all forms of revenue above what would
be expected from the win shares added by the player. There are several ways to define a star
player, but only two have been used for this analysis. The first and more prominent method is
using the twenty best position players and ten best pitchers in a given season. ‘Best’ players is
defined by highest VORP. The total number of thirty stars was chosen to allow for all teams to
have one star (although considering the competitive landscape of MLB teams with zero stars
were expected). The division of twenty field players and ten pitchers was chosen due to there
generally being nine significant position players on each team and five significant pitchers
(approximately a 2:1 ratio). The variable used in the regressions is the number of star players on
the given team in the given year. As seen in table 2, the number of stars on a team varies
between zero and four.
1
VORP data for Stars and Best VORP was obtained from Baseball Prospectus’ website
21
The biggest problem with the measure is the inability to account for popular players who
do not necessarily perform well, or players who perform well and are not necessarily as
marketable. VORP also favors players who play more games, and most notably, the best relief
pitchers in baseball (of whom about three per season could be considered stars) are not included
as stars due to their limited number of innings pitched. VORP is also based on position, thus
certain positions are easier to obtain a higher VORP. Corner outfielders are generally the best
hitters in baseball, while second basemen and catchers are generally weak-hitting positions. The
result is that a catcher or second baseman who is a worse hitter than a particular right fielder
could receive a higher VORP. The variable in the regressions is essentially assuming that a
player’s relative, not absolute, value is recognized.
All Stars1
Variables have been included that represent All-Star game participants from the current
and previous seasons combined2. The variable only counts players who played in the All-Star in
the current or previous season; a player who played in an All-Star game anytime before 1999 is
not counted. As mentioned previously, All-Stars are determined by a fan vote and manager
selection. Every team has at least one All-Star representative each season. All-Star selections
who were unable to play in the game, as well as their injury replacements have both been
counted. Thus, there are about sixty to seventy All-Stars in each season. As seen in table 2, the
mean number of All-Stars is 4.353, with a standard deviation of 2.363.
1
All-Star data was obtained from MLB.com (2006)
Variables for All-Stars in the current season and All-Stars in the previous season were also examined separately,
but were not as statistically significant as combined number of All-Stars over the two-year period. The lagged AllStar variable was statistically significant, and indicates an over $3.4 million increase in total revenue for each AllStar, with $2.4 million manifested in gate revenue.
2
22
The reasoning for not using career All-Star appearances is that many of the players who
are commonly considered stars are young and have not been selected to many All-Star games.
Similarly, there are many players who accumulated All-Star game appearances in their prime,
but fade from stardom in the last few years of their careers. A variable using career All-Star
appearances would not have counted Derek Jeter as an All-Star, despite the fact that he is
arguably the biggest star in baseball.
The variable used is nonetheless flawed. Despite hardly being considered stars, there are
always several players who have one spectacular season and are selected. Baseball’s biggest
stars are also prone to injury, and thus occasionally miss an All-Star game. Generally, however,
most of the biggest stars receive All-Star recognition based on reputation and past performance
(usually by fan balloting). The lagged All-Star idea is also be troublesome as the variable does
not account for All-Stars who change teams after the season. The reasoning behind using AllStar appearances from the previous and current seasons combined is an attempt to find players
who are truly stars. If a team has two All-Stars, those two players should be on the All-Star team
every season. Problems arise if one other player on the team suddenly has a great season and
becomes the team’s third selection to the All-Star game. By combining two seasons of All-Stars,
those abnormal All-Star appearances are given less weight than players who are All-Stars every
season. Another problem with this variable (as well as the other two All-Star variables) is that a
team with one star player will appear similar in the data as a team with no star players, as both
teams will receive one All-Star selection per season.
23
Revenue Findings1
Table 3: The Effect of Stars and Winning on Total Revenue, Gate Revenue, Local Media
Revenue, and Total Expenditure
Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
Total Revenue
4.314***
(2.60)
0.243
(1.02)
5.234***
(5.76)
6.310***
(7.32)
1.177***
(3.09)
1.321***
(3.40)
6.049*
(1.67)
0.976***
(7.10)
9.878**
(2.17)
11.399**
(2.51)
17.948***
(3.97)
27.950***
(6.15)
145
Gate Revenue
5.213***
(3.38)
0.568**
(2.57)
1.984**
(2.35)
2.736***
(3.42)
0.701*
(1.98)
1.284***
(3.55)
7.696**
(2.29)
0.721***
(5.64)
-0.171
(-0.04)
-3.816
(-0.90)
-1.779
(-0.42)
2.910
(0.69)
145
Local Media Revenue
1.258
(0.92)
-0.461**
(-2.41)
4.034***
(5.33)
1.948***
(2.90)
0.270
(0.89)
0.133
(0.45)
-4.490
(-1.57)
0.334***
(3.10)
0.459
(0.17)
n/a
1.632
(0.59)
n/a
85
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
1
All revenue findings do not account for MLB revenue sharing payments unless otherwise noted. MLB revenue
sharing is a payment of 34% of all locally generated revenues from each team into a league-wide pool, which is then
divided equally amongst all thirty teams. There is also a second form of revenue sharing as described by Silver
(2006) called a ‘split pool’ system, which varies the revenue sharing payments such that in 2005, the highest
grossing team, the New York Yankees, paid 39% of their local revenues and the lowest grossing team, the Kansas
City Royals, paid 47%. In the rest of the analysis, revenue sharing payments of 47% and 43% are used, which
account for the highest payment and the average of the Yankees and Royals figures.
24
Market Characteristics
City Population
Table 3 reveals the total revenue, gate revenue, and local media revenue effects of the
independent variables. All of the variables generally agree with their individual hypotheses. As
assumed, higher city populations lead to higher revenues. Table 3 indicates that a one million
person increase in city population leads to a $6.31 million increase in total revenue. The revenue
gain is manifested almost equally in gate revenue and other revenue streams.
Income
Table 3 shows that per capita income effects also support the hypothesis that cities with
higher median per capita income have greater revenue flows. A one unit increase in median per
capita income leads to a $1.177 million increase in total revenue. The revenue gains are realized
relatively equally between gate revenue and other revenue. The data gives slightly different
results, however, than Nate Silver’s (2006) findings that indicated only a $7 million revenue
difference between the highest and lowest per capita income cities. This data shows an over $40
million revenue difference between the highest and lowest per capita income markets per season.
Team Characteristics
Championships
As hypothesized, table 3 indicates winning a championship has a positive and statistically
significant effect on revenue. The data estimates a $1.321 million increase in total revenue for
every championship won, with almost all of the revenue coming from gate receipts.
