free agency and competitive balance in major league baseballnp2015.tripod.com/m.a.pdf · academy...

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Free Agency and Competitive Balance

in Major League Baseball

Reporter: “Ben, your thoughts on A-Rod joining the Yankees?”Ben Affleck: “You know, George Steinbrenner is the center of evil in the Universe there’s no question about that.”Ben Affleck: “Eventually, they might be able to just buy everybody…why not?”Academy Award winning actor Ben Affleck and an avid Boston Red Sox fan asked about the New York Yankees acquiringshortstop Alex Rodriguez and his $252 million contract in a trade, in Feb. of 2004 at the Daytona 500.

Nicholas PritzakisState University of New York at Albany

Economics DepartmentMaster’s Essay

Advised by Michael SattingerNovember 2004

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Acknowledgements

I would like to thank Professor Michael Sattinger for

his input and guidance throughout this project. I would also

like to acknowledge Professor Craig A. Depken, II for his

insight and advice on constructing my econometric model.

Lastly, I would like to thank the late Doug Pappas for

making his free agent data readily available to the public.



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Section I: Introduction

The aforementioned comments made by actor Ben Affleck

mirror those beliefs that some fans and sportswriters had

about free agency in Major League Baseball. Through free

agency a team owned a player for the first six years of his

career. After that a player became his own owner or free

agent, and was then able to sell his services to the highest

bidder. The six years, however, did not include the player’s

minor league career. For example, if a player served seven

years on a minor league club and then later was promoted to

a Major League Baseball club he would still have to give the

Major League Baseball club six years of service before he

could be eligible for free agency. Major League Baseball

also has a draft that determines an amateur player’s initial

professional contract assignment. The reverse-order amateur

draft allows teams to select amateur prospects in reverse

order of standings. The free agency system and the draft

both represent a reassignment of property rights to the

player’s labor services.

So why does an overwhelming perception of free agency

cause a lack of competitive balance? Would an open player’s

market generate the most efficient results? One element that

is unmistakable to fans and sportswriters is that there are

no team payroll restrictions in Major League Baseball. The



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2003 New York Yankees had a team payroll exceeding $150

million and they competed in the same division as the Tampa

Bay Devil Rays whose team’s payroll was just under $32

million.1 If teams bid for the same players in the free

agent market, it is apparent that the clubs with a higher

payroll have a distinct advantage over clubs with a lower

payroll.

Prior to the 1970s, players were largely bound, for

their entire baseball career, to the original team that

drafted them. The only way a player could switch teams was

if the team that owned that player’s rights either sold him

or traded him to another team. This previous system was

known as the Reserve Clause. In 1976, The Basic Agreement,

an agreement between the player’s union and the owners,

introduced free agency to Major League Baseball. This

shifted the team’s monopolistic rights of a player’s

services to the player, could now own his own rights.

In the late 1990s the New York Yankees won four World

Series championships in a five-year period (1996-2000) while

having a payroll that dwarfed most of its opponents.2 With

the on-the-field success of such large market clubs as the

New York Yankees and the Atlanta Braves the issue of

competitive balance became a focal point in Major League

Baseball.

1 2003 team payroll was obtained from www.baseball-almanac.com

2 World Series results and team records obtained from www.baseball-reference.com


http://www.baseball-almanac.com


http://www.baseball-reference.com

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In July of 2000, The Independent Members of the

Commissioner’s Blue Ribbon Panel on Baseball Economics

issued its report recommending broad changes to Major League

Baseball’s economic structure. This report intended to close

the gaping disparity between what the member’s called the

game’s “haves and have-nots.”

After an 18-month investigation, these problems were

stated in the report:

A. Large and growing revenue disparities exist and are

causing problems of chronic competitive imbalance.

B. These problems have become substantially worse during the

five complete seasons since the strike shortened season of

1994, and seem likely to remain severe unless Major League

Baseball undertakes remedial actions proportional to the

problem.

C. The limited revenue sharing and payroll tax that were

approved as part of Major League Baseball’s 1996 Collective

Bargaining Agreement with the Major League Baseball Players

Association have produced neither the intended moderating of

payroll disparities nor improved competitive balance. Some

low-revenue clubs, believing the amount of their proceeds

from revenue sharing insufficient to enable them to become

competitive, used those proceeds to become modestly

profitable.



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D. A majority of Major League Baseball markets; the cost of

clubs trying to be competitive is causing escalation of

ticket and concession price, jeopardizing Major League

Baseball’s traditional position as the affordable family

spectator sport.3

According to economic theory, free agency would not

have a detrimental effect on the competitive balance in

Major League Baseball. I intend to test the claims of the

economic theory by putting them through an econometric

model. Section II of my paper will detail an overview of the

economic theory on competitive balance relating to Major

League Baseball. Section III will provide an overview of

some of previous empirical literature on the subject.

Section IV will propose an econometric model to test

economic theory of competitive balance. Section V will

provide my hypothesis on the model. Section VI will explain

my results from the econometric model. Section VII will

propose an alternative model and explain why it is preferred

to the first. Section VIII will offer my conclusions based

on the results from the econometric model. Section VIIII

proposes material that should be considered for future

researchers studying competitive balance in Major League

Baseball.

3 Source: http://mlb.mlb.com/mlb/downloads/blue_ribbon.pdf



http://mlb.mlb.com/mlb/downloads/blue_ribbon.pdf

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Section II: Relevant Theoretical Literature

The theory of competitive balance in Major League

Baseball was first introduced by Rotenberg (1956). According

to Rotenberg, the concerns many owners and fans had about

the competitive balance in Major League Baseball would be

checked by the law of diminishing returns, which operated

concurrently with each team’s strategic avoidance of

diseconomies of scale.

