On the evolution of competitive balance: the impact of an increasing global search.
Schmidt, Martin B. ; Berri, David J.
When there are no transaction costs the assignment of legal rights
have no effect upon the allocation of resources among economic
enterprises.
--Stigler (1988)
I. INTRODUCTION
The epigraph captures the essence of what is generally referred to
as the Coase theorem. Rottenberg (1956), preceding Coase by four years,
made the same point in the context of professional baseball.
Specifically, Rottenberg examined the distribution of playing talent
under two institutions. The first allocated the rights to buy and sell
players to the owners of Major League Baseball teams. The second system
allowed the players to freely choose their employer. Rottenberg (1956,
255) offered the following proposition: (1) "When there are no
impediments to the buying and selling of playing talent, the assignment
of the rights to this talent will have no effect upon the allocation of
players among Major League Baseball teams."
Following the argument of Rottenberg, institutional changes, such
as a free market for veteran players and a reverse-order amateur draft,
should not affect the distribution of players. Furthermore, because the
allocation of talent within a sport is intimately related to the degree
of competitive balance, these changes should not impact the distribution
of wins. (2) If such policies, though, do not alter competitive balance,
what factors are important?
As will be detailed, prior research has suggested that competitive
balance in Major League Baseball is not constant but rather has improved
for much of the latter half of the 20th century. The present study
examines whether the observed changes in the level of competitive
balance contradict the precepts of the Coase theorem. Additionally, we
desire to examine a separate, largely ignored factor described in the
works of evolutionary biologist Stephen Jay Gould (1986; 1996) and
economist Andrew Zimbalist (1992a; 1992b). Specifically, these authors
argue that an expanding population of athletes would influence the
convergence of team performance.
Overall, our results suggest that the driving force behind Major
League Baseball's improved competitive balance has been increases
in the population of players Major League Baseball can employ. Although
there exist marginal evidence of an impact from institutional changes,
these vary and are quite small.
Our study begins with a review of how competitive balance is
measured. The measure of competitive balance will then be contrasted
with Major League Baseball's stated position. From this discussion
we move on to a discussion of the various institutions baseball has
enacted to alter the distribution of wins in the sport and the works of
Rottenberg and Gould, all of which suggests that such institutions are
not the primary cause of competitive balance in Major League Baseball.
We then examine the empirical validity of these views via an examination
of the time-series nature of competitive balance. The final section
offers some concluding observations.
II. THE MEASUREMENT OF COMPETITIVE BALANCE
The examination of competition balance begins with a measure of the
distribution of wins in Major League Baseball. Following the lead of
Quirk and Fort (1992, 244), who built on Noll (1988), competitive
balance can be measured by comparing "the actual performance of a
league to the performance that would have occurred if the league had the
maximum degree of competitive balance in the sense that all teams were
equal in playing strengths. The less the deviation of actual league
performance from that of the ideal league, the greater is the degree of
competitive balance."
The intuition suggests the following Noll-Scully measure of
competitive balance (CB):
C[B.sub.it] = [sigma][(wp).sup.actual.sub.it]/[sigma][(wp).sup.ideal.sub.it]; where [[sigma].sup.ideal.sub.it] = [mu] (wp)
where [sigma][(wp).sub.it] is the standard deviation of winning
percentages within league (i) in period (t). Also, [mu][(wp).sub.it] is
league (i)'s mean and N the total number of games. (3) Finally, as
noted by Quirk and Fort, the idealized standard deviation represents the
standard deviation of winning percentage if each team in a league has an
equal probability of winning. The greater the actual standard deviation
is relative to the ideal, the less balance exists within the
professional sports league.
Utilizing this measure, C[B.sub.t], we calculated the level of
competitive balance in Major League Baseball for both leagues for the
years 1901 to 2000. The results of these calculations are reported in
Figure 1. The figure highlights the fact that the level of competitive
balance in Major League Baseball has improved for much of the latter
half of the 20th century, that is, both measures show a marked increase
in the level of competitive balance beginning after 1960. (4) Finally,
Table 1 reports the trend estimates for the (2) series. Specifically,
whether one examines the entire period or the past (40) years, each
series has experienced a similar and significant downward trend.