25
New Stadium
Table 3 shows a $6.049 million increase in revenues from having built a stadium in the
past five years. Although the regressions do not match up well (showing a new stadium as
having a negative effect on other revenue), the data does show that almost all of the revenue gain
is realized in the form of gate receipts. The results generally agree with the hypothesis, although
one would expect sponsorship, concession, and merchandise sales to increase from the presence
of a new stadium in addition to gate revenue.
Stadium Quality
In accordance with Nate Silver’s (2006) findings, the stadium quality variable in table 3
was highly statistically significant. The data indicates a $976,000 revenue gain from a one point
increase on the rating scale. As expected, the revenue gain is mostly realized in gate receipts.
Oddly, however, table 3 indicates that the other revenue gains appear to mostly be attained from
local media contracts. Such a finding is perplexing, as logically the revenue input that should be
least affected by stadium quality is local media contracts. The variable is the only one obtained
through an arbitrary measure, which could be the cause of confusing findings. The high
statistical significance, however, should remove some of the doubt.
Lagged Winning Percentage
Table 3 shows lagged winning percentage to only be statistically significant and logically
correct for gate revenue. A one percent increase in lagged winning percentage leads to about a
$568,000 increase in gate revenue. The lack of statistical significance limits the analysis in
finding the effects of lagged winning percentage on total revenue and other revenue sources. A
26
simple solution to the problem was achieved by running a regression similar to those in tables 3
and 4, but excluding past playoff appearances. The data shows an over $700,000 revenue gain
from each percent increase in winning percentage the previous season, with almost all of the
money coming from gate revenue. The revenue value is being overestimated, but the more
important portion of the analysis is that almost all of the revenue comes from gate receipts.
Playoff Appearances in the past ten seasons
In agreement with Nate Silver’s (2006) findings, table 3 shows the variable for playoff
appearances in the past ten seasons to be highly statistically significant. The data indicates a
$5.234 million revenue increase for each playoff appearance in the past ten seasons.
Interestingly, less than $2 million comes from gate revenue. The data is thus affirming the logic
that although past success will lead to revenue gains from all inputs, the most affected mediums
are sponsorship and local media revenue.
Stars
As hypothesized, table 3 indicates the presence of a Star player boosts revenues after
holding constant for all other variables (most notably winning percentage). Over the five year
period, each Star player adds $4.314 million to total revenue per year. Contrary to the
hypothesis, however, the revenue gains appear to mostly be realized in the form of gate revenue.
One would think that star players could have a very noticeable effect on merchandise sales in
particular.
27
Table 4: The Effect of All-Stars and Winning on Total Revenue, Gate Revenue, Local Media
Revenue, and Total Expenditure
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
Total Revenue
3.275***
(3.57)
0.020
(0.08)
4.438***
(4.76)
6.429***
(7.61)
1.181***
(3.20)
0.891**
(2.20)
6.210*
(1.75)
1.000***
(7.47)
10.064**
(2.26)
11.919***
(2.67)
17.726***
(4.01)
27.742***
(6.24)
145
Gate Revenue
2.374***
(2.69)
0.477*
(1.99)
1.535*
(1.71)
2.740***
(3.37)
0.794**
(2.23)
1.007**
(2.58)
7.575**
(2.22)
0.755***
(5.85)
-0.053
(-0.01)
-3.511
(-0.82)
-2.080
(-0.49)
2.571
(0.60)
145
Local Media Revenue
0.795
(0.99)
-0.518**
(-2.44)
3.892***
(4.93)
2.073***
(3.07)
0.320
(1.11)
0.020
(0.06)
-4.580
(-1.61)
0.345***
(3.23)
0.538
(0.19)
n/a
1.597
(0.58)
n/a
85
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Table 4 displays a regression identical to that in table 3, except the variable for Stars has
been replaced with All-Stars (combined from the past and current season). The values for the
other independent variables are similar to those found in table 41.
1
One should note that the revenue values for lagged winning percentage and past playoff appearances are slightly
lower, albeit similar, in table 4 compared to table 3. The decreased effect is likely due to the fact that there are
almost twice as many All-Stars as Stars, and the cumulative effect on revenue of All-Stars is thus higher.
28
All Stars
The variable for combined All-Star appearances from the previous and current season is
has a positive and statistically significant effect on total revenue. Table 4 indicates a $3.275
million revenue increase from each additional All-Star over the two season period. A true star
will appear in the All-Star game every year, and is thus worth $6.55 million in revenue per year.
Table 4 indicates that $4.748 of the $6.55 million will come from gate revenue.
The results from tables 3 and 4 agree with the hypothesis that star players have a positive
effect on revenue beyond helping a team win. The results vary between definitions of a star
player, but the most conservative figure from table 4 indicates a $4.314 million revenue boost
from the presence of each Star. After accounting for revenue sharing by using the same
methodology as Nate Silver (2006) by averaging the highest and lowest revenue sharing
payments made in 2005, which is 43% of all local revenue, the conservative estimate of a star’s
value becomes $2.459 million. Revenue sharing was only 20% prior to 2003, leaving the most
conservative star valuation at $3.451 million for the first three years analyzed. The values
should be much higher, however, considering the definitions used for star players are flawed.
Although the measure using VORP to determine the twenty best position players and ten
best pitchers includes baseball’s best players as stars, there are also several players included each
year who would not be considered stars, as well as several other players who are considered
stars, but fail to make the cut-off. For example, Derek Jeter is only counted as a star by the
VORP measure in two of the five years analyzed. The VORP measure is not actually indicating
the thirty biggest stars in baseball, and is thus under-estimating the effect of a star. The same
logic applies to the measure using All-Star appearances; the value of each star player is being
under-estimated in all regressions run for this analysis.
29
Table 5: The Effects of Lagged Winning Percentage and Past Playoff Appearances on Total
Revenue and Gate Revenue1.