Rotenberg pointed out that no team could be successful

unless its competitors also survive and prosper sufficiently

such that the differences in quality of play among teams are

not that far off. Rotenberg (1956,p.255) provides the

following assertion of this argument

Beyond some point-say, when a team already has three .350 hitters-it willnot pay to employ another .350 hitter. If a team goes on increasing thequantity of the factor, players, by hiring additional stars, it will findthat the total output-that is, admission receipts-of the combined firmswill rise at a less rapid rate and finally fall absolutely. At some point,therefore, a first star player is worth more to poor Team B then say, athird star to rich Team A.

The key element to this argument is that teams need

each other to be successful. For the sake of simplicity,

they work together to form one single product, entertainment

for their fans. The closer the contests are between teams

the higher the fan interest will be, increasing attendance

at baseball games. Acquiring too much talent would be

detrimental to a team because this would create lopsided

games, and consequently fan interest will be lost and team



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revenues will decrease. According to Rotenberg, all teams

will strike a balance between revenue and cost of talent no

matter if the rules entail free agency or the reserve

clause; teams will limit themselves from becoming dominant.

Rotenberg offered an interesting remedy for those who

feared eliminating the reserve clause would threaten the

competitive balance of Major League Baseball; let a

franchise(s) be distributed so that the size of the product

market is equal for all teams. If teams move to areas where

the marginal revenue per win is greater than that of their

initial location, the competition among teams in the same

league within the same metropolitan area will reduce

revenues earned by the original teams in that area. This

could potentially reduce the financial discrepancies amongst

teams, assuming that attendance is a unique function of the

size of the market. For example, adding a team in the New

York metropolitan area would make it more difficult for the

Yankees and the Mets to attract free agents. Evidence of

this is found when you drive down the street and see a

Burger King located right next door to a McDonald’s fast-

food chain.

Many economists have also found the work of Ronald

Coase in, “The Problems of Social Cost”(1960) to be

applicable to Major League Baseball. The Coase Theorem

requires two assumptions. If there are well-defined property

rights for production of externalities or for protection



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from their effects, and if transaction costs are zero,

private negotiations among producers of the externalities

and the victims or beneficiaries lead to efficient

allocations. In regards to these assumptions, Coase claims

that a monopoly with zero transaction costs producing a

durable good with consumers able to substitute consumption

for consumption in the future, behaves like a perfect

competitor, since it will seek to maximize profits. The

Coase Theorem also states that a change in property

ownership should have no effect on mobility of players

between teams. In a competitive market teams will bid for a

player’s service up to the point where the salary offer

equals the value of the player’s worth to the team, and as a

result the player will capture the rents.

For example, suppose Team A has a player who they value

at six million dollars, but Team B values him at eight

million dollars. There are gains to be made from trading, so

Team B will offer Team A more then six million dollars but

less than eight million dollars in resources to acquire this

player, the distribution will be efficient and the rewards

will go to the player. The free agent market simply provides

a more direct way of player movement amongst teams.

Most academic study on competitive balance in Major

League Baseball is based on defending or refuting the

theories of Rotenberg and Coase. Competitive balance has

been measured in two ways in the past. The first method



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focuses on the effects of fan interest and revenue from the

competitive balance within a game. The second method

emphasizes policy changes made throughout the history of

Major League Baseball, most importantly changes in the role

of free agency. This paper focuses on the latter.

Section III: Relevant Empirical Literature

An enormous amount of research has been done on free

agency and its effect on competitive balance in Major League

Baseball. Although most previous research tends to coincide

with the Coase Theorem, which states that free agency has

had a non-detrimental effect on competitive balance in Major

League Baseball, there have been studies refuting its

validity. The first part of this section will focus on those

studies that feel that free agency has a detrimental effect

on the competitive nature in Major League Baseball.

The second part of this section will concentrate on

studies that feel that free agency does not have an impact

on the competitive balance in Major League Baseball. The

last part of this section will describe studies that fell in

the middle, not fully agreeing or disagreeing with the Coase

Theorem.

Daly and Moore (1981) investigated player movement

before and after free agency and after the amateur draft.

They used the Spearman’s rank correlation coefficient to

compare league standings from one year to the next. They



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argued that the change in migration property rights did

affect the final allocation of players, as well as affecting

their relative team’s performances. They discovered that

players were more likely to move toward large market cities

as free agents than when bound by the reserve clause. They

stated that if earnings for ineligibles were proportionate

to productivity, eligible players would be able to take

better advantage of migration opportunities. This supported

their belief that market structure did influence the outcome

of the market.

Cymrot and Dunlevy (1987) used an earnings equation,

which related a player’s earnings to his personal

characteristics, the characteristics of the team for which

he played, and the factors, that represented interplay

between the player’s ability and that of his teammates. They

also included “The Gain from Migration” equation, which was

a salary function used to calculate the gain from moving.

They supplemented that equation with “The Migration

Equation”, which was used to determine whether the

probability of moving was affected by the magnitude of Gain.

They concluded that players who were eligible for free

agency tended to migrate to a different team when it was to

their monetary advantage. Cymrot (1983) developed a similar

conclusion in that quality free agents had the tendency to

move from successful teams to teams in large cities.



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Vrooman (1996), throughout his studies, believed that

superior small-market teams were dismantled in the pursuit

of maximum profit through the inefficient free agent

acquisitions of large-market clubs. He concluded that the

free agency was a zero sum game.