Stars
Lagged Winning Percentage
Total Revenue
5.386***
(2.93)
0.797***
(3.29)
Gate Revenue
5.619***
(3.61)
0.779***
(3.79)
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
5.989***
(6.25)
1.544***
(3.70)
2.029***
(4.93)
1.838
(0.47)
1.080***
(7.11)
10.797**
(2.13)
12.640**
(2.50)
19.588***
(3.90)
30.571***
(6.07)
145
2.614***
(3.22)
0.840**
(2.37)
1.552***
(4.45)
6.100*
(1.82)
0.760***
(5.90)
0.177
(0.04)
-3.346
(-0.78)
-1.158
(-0.27)
3.904
(0.91)
145
Total Revenue
4.714***
(2.92)
Gate Revenue
6.148***
(4.02)
5.609***
(6.75)
6.346***
(7.37)
1.264***
(3.41)
1.339***
(3.44)
5.915
(1.64)
0.963***
(7.04)
9.878**
(2.17)
11.441**
(2.52)
17.907***
(3.96)
27.859***
(6.13)
145
2.861***
(3.63)
2.820***
(3.45)
0.905**
(2.58)
1.325***
(3.60)
7.383**
(2.16)
0.690***
(5.32)
-0.173
(-0.04)
-3.716
(-0.86)
-1.875
(-0.44)
2.698
(0.63)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
To further examine the revenue effects of winning, regressions were run in table 5 that
are similar to the basic regressions for total revenue, but instead use only one of the winning
variables. The regression using lagged winning percentage as the only winning variable reveals
1
For sake of simplicity, regressions that were run to find the value of winning, all use Stars instead of All-Stars as
an independent variable. The findings for the team success regressions using All-Stars as an independent variable
will be noted in footnotes.
30
an almost $800,000 revenue increase from a one percent increase in winning percentage the
previous season, with almost all of the revenue increase realized through gate revenue. The gate
revenue figure is about $200,000 different from the regression that includes past playoff
appearances in tables 3 and 4. The regression for past playoff appearances yields a $5.6 million
revenue increase from each playoff appearance in the past ten years, with almost $2.9 coming
from gate revenue. The past playoff appearance figure for total revenue is about $400,000 less
than in tables 3 and 4, with almost all of the revenue difference manifested in gate revenue. The
variation in coefficients in the different regressions indicates that the best estimate of the revenue
effects of winning should be gleaned from the regressions in tables 3 and 4 that feature both
winning variables. The only safe conclusion is thus that each one percent increase in lagged
winning percentage is worth at least $500,000 to total revenue, with most of the money realized
through gate revenue, and that each playoff appearance in the past ten seasons is worth over $5.2
million in total revenue, with almost $2 million coming from gate revenue.
What is the total value of a one percent increase in winning percentage? The exact value
of a one percent increase in current winning percentage is difficult to decipher. The lagged
winning percentage variable shows that a one percent increase in current winning percentage will
increase revenues in the following season by at least $500,000. The figure should rise
dramatically given that current team success should also fuel greater gate revenue in the current
season, and when considering Silver’s (2006) ‘Two Tiered Model’. As Silver discusses, each
win is not worth the same amount; more importantly, the additional value of each win towards a
playoff appearance is not realized by teams that do not make the playoffs. The value of winning
can thus be segmented into teams that know before a season that they are not going to contend
for the playoffs, and teams that know they are playoff contenders. If each playoff appearance in
31
past ten seasons is worth over $5 million, then there is an over $50 million increase in revenues
over a ten year period for each playoff appearance. The difference in value of a win for teams
from the different groups is therefore very large.
Effect of City Size on Revenue
Table 6: The Effect of Stars, All-Stars, Lagged Winning Percentage, and Past Playoff
Appearances on Total Revenue and Gate Revenue, excluding the New York Yankees from the
regressions.
Stars
Total Revenue
5.343***
(2.97)
Gate Revenue
5.867***
(3.58)
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.278
(1.14)
4.827***
(5.08)
6.100***
(6.86)
0.988**
(2.38)
0.489
(0.59)
5.548
(1.51)
1.011***
(7.14)
9.603**
(2.06)
11.548***
(2.47)
17.996***
(3.88)
27.294***
(5.87)
140
0.550**
(2.48)
1.712*
(1.98)
2.773***
(3.42)
0.724*
(1.91)
1.430*
(1.89)
7.590**
(2.27)
.720***
(5.58)
-0.762
(-0.18)
-3.842
(-0.90)
-2.591
(-0.61)
1.111
(0.26)
140
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
32
Total Revenue
Gate Revenue
3.351***
(3.46)
-0.011
(-0.04)
4.450***
(4.64)
6.524***
(7.35)
1.243***
(3.15)
1.207
(1.54)
6.368*
(1.75)
0.987***
(7.04)
10.010**
(2.17)
12.044***
(2.61)
17.498***
(3.82)
27.351***
(5.95)
140
2.590***
(2.85)
0.369
(1.48)
1.588*
(1.76)
3.093***
(3.71)
1.034***
(2.79)
2.222***
(3.01)
8.159**
(2.39)
0.707***
(5.37)
-0.482
(-0.11)
-3.656
(-0.84)
-3.188
(-0.74)
1.015
(0.24)
140
Table 6 indicates that the results from tables 3 and 4 are somewhat flawed, as the New
York Yankees skew the data by having won twenty-six championships. Table 6 yields a total
revenue coefficient that is not statistically significant, thus indicating that past championships
won may not be a good predictor of revenue.
When the New York Yankees data is removed from the regression, table 6 shows the
total revenue value of a Star increases by $1.029 to $5.343 million per year, and the value of an
All-Star increases by $76,000 to $3.351 million per year. Similar gains are also seen in the gate
revenue figures for All-Stars and Stars. Table 6 shows that teams other than the Yankees receive
$654,000 more in gate revenue from each Star, and a $216,000 increased gate revenue effect
from each All-Star.
On the other hand, teams other than the Yankees are receiving less revenue from team
success. Using the regression with the Stars variable, the other twenty-nine teams are gaining
$18,000 less gate revenue from each one percent increase in lagged winning percentage and
$407,000 less total revenue from each playoff appearance in the past ten seasons1.
1
The regressions using the All-Stars variable indicate that the other twenty-nine teams receive $12,000 more total
revenue from each past playoff appearance. The All-Star regressions, however, do not yield statistically significant
coefficients for lagged winning percentage.
33
Table 7: The Effects of City Population on the value of a Star and All-Star, as measured in Total
Revenue and Gate Revenue.