Jewell & Molina (2001) analyzed the effect of salary

dispersion on team winning percentage in Major League

Baseball, by measuring how payroll inequality affected a

team’s ability to reach its production potential. According

to their results, the distribution of salaries within Major

League Baseball teams had a significantly negative effect on

team success as measured by the team’s winning percentage.

Fishman (2002) measured competitive balance by using

the standard deviation of team winning percentages as the

model’s dependent variable. Contrary to previous work, he

included a variable to count the number of free agents,

which would measure free agency’s effect on competitive

balance. Previous studies used a dummy variable equal to one

for years where free agency was implemented. The estimated

coefficient of the free agent variable was positive and

highly significant, which implied that free agency did

indeed have an effect on competitive balance, although his

free agent variable did not offer a quality measurement of

the players, nor did it involve if the free agent

transferred clubs or stayed with his initial club.



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Basanko and Simon (1985) measured the competitive

balance by using the standard deviation of team winning

percentages. They compared the seven years before, 1970-

1976, and after free agency, 1977-1983. Although the

standard deviation decreased, which indicated a more

competitive balance; their findings were not statistically

significant, which therefore made them inconclusive.

Scully (1989) used two measures to test free agency’s

impact on competitive balance. One measure was the annual

standard deviation of league win percents, and lower

standard deviations indicated there was less variation

between team win percents and greater competitive balance.

His second measure was the Spearman rank correlation between

team cumulative wins percent rank and population rank within

leagues. He found that there were some indications of

improved competitive balance in the National League for the

ten years, mean standard deviation fell by a statistically

significant amount from 1962-76 to 1977-87 and the American

League showed no change.

Vrooman (1995) used the ratio of annual league win

percent standard deviation to an “idealized” standard

deviation that would occur if each team had a 50 percent of

winning every game. After observing the annual ratios from

1970-1992, he concluded that both the American League and

the National League became increasingly competitive, though

he did not support this with significance tests.



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Fort and Quirk (1995) expanded on Basanko & Simon’s

study, and also reached equivalent results. Empirically,

they showed there were no significant changes in the

standard deviation of winning percentages in the period of

1966-1975 versus 1976-1985. They also examined changes in

the Gini coefficients of concentration in league pennant

winners between the same periods. In this study a lower

value would indicate less concentration and more competitive

balance. Their findings concluded that the coefficients were

slightly lower in both leagues and there was no significant

change in either league.

Horowitz (1997) used a relative entropy measure of

balance derived from the annual distribution of a team’s

wins within leagues. His multiple regression analysis

covered the period of 1903-1995. He concluded that free

agency did not cause an imbalance in winning when compared

to the pre-free agency period.

Lee and Fort (2002) calculated a time series analysis

of structural change from the early 20th century to the 21st

century. In their results they concluded that competitive

balance in Major League Balance had improved over time, both

in trend and in episodes that altered the structure of

competitive balance itself.

Depken (2002) calculated the concentration of wins

using the Herfindahl-Hirschman Index (HHI) with “market

share” defined as a team’s percentage of total wins,



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measured relative to a hypothetical HHI corresponding to an

equal distribution of wins; a nonlinear transformation of

win percent standard deviation. He used home runs and

strikeouts as variables to measure the HHI. His evidence

suggested that free agency has been beneficial in reducing

the overall concentration of home runs in the individual

leagues and the overall major leagues.

Eckard (2001) examined competitive balance from season

to season rather than within one season as was done in

previous studies. The logic being that league standings

fluctuate from year to year and they cannot be conveyed by

the conventional single-season standard deviation of team

win percents. Empirically, he showed that competitive

balance improved after free agency. He agreed with Rotenberg

by explaining that there were diminishing marginal returns

in each additional year’s “production” of contenders,

reducing the incentive to continually bid for top players.

This allowed non-contenders to obtain players in the free

agent market that would help their chances of improving.

Barra (2002) proposed two complementary competitive

imbalance measures with regard to post-season play: the

number of different measures with regard to post-season play

for a championship. He compared Major League Baseball to the

National Football League and the National Basketball

Association. Although Major League Baseball had available

playoff spots, over the last two decades, 20 franchises have



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appeared in the World Series, compared with 19 teams in the

Super Bowl and 15 in the NBA Finals.

Krautman and Oppenheimer (1994) ran a logit model

testing the probability that a player will move with the

assumption that free agents view migration as an investment

allowing them to maximize utility. They found that migration

decisions of free agents were affected by the preference of

the player, suggesting that the allocation of labor is

likely to be different under free agency than under the

reserve clause. Also, large market teams are more attractive

to potential migrants than small-market teams. They

concluded that big-city teams have not dominated the sport,

despite the magnitude of their attractiveness, because of

the existence of the draft and the relatively small impact

free agents have on team wins.

Hylan, Lage and Treglia (1996) refuted the Coase

Theorem. They examined the mobility of all Major League

Baseball pitchers during 1961-1992 through panel data; using

the beginning of free-agency in 1976-1977 as the midpoint of

their interval. They found that before 1976 total player

service time was positively significant with mobility, other

things equal; after 1976, this was still true, but the

effect of longer service on mobility was much smaller than

before free-agency.

Dunlevy, Even and Cymrot (2000) tested the Coase

Theorem by examining whether the effect of gain on player



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migration is independent of the player’s eligibility for

free-agency. Their results indicated that the effect of an

increase in a player’s marginal revenue product from moving

on player movement is independent of free agent status. They

later noted that free agency had created a wealth affect due

to increased salaries of players, shifting rents from the

owners to the players. They felt that the wealth affect

might threaten teams located in economically small markets.

They concluded that movement of teams would result from free

agency as the gains of movement to the owners rose to exceed

the transaction costs of team movement.

Maxcy (2002) ran a logit model to examine the marginal

effects of the factors that determine the likelihood that an

individual player between clubs. He also used the Spearman’s

rank correlation coefficient to compare league standings

from one year to the next as well as using a dispersion of

win percentage which measured the ratio of actual standard

deviation, were each club to be equal strength. He showed

from his empirical analysis that the increased player

mobility appeared to have improved competitive balance when

measured by a club’s ability to improve their standing year

to year. There seemed to be less evidence of improvement

when competitive balance was measured by the distribution of

talent across teams within a given season. He concluded by

stating that competitive balance has not declined since the

inception of free agency.



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Chatterjee and Wiseman (2003) examined the relationship

between team salary and team performance by focusing on

three variables, team win/loss percentage, team payroll and

allocation of payroll among players. Their results suggested

that the large disparity in team payrolls does have an

effect on the competitive balance of Major League Baseball.

In conclusion they noted that owners with a fixed payroll

who built an evenly balanced team as measured by individual

salaries of its players do better than owners who spend a

large percentage of its payroll on only a few highly paid

“superstar” players.

The majority of studies in this field have found little

to refute the theory of Rotenberg and Coase that free agency

does not affect competitive balance in Major League

Baseball. Over the years the econometric models have

improved, adding dummy variables for league expansion, free

agent years and work stoppages. Fishman used the number of

free agents in his free agent variable; previous work used a

dummy variable for free agent years. Although this was a new

take on the competitive balance model, his free agent

variable tells us nothing about the quality of free agents.

In the next section I will try to improve on the competitive

balance model done by previous researchers.

Section IV: Empirical Model



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The standard deviation of team winning percentages will

be my model’s dependent variable and will be used to measure

competitive balance in Major League Baseball. We take the

winning percentage of each team in the league in year i and

then calculate the standard deviation of each teams winning

percentage in year i to get the standard deviation of team

winning percentages, looking at competitive balance within a

season. The standard deviation of team winning percentages

is used instead of team winning percentages because it shows

diversity in the winning percentages of each team, making it

a better measure of competitive balance than simply using

team-winning percentages. The data starts in the 1950 season

and concludes in the 2003 season. The model also includes

eight independent variables.

The first independent variable is the average number of

GAMES played. This variable is used for two specific

reasons. The first reason is that there was an increase of

games played in 1962. Prior to 1962, the average number of

games played by a team was 154 games, after the 1961 season

the average number of games played increased to 162. This

variable is also used to control for work stoppages and

strikes that might have occurred in Major League Baseball.

In 1972, there was a strike concerning pensions, which

resulted in a loss of 86 total games for the league. In

1981, there was a strike concerning compensation for losing

a free agent, which resulted in a loss of 712 total games



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for the league. In 1994, there was a strike concerning

salary arbitration and a salary cap, which resulted in a

loss of 920 total games for the league. The 1994 strike

extended into the 1995 season, which resulted in a total

loss of 504 games for the league in the 1995 season.

The second independent variable is TEAMS. This

variable is added to account for league expansion. The

standard deviations are dependent on the size of the

population; therefore the standard deviation will get

smaller when more teams are added to the league. The TEAMS

variable is added to control this problem. In 1950 there

were only 16 teams, versus the 30 teams there are now. The

league expansion years are as follows: 1961,

1962,1969,1977,1993 and 1998.

The third independent variable is DRAFT. This is a

dummy variable used to control for the reverse-order amateur

draft, which was instituted in 1965. The reverse-order

amateur draft allowed teams to select amateur prospects in

reverse order of standings, for example the team with the

worst record would have the top pick in the amateur draft.

The amateur draft was instituted to give weaker teams an

opportunity to improve by getting the chance to select the

top-level prospects.

The fourth variable is FREEAG_ALL_STAR. Most of the

relevant research uses a dummy variable for the effect of

free agency on competitive balance. Fishman used the number



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of free agents in his model, but his variable explained

nothing about the quality of the free agent, nor did it

account for the free agent transferring clubs. This model

tries to improve on previous research by adding a quality

measure for six-year free agents and if the free agent

transferred or stayed with his team. The quality measure

used for free agents is future all-star appearances. For

example, in 1976 Reggie Jackson played for the Baltimore

Orioles but was signed by the New York Yankees when he

became eligible for free agency that season. At the time

Jackson was a 6-time all-star, and he turned out to be a 12-

time career all-star. Only free agents who became future

all-stars and transferred clubs are included. This variable

also confronts the accusations made by fans and

sportswriters. We can assume that all-star players are

amongst the highest paid players in the league, and if only

high revenue teams can bid for the best players, the results

of this variable in the model will explain if this is true

or not. The variable FREEAG_ALL_STAR also includes players

that made the 2004 All-Star game. The starting position

players of the all-star game are selected by the fans, the

remainder of the roster is filled by the manager of the game

as well as the selection of the starting pitcher. From 1976-

1988, there were 33 future all-star free agents that

transferred clubs. From 1989-2002 there were 112 future all-

star free agents that transferred clubs. The graph below



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depicts how well teams have faired in gaining, or losing

future all-star free agents from 1976-2002.4

AMERICAN LEAGUE FUTURE ALL-STAR FREE AGENTS

0

2

4

6

8

10

12

14

ANA BAL BOS CWS CLE DET KC MIN NYY OAK SEA TAM TEX TOR

TEAM

#O

FPL

AYE

RS

LOST

STAYED

GAINED

NATIO NAL LEAG UE FUTURE ALL-S TAR FREE AG ENTS

0

1

2

3

45

6

7

89

10

ARI

ATL

CHC CIN CO

LFLA HO

U LA MILMON

NYM PH

IPIT ST

L SD SF

T EA M

#O

FPL

AYE

RS

LOST

STA Y ED

GA INED

The fifth independent variable is EXPANSION. This is a

dummy variable used to control the shocks associated with

league expansion. New teams had to acquire the players for

their roster from existing teams in the league. As noted

earlier, league expansion occurred in 1961, 1962, 1963,

1969, 1977, 1993 and 1998.