City Population and Stars
(Interaction Term)
Stars
Total Revenue
-0.782
(-1.20)
5.698***
(2.82)
Gate Revenue
-1.739***
(-2.95)
8.293***
(4.54)
City Population and All-Stars
(Interaction Term)
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.242
(1.02)
5.072***
(5.53)
7.104***
(6.54)
1.144***
(3.01)
1.399***
(3.55)
6.160*
(1.71)
0.980***
(7.14)
9.245**
(2.02)
11.053**
(2.43)
17.631***
(3.90)
26.938***
(5.84)
145
0.567***
(2.64)
1.624*
(1.96)
4.504***
(4.59)
0.628*
(1.83)
1.458***
(4.09)
7.944**
(2.43)
0.729***
(5.87)
-1.581
(-0.38)
-4.586
(-1.11)
-2.487
(-0.61)
0.659
(0.16)
145
Total Revenue
Gate Revenue
-0.179
(-0.58)
3.550***
(3.43)
-0.008
(-0.03)
4.460***
(4.77)
7.186***
(4.63)
1.220***
(3.24)
1.169*
(1.87)
6.475*
(1.81)
0.987***
(7.25)
10.172**
(2.28)
12.031***
(2.69)
17.735***
(4.00)
27.857***
(6.24)
145
-0.370
(-1.25)
2.940***
(2.97)
0.418*
(1.72)
1.580*
(1.76)
4.300***
(2.89)
0.876**
(2.43)
1.578***
(2.63)
8.120**
(2.37)
0.729***
(5.58)
0.170
(0.04)
-3.279
(-0.76)
-2.061
(-0.49)
2.808
(0.66)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
One of the goals of the analysis is to determine the best strategy for individual teams to
maximize revenues. As evidenced by Silver (2006), the value of a star player is different to each
team. In an attempt to see the if value of star players differs by market size, I re-estimated the
34
regressions including two new variables that are the product of city population and number of
stars (or number of All-Stars), the results are presented in table 71. A positive and statistically
significant coefficient would indicate that the value of each star increases as city population
increases, and a negative coefficient would indicate that the value of each star decreases as city
population increases. All of the coefficients for the All-Stars are statistically insignificant, but
the analysis finds that Star players generate more gate revenue for teams from smaller cities.
The gate revenue coefficient does not allow for the conclusion that teams from smaller cities are
receiving greater total revenue from Star players, as the teams from smaller markets may just be
receiving a higher proportion of their total revenue from a Star player in the form of gate
revenue. The insignificant coefficients hinder any stronger conclusions from being made about
whether Stars and All-Stars are more valuable to teams from smaller cities or larger cities.
1
Interaction terms for city population and lagged winning percentage, and city population and past playoff
appearances were also created, but did not yield statistically significant coefficients.
35
Marginal Revenue Product of a Star Player
Table 8: The Marginal Revenue Product of Stars and All-Stars as measured in Total Revenue
and Gate Revenue.
Stars Squared
Stars
Total Revenue
1.820
(1.43)
-0.979
(-0.24)
Gate Revenue
2.359**
(2.02)
-1.646
(-0.44)
All-Stars Squared
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.2507
(1.06)
5.257***
(5.81)
6.412***
(7.44)
1.210***
(3.19)
1.271***
(3.27)
6.182*
(1.72)
0.997***
(7.24)
9.981**
(2.20)
11.250**
(2.48)
17.148***
(3.78)
28.197***
(6.23)
145
0.578***
(2.65)
2.014**
(2.41)
2.869***
(3.61)
0.745**
(2.13)
1.219***
(3.40)
7.869**
(2.37)
0.747***
(5.89)
-0.039
(-0.01)
-4.009
(-0.96)
-2.817
(-0.67)
3.231
(0.77)
145
Total Revenue
Gate Revenue
0.131
(0.60)
1.714
(0.62)
0.067
(0.26)
4.349***
(4.60)
6.423***
(7.58)
1.169***
(3.15)
0.800*
(1.84)
5.663
(1.55)
1.014***
(7.44)
9.989**
(2.24)
11.492**
(2.54)
17.398***
(3.90)
27.564***
(6.17)
145
0.068
(0.32)
1.570
(0.59)
0.501*
(1.99)
1.489
(1.63)
2.737***
(3.35)
0.788**
(2.21)
0.959**
(2.29)
7.293**
(2.07)
0.762***
(5.81)
-0.091
(-0.02)
-3.731
(-0.86)
-2.249
(-0.52)
2.479
(0.58)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
The analysis has thus far only answered the question of the general value of a star, but
what is the marginal value of each star? If a team has one star, is pursuing another star an
36
economically viable tactic? Logic leads to the hypothesis that marginal value of a star decreases
as number of stars increases. I created two new variables to address the question. The variables
are the number of Stars squared and number of All-Stars squared in a given season. The idea
behind the variable is that the analysis has thus far assumed a linear relationship for revenue,
expenditures, and star players. The new variables will indicate if revenue, expenditures, and
stars have a non-linear relationship. In table 8, all of the coefficients for All-Stars squared are
statistically insignificant on their own, however, F-tests for joint statistical significance of AllStars squared and All-Stars reveals that the coefficients for total revenue and gate revenue are
jointly statistically significant. The data indicates that revenue associated with each All-Star
increases as the number of All-Stars increases. The marginal value of the third All-Star
appearance for a team over the two-year period is about $2.37 million, compared to $4.99
million marginal value for the thirteenth All-Star. The Stars squared values are all statistically
insignificant on their own, except for the gate revenue coefficient. F-tests, however, reveal that
Stars squared and Stars are jointly statistically significant for total revenue and gate revenue.
The data thus indicates that the total revenue received from a Star player increases as number of
stars increases. Simple math yields the revenue value of the first Star to be about $814,000, the
second Star about $4.481 million, the third Star about $8.12 million, and the fourth Star about
$11.76 million. Therefore, despite the lack of statistical significance, the results indicate that the
marginal revenue product of a star increases as number of stars increases.
The results have interesting implications for team strategy. Teams should attempt to
obtain as many stars as possible. The strategy is fairly simple for higher revenue teams that have
the operating budget to pursue several star players. Lower revenue teams face a dilemma,
however, as these teams may only have the budget to employ one star. Although a second star
37
has greater value, a lower revenue team’s budget restraint leaves them unable to accept the risk
associated with paying another player a high salary. The reason is that a supposed star player
may under perform, which is unacceptable if a player were to be paid a high percentage of his
team’s payroll. Therefore, the analysis indicates that higher revenue teams should be more
inclined to take risks on star players, whereas lower revenue teams should employ a far more risk
averse strategy.
38
Table 9: The Marginal Revenue Product of Stars and All-Stars on Total Revenue and Gate
Revenue, excluding the New York Yankees from the regressions.
Stars Squared
Stars
Total Revenue
Gate Revenue
2.028
(1.54)
-0.427
(-0.10)
2.255*
(1.89)
-0.550
(-0.15)
All-Stars Squared
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.293
(1.21)
4.819***
(5.10)
6.171***
(6.97)
.988**
(2.39)
0.259
(0.31)
5.623
(1.54)
1.040***
(7.32)
9.732**
(2.10)
11.562**
(2.49)
17.137***
(3.69)
27.765***
(5.99)
140
0.566**
(2.58)
1.704*
(1.99)
2.852***
(3.55)
0.723*
(1.93)
1.175
(1.54)
7.674**
(2.32)
0.752***
(5.84)
-0.619
(-0.15)
-3.826
(-0.91)
-3.546
(-0.84)
1.634
(0.39)
140
Total Revenue
Gate Revenue
0.168
(0.65)
1.436
(0.46)
0.027
(0.10)
4.380***
(4.53)
6.565***
(7.36)
1.244***
(3.14)
1.202
(1.52)
5.802
(1.55)
0.997***
(7.05)
9.978**
(2.16)
11.683**
(2.50)
17.165***
(3.72)
27.351***
(5.93)
140
0.033
(0.14)
2.213
(0.76)
0.377
(1.47)
1.575*
(1.73)
3.101***
(3.70)
1.034***
(2.78)
2.221***
(3.00)
8.048**
(2.29)
0.709***
(5.34)
-0.489
(-0.11)
-3.727
(-0.85)
-3.254
(-0.75)
1.015
(0.23)
140
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Furthering the analysis from table 8, regressions were run that measure the marginal
revenue value of star players for teams other than the Yankees. Individually, the coefficients for
39
the non-linear variables are not statistically significant, but F-tests indicate that all four
regressions in table 9 yield jointly statistically significant values for Stars squared and Stars, and
All-Stars squared and All-Stars, on total revenue and gate revenue. The data is thus indicating
that the revenue value of a star increases as the number of stars increases for teams other than the
Yankees. Specifically, the total revenue value of the first Star is $1.601 million, the second Star
$5.657 million, the third Star $9.713 million, and the fourth star $13.769 million. The marginal
value of the third All-Star appearance over the two-year period is $1.94 million, and the
thirteenth All-Star has a marginal value of $5.636 million. The total revenue value of each star is
greater in the model that excludes that Yankees.
40
Expenditures and Profits from Star Players and Winning
Table 10: The Effect of Stars, All-Stars, Lagged Winning Percentage, and Past Playoff
Appearances on Total Expenditures and Player Expenditures.
Total
Expenditure
3.500*
(1.72)
Stars
Player
Expenditure
4.446**
(2.53)
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.402
(1.38)
5.101***
(4.57)
6.725***
(6.35)
0.726
(1.55)
1.302***
(2.72)
-0.572
(-0.13)
0.926***
(5.48)
10.443*
(1.87)
17.449***
(3.12)
24.342***
(4.38)
28.391***
(5.08)
145
0.507**
(2.01)
4.287***
(4.45)
6.395***
(7.00)
0.132
(0.33)
0.208
(0.51)
-2.613
(-0.68)
0.617***
(4.23)
7.778
(1.61)
17.352***
(3.60)
19.591***
(4.09)
16.851***
(3.50)
145
Total
Expenditure
Player
Expenditure
3.571***
(3.18)
0.119
(0.39)
4.159***
(3.65)
6.902***
(6.67)
0.679
(1.50)
0.814
(1.64)
-0.258
(-0.06)
0.943***
(5.75)
10.654*
(1.96)
18.058***
(3.31)
24.180***
(4.47)
28.274***
(5.20)
145
1.796*
(1.79)
0.455*
(1.67)
3.978***
(3.89)
6.379***
(6.89)
0.225
(0.56)
0.007
(0.02)
-2.763
(-0.71)
0.647***
(4.41)
7.864
(1.61)
17.566***
(3.60)
19.331***
(3.99)
16.549***
(3.40)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Another question stemming from the analysis is whether stars are being overpaid. The
analysis has thus far been primarily concerned with the revenue effects of star players, with little
mention of expenditures associated with these revenue gains. Regressions using operating
income as the dependent variable were not statistically significant; instead, regressions using
41
total expenditures and player expenditures as the dependent variable were estimated with the
same independent variables from the earlier analysis; the results are presented in table 10. The
rationale behind using total expenditure and not just player expenditure is that there is a greater
cost of each player above their contract; teams must market their star players, which is costly,
although likely worthwhile. Considering the exorbitant contracts routinely given to star players,
the expenditures values appear low. One must bear in mind, however, that the coefficients in the
regressions give the additional cost of a star; the coefficients are indicating the extra cost
associated with having a star instead of an average player. Table 10, however, yields
problematic results. The cost of a Star player is about $1 million greater in terms of player
expenditures, but All-Stars cost an additional $1.8 million in total expenditures. Using total
expenditures, teams are overpaying by $296,000 for each All-Star, but gaining over $800,000 in
profit from each Star. Although the revenue values for star players are considered conservative
due to shortcomings in the Star variable, the expenditure variables suffer from the same
shortcomings. The star players included in the Star variable are not necessarily baseball’s
biggest stars and thus are yielding conservative estimates for revenue. The players included in
the Star variable, however, are also being paid less; players such as Derek Jeter are stars who
generate more revenue than the players included in the Star variable, but also have much larger
contracts. The figures for expenditure are also conservative and should balance-out the
conservative revenue estimates; therefore, the figures for profits should be deemed accurate.
The gains from on-field success must also be compared with the associated expenditures.
In table 10, total expenditure and player expenditure are used in place of total revenue and gate
revenue in the same regressions from tables 2 and 3. Table 10 reveals that each playoff
appearance in the past ten seasons also increases total expenditure by over $5 million, meaning
42
teams are barely profiting from their past success. Table 10 does not yield a statistically
significant coefficient for total expenditure and lagged winning percentage, but does indicate a
one percent increase in lagged winning percentage to cause an approximately $507,000 increase
in player expenditure.
Table 11: The Effect of Lagged Winning Percentage and Past Playoff Appearances on Total
Expenditures and Player Expenditures.
Stars
Lagged Winning
Percentage
Playoffs (past 10
seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
Total Expenditure
3.835
(1.59)
0.856***
(2.73)
Player Expenditure
4.318**
(2.10)
0.838***
(3.13)
6.531***
(5.54)
1.032**
(2.05)
1.888***
(3.59)
-4.493
(-0.95)
1.036***
(5.70)
11.410*
(1.89)
18.774***
(3.12)
26.048***
(4.36)
31.038***
(5.18)
145
6.414***
(6.36)
0.358
(0.83)
0.586
(1.30)
-5.909
(-1.47)
0.721***
(4.63)
8.792*
(1.70)
18.566***
(3.60)
21.150***
(4.14)
19.183***
(3.74)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level;
** indicates significant at the 95% level
*** indicates significant at the 99% level
43
Total Expenditure
4.163**
(2.09)
Player Expenditure
5.281***
(3.05)
5.722***
(5.58)
6.784***
(6.39)
0.871*
(1.91)
1.331***
(2.78)
-0.794
(-0.18)
0.905
(5.36)
10.441*
(1.86)
17.520***
(3.12)
24.274***
(4.36)
28.241***
(5.04)
145
5.069***
(5.69)
6.470***
(7.01)
0.315
(0.79)
0.246
(0.59)
-2.893
(-0.75)
0.590***
(4.02)
7.777
(1.59)
17.441***
(3.58)
19.506***
(4.03)
16.662***
(3.42)
145
Although table 10 yields better coefficients for interpreting the expenditure effects of
winning, table 11 serves to give an idea of the relative importance of player expenditure in the
total expenditure effects of lagged winning percentage. Table 11 indicates an $856,000 increase
in expenditures for every one percent increase in lagged winning percentage, with almost all of
the money being used on player expenditures. Table 11 thus allows for the conclusion that the
$507,000 player expenditure cost for each one percent increase in lagged winning percentage in
table 10 is similar to the total expenditure attributed to each one percent increase in lagged
winning percentage. Therefore, the data indicates that teams are profiting $133,000 from each
past playoff appearance, and about $60,000 from a one percent increase in lagged winning
percentage1.