4 All-Star information obtained from www.retrosheet.org



http://www.retrosheet.org

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The sixth independent variable is REENTRY. This is a

dummy variable used to control the effects of the free agent

reentry draft. The first free agents in 1977 were placed in

a reentry draft and could only negotiate with those teams

that chose them. The reentry draft allowed a team only five

draft choices, which put restrictions on free agency. The

reentry draft only affected the 1977-1981 seasons.

The seventh independent variable is COMPENSATION. This

is a dummy variable used to control the effect of the

compensation rule for signing a free agent. The 1981 Basic

Agreement stated that a team signing one of the top nine

free agents (Type A) could protect 24 players on their

roster; a non-signing team could protect 26 players. A team

losing a Type A free agent could choose from a pool of

unprotected players. No team could lose more than one player

in the compensation pool. A non-signing team that lost a

player in the pool would receive $150,000 from the industry

fund, while lesser free agents were compensated for with

draft picks. According to the rating system established by

Elias Sports Bureau, a Type A free agent is ranked among the

top 30 percent of major leaguers at his position, a Type B

free agent is ranked among the top half (but not the top 30

percent) of major leaguers at his position, and a Type C

free agent is ranked among the next 10 percent of major

free agent player mobility obtained from Doug Pappas of SABR.



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leaguers at his position.5 This affected the 1981-1984

seasons.

The eighth independent variable is COLLUSION. This is a

dummy variable used to control the effect of collusion of

the owners. The owners colluded to not sign free agents in

order to keep salaries low. This affected the 1986-1988

seasons. During this period only three future all-star free

agents transferred teams.

The econometric model to be estimated is as follows

using the ordinary least squares method:

STDWPi = Bo + B1COLLUSIONi + B2COMPENSATIONi + B3DRAFTi +

B4EXPANSIONi + B5FREEAG_ALL_STARi + B6GAMESi + B7REENTRYi +

B8TEAMSi + ei

STDWPi= Standard Deviation of team winning percentage in ith

year.

COLLUSION= A dummy variable used to control for years of

collusion. (Coded 1 for years 1986,1987,1988; all other years equal 0).

COMPENSATION= A dummy variable used to control for the years

of compensation for the loss of a free agent. (Coded 1 for years

1981-1984; all other years coded 0).

5 Classification of free agents and definitions were obtained from http://www.baseballamerica.com



http://www.baseballamerica.com

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DRAFT= A dummy variable to control for the amateur draft.

(Coded 0 for 1950-1964; Coded 1 for 1965-2003).

EXPANSION= A dummy variable used to control for the years of

league expansion. (Coded 1 for the years of 1961,1962,1963,1969,1977,1993 and

1998; all other years coded 0).

FREEAG_ALL_STAR= Future free agent all-stars that

transferred clubs in the ith year. (Year:FREEAG_ALL_STAR)

(1977:9),(1978:7),(1979:4),(1980:1),(1981:1),(1982:1),(1983:1),(1984:2),(1985:1),(1986:0),

(1987:2),(1988:1),(1989:3),(1990:4),(1991:6),(1992:2),(1993:15),(1994:6),

(1995:6),(1996:12),(1997:9),(1998:9),(1999:12),(2000:9),(2001:9),(2002:6),(2003:6).

GAMES= The average number of games played by a team in the

ith year. Variable added to control for the increase of

games played as well as shocks caused by strikes and work

stoppages. (1950-1960= 154 games played.1972 = 158 games played.1981= 134 games

played. 1994= 129 games played. 1995= 144 games played. All other seasons not mentioned

averaged 162 games played.)

REENTRY= A dummy variable used to control for the effect on

the free agent entry draft. (Coded 1 for 1977-1981; all other years coded

0.)

TEAMS= The number of teams in the league in ith year.

Variable added to account for league expansion.

(1950-1960= 16 teams. 1961= 18 teams. 1962-1968= 20 teams. 1969-1976= 24 teams. 1977-1992=

26 teams. 1993-1997= 28 teams. 1998-2003= 30 teams.)

Section V: Hypothesis

A smaller standard deviation of team winning

percentages would represent a greater degree of competitive

balance. A negative coefficient would lower the standard



- 26 -

deviation and therefore have a positive effect on

competitive balance. A positive coefficient would increase

the standard deviation and therefore be a detriment to

competitive balance. We would expect COLLUSION, REENTRY,

DRAFT, FREEAG_ALL_STAR and COMPENSATION to be zero, or have

no effect on competitive balance according to the Coase

Theorem. These variables are just a reassignment of property

rights. We should expect TEAMS to have a negative

coefficient. The more teams in the league, the harder it

will be for a single team to affect the overall distribution

of team winning percentages. The GAMES variable should also

have a negative coefficient because the more games played by

teams, the lower the standard deviation should be. The

EXPANSION variable should have a positive coefficient

because it would take a while for a new team to become

competitive, therefore it would cause a higher standard

deviation of winning percentages.

Variable Predicted Sign

Freeag_all_star Negative

Expansion Positive

Draft Negative

Games Negative

Teams Negative

Collusion Negative

Compensation Negative



- 27 -

Reentry Negative

Section VI: Results

When the model was run the first time, the Durbin-

Watson statistic showed that there was serial correlation.

In order to correct this problem a first-order

autoregressive process, AR (1), was added to alleviate the

serial correlation.

Variable Coefficient Std. Error t-Statistic

C 0.130658 0.047527 2.749150COLLUSION -0.002655 0.008272 -0.320926

COMPENSATION -0.005132 0.008229 -0.623620DRAFT -0.010711 0.009748 -1.098774

EXPANSION 0.016907 0.004661 3.627435FREEAG_ALL_STAR -0.000436 0.000671 -0.649153

GAMES -0.000322 0.000260 -1.238771REENTRY 0.007262 0.008185 0.887217

TEAMS 0.000138 0.001090 0.126574AR (1) 0.532951 0.134723 3.955909

The estimated coefficient for COLLUSION is negative

meaning that it decreased the standard deviation of team

winning percentages and improved competitive balance. This

was consistent with the hypothesis although this variable

was not statistically significant (p-value= .75).

The estimated coefficient for COMPENSATION was

negative, meaning that it decreased the standard deviation



- 28 -

of team winning percentages and improved competitive

balance. This was consistent with the hypothesis although

the variable was not statistically significant

(P-value=. 54).

The estimated coefficient DRAFT had a negative

coefficient implying that it decreased the standard

deviation of team winning percentages and therefore improved

the state of competitive balance. This was equivalent to the

hypothesis that drafting top-level prospects can help weaker

teams become more competitive. This statistic was not

statistically significant

(P-value=. 28).

The estimated coefficient EXPANSION had a positive

coefficient meaning that it increased the standard deviation

of team winning percentages and therefore had a detrimental

impact on competitive balance. This matched the hypothesis

that an expansion team would not be competitive in its

initial first season; this statistic was highly significant

(p-value=. 00).

The estimated coefficient FREEAG_ALL_STAR had a

negative coefficient meaning that it improved competitive

balance. This result was equal to the hypothesis. The Coase

Theorem states that free agency is just a reassignment of

property rights, and because this variable was not

significant (p-value=. 52), we accept the Coase Theorem that



- 29 -

free agency would have zero or no effect on competitive

balance.

The estimated coefficient GAMES had a negative

coefficient and therefore improved competitive balance. This

followed the hypothesis that the more games played the lower

the standard deviation of team winning percentage will be.

This variable was not statistically significant (P-value=.

22).

The estimated coefficient REENTRY had a positive

coefficient and therefore increased the standard deviation

of team winning percentages and hurt the competitive balance

of major league baseball. The variable was not consistent

with the hypothesis that the reentry draft is just a

reassignment of property right. This variable was not

statistically significant (p-value=. 38).

The TEAMS coefficient was positive implying that it

decreased the standard deviation of team winning percentages

and therefore was detrimental to competitive balance. This

went against the hypothesis that the more teams added, the

less one single team can affect the outcome of overall

standard deviation team winning percentage. This statistic

was not statistically significant (p-value=. 90).

Lastly, many of the variables were statistically

insignificant. This should not be that discouraging because

theory suggests that only certain activities should have a

direct impact on competitive balance. The coefficients



- 30 -

REENTRY and TEAMS were positive, making them different from

their hypothesized sign. The results of the regression tend

to agree with previous literature and therefore accept the

theories of Coase and Rotenberg. There seemed to be a

problem with the model, which will be examined in the next

section.

Section VII: Alternate Model

Although the previous model agreed with the Coase

Theorem, all of the variables were statistically

insignificant except for the EXPANSION variable. A

correlation matrix was built to see how correlated the

variables are amongst each other. The correlation matrix

below shows that the TEAMS variable is correlated with both

the FREEAG_ALL_STAR and DRAFT variables.

Correlation Matrix

STDWP COLLUSION COMPENSATION DRAFT EXPANSION FREEAG_ALL_STAR

GAMES

REENTRY TEAMS

STDWP 1 -0.16 -0.18 -0.57 0.30 -0.18 -0.16 0.05 -0.45COLLUSION -0.16 1 -0.06 0.15 -0.08 -0.10 0.11 -0.07 0.13

COMPENSATION -0.18 -0.06 1 0.17 -0.1 -0.10 -0.16 0.15 0.15

DRAFT -0.57 0.15 0.17 1 -0.04 0.42 0.25 0.19 0.85EXPANSION 0.30 -0.08 -0.1 -0.04 1 0.25 0.16 0.09 0.07

FREEAG_ALL_STAR -0.18 -0.1 -0.10 0.42 0.25 1 0.08 0.14 0.68GAMES -0.16 0.11 -0.16 0.25 0.16 0.08 1 -0.11 0.19

REENTRY 0.05 -0.07 0.15 0.19 0.09 0.14 -0.11 1 0.17TEAMS -0.45 0.13 0.15 0.85 0.07 0.68 0.19 0.17 1



- 31 -

When the Teams variable was eliminated from the

equation, all the variables except for EXPANSION were

statistically insignificant. After the elimination of the

TEAMS variable the dependent variable becomes unstable. The

standard deviations are dependent upon the size of the

population. As you add more teams, the standard deviation

gets smaller, deceptively making the league appear more

competitive as time goes on. The use of standard deviation

may have also caused some other problems with the model.

First, the outliers influence the standard deviation;

one value may have contributed largely to the results of the

standard deviation. In regards to the model, the independent

variables selected may not have been picking up on any of

the limited variation of the dependent variable. With the

elimination of the TEAMS variable a new dependent variable

must be selected.