1
The regressions using All-Stars as an independent variable instead of Stars indicate that teams are profiting
$279,000 from each past playoff appearance, and about $20,000 from each one percent increase in lagged winning
percentage.
44
City Population Effects on Expenditures for Star Players and Winning
Table 12: The Effects of Stars, All-Stars, Lagged Winning Percentage, and Past Playoff
Appearances on Total Expenditure and Player Expenditure for Teams that are not the Yankees.
Total
Expenditure
5.222**
(2.47)
Stars
Player
Expenditure
5.177***
(2.80)
All-Stars
Lagged Wining
Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.404
(1.41)
4.343***
(3.88)
6.524***
(6.24)
0.571
(1.17)
0.574
(0.59)
-1.360
(-0.32)
0.965***
(5.79)
10.038*
(1.83)
17.621***
(3.21)
22.965***
(4.21)
25.789***
(4.71)
140
0.472*
(1.89)
3.921***
(4.01)
6.412***
(7.02)
0.170
(0.40)
0.337
(0.39)
-2.901
(-0.77)
0.620***
(4.26)
7.625
(1.59)
17.370***
(3.62)
18.125***
(3.80)
14.770***
(3.09)
140
Total
Expenditure
Player
Expenditure
3.500***
(3.07)
0.093
(0.30)
3.914***
(3.47)
6.969***
(6.67)
0.813*
(1.75)
1.275
(1.38)
-0.490
(-0.11)
0.940***
(5.70)
10.470*
(1.93)
18.181***
(3.35)
22.490***
(4.18)
25.877***
(4.79)
140
1.940*
(1.89)
0.356
(1.27)
3.904***
(3.85)
6.648***
(7.08)
0.453
(1.09)
1.036
(1.25)
-2.504
(-0.65)
0.612***
(4.13)
7.819
(1.60)
17.420***
(3.57)
17.581***
(3.63)
14.636***
(3.01)
140
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Table 12 gives the expenditures associated with Stars, All-Stars, lagged winning
percentage, and past playoff appearances for teams other than the Yankees. Surprisingly, table
12 reveals that teams other than the Yankees are spending $1.722 million more in total
expenditure and $731,000 more in player expenditure per Star than the Yankees. The All-Stars
45
variable does not give as decisive results, indicating that teams other than the Yankees spend
$71,000 less on each All-Star in total expenditure, but spend $144,000 more in player
expenditure on each All-Star. The contrasting results for the expenditures on All-Stars may be
indicating that the Yankees spend lavishly on marketing their All-Stars. Overall, the table
appears to indicate that teams other than the Yankees are spending more on star players, which is
consistent with the data from table 6 that indicates teams other than the Yankees are also
receiving more revenue from star players. By comparing the profit figures for data including and
excluding the Yankees, the regression including the Yankees reveals teams to be profiting
$693,000 more from each Star, and losing $147,000 less from each All-Star.
In terms of team success, however, teams other than the Yankees are far more profitable.
The other twenty-nine teams are spending $758,000 less for each past playoff appearance and
$35,000 less for each one percent increase in lagged winning percentage. The other twenty-nine
teams are profiting $484,000 from each past playoff appearance, and about $78,000 from each
one percent increase in lagged winning percentage, which is $351,000 more for each past playoff
appearance and about $18,000 more for each one percent increase in lagged winning
percentage1.
1
The regressions using All-Stars as an independent variable instead of Stars indicate that the other twenty-nine
teams are profiting $536,000 for each past playoff appearance, which is $257,000 more than the figure from the
regression including the Yankees.
46
Table 13: The Effects of City Population on Expenditures on Lagged Winning Percentage and
Past Playoff Appearances, as Measured in Total Expenditure and Player Expenditure.
Stars
City Population and Lagged Winning
Percentage (Interaction Term)
Lagged Winning Percentage
City Population and Playoffs
(Interaction Term)
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
Total
Expenditure
5.425**
(2.57)
Player
Expenditure
5.123***
(2.75)
0.494*
(1.72)
1.451***
(2.77)
3.275**
(2.57)
3.589**
(2.34)
0.328
(0.69)
-0.473
(-0.60)
-2.455
(-0.56)
0.990***
(5.94)
9.766*
(1.79)
16.615***
(3.04)
23.766***
(4.38)
27.841***
(5.11)
145
0.539**
(2.13)
0.510
(1.10)
3.645***
(3.24)
5.293***
(3.91)
-0.008
(-0.02)
-0.416
(-0.59)
-3.276
(-0.85)
0.639***
(4.35)
7.540
(1.56)
17.058***
(3.53)
19.389***
(4.05)
16.657***
(3.46)
145
Total
Expenditure
3.5367*
(1.72)
0.029
(0.20)
0.369
(1.10)
Player
Expenditure
4.696***
(2.68)
0.200
(1.65)
0.276
(0.96)
5.109***
(4.56)
5.227
(0.71)
0.721
(1.53)
1.242**
(2.21)
-0.656
(-0.15)
0.927***
(5.46)
10.507*
(1.87)
17.493***
(3.11)
24.418***
(4.37)
28.478***
(5.07)
145
4.348***
(4.54)
-3.921
(-0.62)
0.095
(0.24)
-0.206
(-0.43)
-3.194
(-0.84)
0.621***
(4.28)
8.223*
(1.71)
17.650***
(3.68)
20.118***
(4.22)
17.447***
(3.64)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
As Aaron Rabinowitz’s (2003) thesis concludes, each team has a different value for
winning. To evaluate the effects of winning for teams from different sized cities, two new
variables were created. Table 13 uses these two new interaction terms, city population and
lagged winning percentage, and city population and past playoff appearances. A positive
47
coefficient on the interaction term would mean teams from larger cities are spending more to
win, whereas a negative coefficient would indicate that teams from larger cities are spending less
to win. The only statistically significant coefficient indicates that teams from larger cities are
spending more in total expenditure for past playoff appearances; the data may sound odd, but this
expenditure is likely manifested in marketing efforts to promote past team success. The
coefficient for the lagged winning percentage and city population interaction term is significant
at the 89.9% level, which is just below the 90% cut-off used in this analysis. If that coefficient is
included as statistically significant, then teams from larger cities are also paying greater player
expenditures associated with lagged winning percentage. The coefficient confirms the
conclusion that teams from larger cities are spending more to promote past team success, while
not necessarily receiving greater revenue benefits.
48
Table 14: The Effects of City Population on Expenditures on Stars and All-Stars, as Measured in
Total Expenditure and Player Expenditure.
City Population and Stars
(Interaction Term)
Stars
Total
Expenditure
-1.658**
(-2.09)
6.436***
(2.62)
Player
Expenditure
0.179
(0.26)
4.128*
(1.92)
City Population and All-Stars
(Interaction Term)
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.401
(1.39)
4.757***
(4.27)
8.409***
(6.37)
0.657
(1.42)
1.468***
(3.07)
-0.335
(-0.08)
0.935***
(5.60)
9.099
(1.64)
16.715***
(3.02)
23.668***
(4.31)
26.246***
(4.68)
145
0.507**
(2.01)
4.324***
(4.43)
6.213***
(5.37)
0.140
(0.34)
0.190
(0.45)
-2.639
(-0.69)
0.616***
(4.21)
7.924
(1.63)
17.431***
(3.59)
19.664***
(4.09)
17.083***
(3.48)
145
Total
Expenditure
Player
Expenditure
0.067
(0.18)
3.469***
(2.74)
0.130
(0.42)
4.151***
(3.62)
6.621***
(3.48)
0.664
(1.44)
0.711
(0.93)
-0.356
(-0.08)
0.947***
(5.68)
10.614*
(1.94)
18.017***
(3.29)
24.177***
(4.45)
28.231***
(5.17)
145
-0.101
(-0.30)
1.950*
(1.72)
0.439
(1.58)
3.990***
(3.89)
6.803***
(4.00)
0.247
(0.60)
0.163
(0.24)
-2.615
(-0.67)
0.640***
(4.29)
7.925
(1.62)
17.628***
(3.59)
19.336***
(3.98)
16.613***
(3.40)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Table 14 uses the same interaction terms as in table 7. Neither of the coefficients for city
population and All-Stars is statistically significant. The only statistically significant coefficient
49
for an interaction term in table 14 is for city population and Stars on total expenditure. The
coefficient is negative, thus indicating that teams from smaller cities are paying more for Star
players. The finding would appear to agree with the figures from table 7, which show that teams
from smaller markets are also gaining more revenue from Star players. No conclusions can be
made about the profitability of star players to teams from different sized cities.
50
Marginal Expenditures from Star Players
Table 15: The Marginal Effect of Stars and All-Stars on Total Expenditure and Player
Expenditure.
Stars Squared
Stars
Total
Expenditure
1.585
(1.01)
-1.108
(-0.22)
Player
Expenditure
2.359**
(2.02)
-1.646
(-0.44)
All-Stars Squared
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.409
(1.40)
5.120***
(4.58)
6.814***
(6.41)
0.756
(1.61)
1.258***
(2.62)
-0.455
(-0.10)
0.944***
(5.56)
10.532*
(1.88)
17.320***
(3.10)
23.645***
(4.23)
28.607***
(5.12)
145
0.514**
(2.04)
4.307***
(4.48)
6.489***
(7.09)
0.163
(0.41)
0.163
(0.39)
-2.491
(-0.65)
0.636***
(4.34)
7.872
(1.64)
17.216***
(3.58)
18.859***
(3.92)
17.077***
(3.55)
145
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
51
Total
Expenditure
Player
Expenditure
0.167
(0.62)
1.588
(0.47)
0.178
(0.56)
4.046***
(3.49)
6.895***
(6.65)
0.664
(1.46)
0.697
(1.31)
-0.952
(-0.21)
0.960***
(5.76)
10.558*
(1.93)
17.515***
(3.16)
23.763***
(4.35)
28.048***
(5.13)
145
-0.049
(-0.21)
2.381
(0.79)
0.438
(1.53)
4.011***
(3.86)
6.381***
(6.87)
0.229
(0.56)
0.042
(0.09)
-2.558
(-0.64)
0.642***
(4.30)
7.893
(1.61)
17.726***
(3.57)
19.454***
(3.97)
16.616***
(3.39)
145
Regressions were run in table 15 using the idea that expenditure and stars do not have a
linear relationship. As mentioned previously, the coefficients for Stars squared and All-Stars
squared are not statistically significant, but are jointly statistically significant with Stars and AllStars in predicting total expenditure and player expenditure. By comparing the coefficients for
total revenue and total expenditure, the data reveals that teams are profiting from All-Stars only
when number of All-Stars is two or three. Teams are thus generally overpaying for All-Stars.
The data for Star players contains similar results. The coefficients for total revenue are not
statistically significant, thus player expenditures must be compared to total revenue. Only teams
with four Stars are receiving more total revenue than player expenditures from Stars, which is
difficult to consider given that only two teams in the five year period had four Stars in a given
season. Total expenditures will be higher than player expenditures, however, thus teams are
overpaying for Star players. The data is indicating that although the marginal value of a star
player increases as number of stars increases, almost all teams are overpaying for star players.
52
Table 16: The Marginal Effect of Stars and All-Stars on Total Expenditure and Player
Expenditure for Teams that are not the Yankees.