An alternative to the standard deviation of team

winning percentage is the normalized standard deviation

(standard error of the mean) of team winning percentage. The

normalized standard deviation of team winning percentage is

the standard deviation of team winning percentage divided by

the square root of the number of teams in the ith year. The

normalized standard deviation of team winning percentage

tells us how much a sample mean differs from the sampling

distribution of sample means. It gives the deviations of the

sample mean around the mean of the sampling distribution.



- 32 -

The alternative model will use the dependent variable NSTWP;

this should correct the problem of eliminating the TEAMS

variable because the formula takes into account the number

of teams in the league.

The alternate model to be estimated is as follows:

NSTDWPi = Bo + B1COLLUSIONi + B2COMPENSATIONi + B3DRAFTi +

B4EXPANSIONi + B5FREEAG_ALL_STARi + B6GAMESi + B7REENTRYi + ei

After running the regression the adjusted R squared of

the alternate model was close to 69 percent compared to 49

percent for the first model. There were still several

variables that were statistically insignificant.

Variable Coefficient Std. Error t-StatisticC 0.029229 0.009404 3.108163

FREEAG_ALL_STAR

-0.000161 0.000140 -1.153014

EXPANSION 0.003262 0.001059 3.081502DRAFT -0.004716 0.001685 -2.798980

COLLUSION -0.000767 0.001898 -0.404324COMPENSATION -0.001160 0.001901 -0.610394

REENTRY 0.001405 0.001890 0.743480GAMES -6.14E-05 5.94E-05 -1.033090AR (1) 0.539600 0.133104 4.053960

It appeared that more variables could be eliminated to

make the model tighter. The variables COLLUSION,

COMPENSATION and REENTRY may be insignificant because they

might already be reflected in the variable FREEAG_ALL_STAR.



- 33 -

From 1976-1988, there were 33 future all-star free agents

that transferred clubs. From 1989-2002 there were 112 future

all-star free agents that transferred clubs. We can

eliminate the GAMES variable as well, due to its awkward

coefficient results.

The revised econometric model is as follows:

NSTDWPi = Bo + B1FREEAG_ALL_STARi + B2EXPANSIONi + B3DRAFTi + ei

Results:

Like the first model, serial correlation was present

and a first-order autoregressive process; AR (1) was added

to alleviate the serial correlation problem.

Variable Coefficient Std. Error t-Statistic

C 0.019604 0.001440 13.60931DRAFT -0.004892 0.001644 -2.974863

FREEAG_ALL_STAR -0.000160 0.000131 -1.221852

EXPANSION 0.003174 0.001019 3.114536AR (1) 0.539297 0.124947 4.316194

The estimated coefficient DRAFT is negative. It

decreased the normalized standard deviation of team winning

percentage and improved competitive balance. The DRAFT

variable was highly significant (p-value = .00).

The estimated coefficient FREEAG_ALL_STAR is negative.

It decreased the normalized standard deviation of the team



- 34 -

winning percentage and improved the competitive balance. The

statistic was not significant (p-value = .23).

The estimated coefficient EXPANSION was positive. It

increased the normalized standard deviation of team winning

percentage and decreased competitive balance. The EXPANSION

variable was highly significant (p-value = .00).

The results of the regression tend to agree with the

theories of Coase and Rotenberg. According to the model, the

DRAFT variable improved the competitive balance of Major

League Baseball. The EXPANSION variable harmed the

competitive balance of Major League Baseball. The model

results displayed that the FREEAG_ALL_STAR variable improved

competitive balance although it was not statistically

significant. The FREEAG_ALL_STAR tested the argument that

big market teams have an advantage over small market teams

because it included only future all-star players who

transferred clubs, and are most likely the highest paid

players in the league.

Section VIII: Conclusion

The July 2000, the Blue Ribbon Report stressed that

there was a growing disparity amongst teams and competitive

balance was indeed a dilemma in Major League Baseball. In my

paper I have not only measured competitive balance by

viewing the policy changes in baseball, but also most



- 35 -

importantly I have measured the role of free agency.

According to economic theory from Rotenberg and Coase, free

agency should not have affected the competitive balance of

major league baseball. The econometric model used a variable

counting the number of future all-stars who were free agents

as a measure of player quality, rather than using a dummy

variable for free agency which was popular in previous

literature. The free agent variable used in this model

showed that free agency has improved the competitive balance

of major league baseball, although the variable was not

significant. The model accepted the Coase Theorem that free

agency would not have an effect on competitive balance.

After examining the correlation matrix of the first

model, there was a problem with the number of teams

variable. With the elimination of that variable the standard

deviation of team winning percentage became an unsuitable

dependent variable. The new dependent variable was the

normalized standard deviation of team winning percentage.

This variable took into account the number of teams in the

formula making it an acceptable dependent variable. The

results of the second model were better than the first

model. The reverse order draft variable displayed that it

improved competitive balance. The dummy variable for

expansion displayed that it was harmful to competitive

balance. The free agent future all-star players who



- 36 -

transferred clubs variable displayed that it improved the

competitive balance.

In respect to improving the model, there are some

interesting variables that may be used for future works. A

better variable than FREEAG_ALL_STAR may be a variable that

include Type A free agents that transferred clubs. This

variable would include more quality players; it would be

naïve to think that only all-star players can improve the

competitiveness of a team.

The Blue Ribbon Report showcased some of the problems

they saw in Major League Baseball, but according to the

results of this model, team payroll disparities do not harm

the competitive balance of Major League Baseball.

Section VIIII: Related issues possibly affecting future

research

Future researchers on this subject matter will have to

deal with new policy changes that were instituted in the

2002-2006 Collective Bargaining Agreement, most importantly

the luxury tax and revenue sharing.