Total
Expenditures
1.578
(1.01)
0.732
(0.15)
Stars Squared
Stars
Player
Expenditures
1.536
(1.13)
0.807
(0.19)
All-Stars Squared
All-Stars
Lagged Winning Percentage
Playoffs (past 10 seasons)
City Population
Median Income
Past Championships
New Stadium
Stadium Quality
Year 2001
Year 2002
Year 2003
Year 2004
n
0.416
(1.45)
4.337***
(3.88)
6.580***
(6.28)
0.570
(1.17)
0.395
(0.40)
-1.301
(-0.30)
0.987***
(5.88)
10.138*
(1.85)
17.632***
(3.21)
22.297***
(4.06)
26.156***
(4.77)
140
0.483*
(1.93)
3.915***
(4.01)
6.465***
(7.07)
0.169
(0.40)
.0162
(0.19)
-2.844
(-0.76)
0.642***
(4.38)
7.722
(1.61)
17.381***
(3.62)
17.474***
(3.64)
15.127***
(3.16)
140
Total
Expenditures
Player
Expenditures
-0.086
(-0.28)
4.477
(1.23)
0.073
(0.23)
3.950***
(3.47)
6.947***
(6.61)
0.813*
(1.75)
1.278
(1.38)
-0.201
(-0.05)
0.935***
(5.62)
10.487*
(1.93)
18.365***
(3.34)
22.660***
(4.17)
25.877***
(4.77)
140
-0.239
(-0.88)
4.667
(1.43)
0.301
(1.04)
4.003***
(3.92)
6.589***
(7.00)
0.451
(1.08)
1.044
(1.25)
-1.698
(-0.43)
0.598***
(4.01)
7.865
(1.61)
17.935***
(3.64)
18.056***
(3.71)
14.636***
(3.01)
140
Notes: T-Values are in parentheses
* indicates significant at the 90% level
** indicates significant at the 95% level
*** indicates significant at the 99% level
Table 16 presents similar regressions to those used in table 15, except the Yankees are
excluded from the analysis. Although none of the regressions yields statistically significant
53
coefficients for the non-linear variables individually, F-tests for joint statistical significance
reveal that Stars squared and Stars are jointly statistically significant in predicting total
expenditure and player expenditure; All-Stars squared and All-Stars are jointly statistically
significant in predicting total expenditure. Similar to the findings in table 15, teams other than
the Yankees are generally not profiting from star players. The other twenty-nine teams receive a
profit from having three or more Stars, a slight improvement over the model in table 15, where
teams only profited from having four Stars. There are only fourteen occurrences (out of 140
observations) of teams other than the Yankees having three or more Stars, thus most teams are
not profiting from Star players. Teams other than the Yankees only receive profits from AllStars if the team has twelve or more. No team other than the Yankees has had more than eleven
All-Stars over the five year period, thus none of teams in this model has profited from All-Stars.
Summary of Findings
Overall, the data generally agrees with the hypotheses that star players and winning have
a positive effect on revenue. The expenditure analysis, however, indicates that teams are not
profiting from star players, but are profiting from team success. Viewing the league as a whole,
teams are overpaying by $296,000 for All-Stars, but gaining $814,000 in profit from each Star.
Multiplying by the standard deviations of All-Stars and Stars yields a loss of $699,448 from a
one standard deviation increase in All-Stars and $800,162 profit from a one standard deviation
increase in Stars. Furthermore, teams that are not the Yankees are only profiting $121,000 from
each Star, and losing $443,000 from each All-Star. Standard deviations indicate a $118,943
profit from a one standard deviation increase in Stars, and about a $1.05 million loss from a one
standard deviation increase in All-Stars. The non-linear model indicates that although the
54
marginal value of a star player increases as number of stars increases, almost all teams are
overpaying for star players. When excluding the Yankees from the non-linear model, the results
indicate that the other twenty-nine teams are overpaying for All-Stars, and rarely profiting from
Stars.
The data yields far different results, however, for team success. As evidenced in previous
research, the data indicates that teams are profiting $133,000 from each past playoff appearance,
and about $60,000 from a one percent increase in lagged winning percentage. Standard
deviations yield a $281,029 profit from a one standard deviation increase in past playoff
appearances, and a $468,240 profit from a one standard deviation increase in lagged winning
percentage. When the Yankees are excluded, the other twenty-nine teams are profiting $484,000
from each past playoff appearance, and about $78,000 from each one percent increase in lagged
winning percentage. Teams other than the Yankees are profiting $1.02 million from a one
standard deviation increase in past playoff appearances and profiting $608,712 from a one
standard deviation increase in lagged winning percentage.
The data for teams from different sized cities is not as clear, but does indicate that teams
from larger cities are spending more to promote past team success, while not necessarily
receiving greater revenue benefits. No conclusions can be made about the profitability of star
players to teams from different sized cities. Further research should be done to complete the
analysis of the effects of market size on the revenue and profit effects of star players and
winning.
By indicating that star players are worth more than the wins they add, this model gives
evidence of why Nate Silver’s (2006) ‘Linear Model’ is incorrect. The reason teams are paying
more per win in free agency is that teams are paying for more than wins. Silver (2005a) agrees
55
with the notion in his creation of Market Value over Replacement Player (MORP), a model that
predicts player value by using Silver’s model in conjunction with Baseball Prospectus’ PECOTA
system. Silver’s reasoning behind teams paying more for star players, however, is that not all
wins are worth the same amount because of the immense economic impact of winning a
championship or making the playoffs. The MORP model is a tremendous idea, but needs to be
modified in light of these new findings. MLB teams should clearly take this analysis into
account. Although the data could be improved by using merchandise sale figures to achieve a
better definition of a star player, the analysis should be extended to teams from the NBA,
National Hockey League, National Football League, and any other professional sports league.
Team Strategy Implications
There appear to be two viable strategies for every MLB franchise to maximize operating
income: attempt to win by spending as little money as possible, or try to obtain recognizable star
players. In either scenario, the team is attempting to win. But which objective should each team
pursue? The analysis has affirmed the previous research that the best approach financially for
MLB teams is to field successful teams. Star players generate revenue, but are not necessarily
profitable, and certainly not as profitable as winning. An important point to note is that the
players on successful teams become stars through increased media exposure. The analysis may
be suggesting that star players obtained through free-agency are less profitable than star players
developed on a winning team; teams that are unlikely to make the playoffs should thus be
hesitant about pursuing an established star player. Obtaining or keeping a star player also
usually has a cost beyond salary. Instead of keeping a star, a team could trade the player for
other players who will better help the team win in the future. Similarly, in order to obtain a star,
56
a team must trade away assets that could be used to help the team win in the future. The
profitability of stars increases as number of stars increases, however, indicating that the best
strategy for high revenue teams from larger cities is to win by obtaining as many stars as
possible; the New York Yankees are a prime example of this strategy. On the other hand, a team
of multiple star players is unaffordable for many teams, indicating that the best strategy for most
teams is to seek to win efficiently, as is the tactic used by the Oakland Athletics.
A question stemming from the analysis is what is the best strategy for a team that has
little hope of making the playoffs? Most importantly, the team should be attempting to win
efficiently and not let the star player interfere with plans for ‘rebuilding’ the team. The data is
thus agreeing with Silver (2005b) that the common ‘rebuilding’ strategy is economically viable.
Teams that spend a lot of money to win and are unsuccessful in winning generally trade away all
of their high salaried players; the effort almost always yields an unsuccessful team on the on the
field. These teams often avoid having veteran star players, as older star players are not going to
be on the team long enough to be a part of the team’s next successful season. The short-term
profitability of a star player does not outweigh the costs of jeopardizing future team success.
57
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