The luxury tax was first implemented in Major League

Baseball in the 1997-1999 seasons and was reinstated in the

2002-2006 Basic Agreement. The luxury tax states that teams

must pay a 17.5 percent penalty on payroll exceeding $117

million for the 2003 season. Teams must pay a 22.5 percent



- 37 -

penalty on payroll exceeding $120.5 million for the 2004

season. Teams must pay a 22.5 percent penalty on payroll

exceeding $128 million and no tax in 2006. Second time

offenders must pay a 30 percent penalty and third and fourth

time offenders must pay a 40 percent penalty. The money from

the luxury tax is said to be used for player benefits,

including a player benefit plan.

Sanderson and Siegfried (2003) believe that the

implementation of the luxury tax can be beneficial in

improving competitive balance if the tax rate is set at the

proper payroll level and the rate is fixed so that it

internalizes the externality. The theory behind the luxury

tax is that acquiring a highly paid team is a luxury for one

owner that imposes negative externalities on other

franchises. The luxury tax should be effective to the point

where incremental talent on the high revenue team creates a

league-wide net negative impact that might be ignored by the

owner of the high revenue team because under league revenue

sharing rules they bear little of the cost of an “over-

accumulation” of talent. If the tax rate accurately reflects

this internal externality, it creates an incentive for the

high revenue team owner to balance their gain against the

cost of third parties.

The revenue sharing base plan states that each team

contributes 34 percent of its net local revenue, after

deductions for ballpark expenses, to pool. This is



- 38 -

redistributed equally to all 30 teams, plus a central fund

to be distributed to low revenue teams.

The central fund component entails that $72 million be

taken from those teams that are net players in the base plan

and redistributed to teams that are net receivers in the

base plan. The central fund component phases in at 60

percent in 2003, 80 percent in 2004, and 100 percent in 2005

and 2006. It is collected by taking a figure in which the

numerator is $72.2 million and the denominator is total net

local revenue after ballpark expenses of all player clubs,

and multiplying the figure by a payer club’s total net local

revenue after ballpark expenses. It is redistributed on a

split-pool to be shared equally each season and the rest be

split up by the Commissioner out of the central and

discretionary funds.

According to Sanderson & Siegfried (2003) the

implementation of revenue sharing could either benefit or

hurt competitive balance. They indicated if revenue sharing

blunts the incentive for all teams to bid aggressively for

talented players, thereby muting salary differentials

between more and less talented players, non-pecuniary

considerations will loom larger in some free agents decision

between competing offers. If players valued the opportunity

to play on championship contenders for reasons beyond

financial rewards, increased revenue sharing could lead to a

greater competitive imbalance.



- 39 -

At this time it is too early to tell what the

implications of the luxury tax and revenue sharing will be.

They will be important factors in coming years when

researchers try to model competitive balance.

Model I

Dependent Variable: STDWPMethod: Least SquaresEviewsSample (adjusted): 1951 2003Included observations: 53 after adjusting endpointsConvergence achieved after 11 iterations



- 40 -

Variable Coefficient Std. Error t-Statistic Prob.C 0.130658 0.047527 2.749150 0.0087

EXPANSION 0.016907 0.004661 3.627435 0.0008FREEAG_ALL_STA

R-0.000436 0.000671 -0.649153 0.5197

DRAFT -0.010711 0.009748 -1.098774 0.2780COMPENSATION -0.005132 0.008229 -0.623620 0.5362

COLLUSION -0.002655 0.008272 -0.320926 0.7498GAMES -0.000322 0.000260 -1.238771 0.2222

REENTRY 0.007262 0.008185 0.887217 0.3799TEAMS 0.000138 0.001090 0.126574 0.8999AR (1) 0.532951 0.134723 3.955909 0.0003

R-squared 0.574972 Mean dependent var 0.075881Adjusted R-squared 0.486012 S.D. dependent var 0.014698S.E. of regression 0.010537 Akaike info criterion -

6.099512Sum squared resid 0.004775 Schwarz criterion -

5.727758Log likelihood 171.6371 F-statistic 6.463303Durbin-Watson stat 1.957912 Prob(F-statistic) 0.000009Inverted AR Roots .53

Model II

Dependent Variable: NSTDWP

Method: Least SquaresEviewsSample (adjusted): 1951 2003

Included observations: 53 after adjusting endpointsConvergence achieved after 10 iterations

Variable Coefficient Std. Error t-Statistic Prob.

C 0.019604 0.001440 13.60931 0.0000DRAFT -0.004892 0.001644 -2.974863 0.0046

FREEAG_ALL_STAR -0.000160 0.000131 -1.221852 0.2277



- 41 -

EXPANSION 0.003174 0.001019 3.114536 0.0031AR (1) 0.539297 0.124947 4.316194 0.0001

R-squared 0.723227 Mean dependent var 0.016034Adjusted R-squared 0.700163 S.D. dependent var 0.004371

S.E. of regression 0.002393 Akaike info criterion -9.142557Sum squared resid 0.000275 Schwarz criterion -8.956680Log likelihood 247.2778 F-statistic 31.35687

Durbin-Watson stat 2.113541 Prob(F-statistic) 0.000000

Inverted AR Roots .54

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Data & Online Resourceswww.retrosheet.orgwww.mlb.comwww.baseball-reference.comwww.baseball-almanac.comhttp://www.all-baseball.com/mikesbballrantshttp://www.cbaforfans.comhttp://web.ics.purdue.edu/~tamerg/roadsidephotos/baseball/data.htmhttp://www.baseballamerica.com


http://www.retrosheet.org

http://www.baseball-reference.com

http://www.all-baseball.com/mikesbballrants

http://www.cbaforfans.com


http://www.baseballamerica.com

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