Finally, the standard deviation of the (2) series has declined. For
1911-59, the standard deviation of C[B.sub.t] was (0.512) and (0.489)
for the American and National Leagues, respectively. These values fell
to (0.335) and (0.377), respectively, for the 1960-2000 period.
[FIGURE 1 OMITTED]
This factual account stands in contrast to the prevailing view
offered by both industry insiders and various members of the media. (5)
From their perspective, baseball has a competitive balance problem.
Major League Baseball's Blue Ribbon Panel suggested that
significant disparities exists in the distribution of both revenue and
wins. (6) From 1995-99, the only years the panel considered, no team
with a payroll in the bottom 50% of the payroll rankings appeared in
Major League Baseball's annual postseason competition. The panel
members argued that such a result renders the outcome of the season a
foregone conclusion for teams without the revenues necessary to compete.
Specifically, these teams understand at the onset of a season that
postseason success is not in their future.
The Blue Ribbon Panel recommended a number of changes, many of
which seem to limit player movement or to convey greater rights to the
teams. For example, the panel proposed to overhaul the amateur draft.
Their proposal recommended that foreign players be subject to the draft
and that teams maintain the rights of draftees beyond the one-year
period they currently hold. In addition, the panel proposed an annual
"competitive balance draft," under which the eight clubs with
the worst records could draft players not on the 40-man roster of the
eight playoff teams. (7)
These proposals hearken back to the arguments offered in support of
baseball's reserve clause. For those unfamiliar with baseball
history, the reserve clause was enacted in a secret meeting of the
National League in 1879 (Eckard, 2001). The clause initially allowed
teams to reserve five players at the end of each season who would not be
allowed to sign with another organization. The number of players was
restricted until eventually every player's contract contained a
clause that stated the team could re-sign the player at the conclusion
of a contract according to the terms set by the team.
As detailed in Eckard (2001), the National League justified the
rule by claiming "the financial results of the past season [1879]
prove that salaries must come down" Later statements issued by the
league couched the defense of the reserve clause in terms of competitive
balance. With a study of league standings, though, Eckard presented
evidence that competitive balance was not a significant issue for the
National League in 1879. Specifically, Eckard shows that the relation
between city population and team wins was actually negative, suggesting
that at the time the reserve clause was instituted the league was
actually dominated by teams from smaller markets. Hence, Eckard
concludes that the reserve clause was only created to limit player
salaries and increase the profits of the National League.
III. THE ROTTENBERG (COASE) THEOREM
Given the precepts of classical theory, the distribution of playing
talent should follow the dictates of the market. In which case, whether
the player or the team holds the right to the athlete's services is
theoretically immaterial. If a player could generate a greater stream of
revenue in any one market, then franchises located elsewhere would have
an incentive to sell the player to the team located in the higherrevenue
market. In essence, the ability of teams to buy and sell playing talent
circumvents the stated intention of the reserve clause.(8)
The reserve clause was removed via negotiations between the
player's union and team own ers in 1976.(9) The two sides agreed
that players who had accumulated six or more years of Major League
experience would become free agents at the conclusion of their current
contracts. Although players with less than six years of service were
still restricted in their ability to sell their services, players who
accumulated such tenure were able to offer their talent on an open
market. The industry argued (and continues to argue), that free agency
has a detrimental impact on the distribution of wins. The theoretical
work of Rottenberg, though, suggests that the institution of a free
market for players should not impact the distribution of playing talent,
hence competitive balance should not change.
The change in institutions in baseball provides a natural test for
the Rottenberg (Coase) theorem. Specifically, the theorem maintains that
the levels of competitive balance before and after the institution of
free agency should not differ. The results of examining Figure 1 suggest
that the tale one can tell depends on the length of time one examines.
If one restricts the analysis to the ten years both before and after
free agency, one finds no statistical difference in the level of
competitive balance observed in either the American League or the
National League. (10) If one considers a larger sample, though, spanning
the 24 years both before and after the institution of free agency, a
different story may be told. Specifically, from 1951 to 1976, the level
of competitive balance according to the C[B.sub.t] measure averaged 1.96
and 1.90 in the American and National Leagues, respectively. For 1977 to
2000, though, the average level of competitive balance fell to 1.70 in
the American League. The average National League number fell to 1.64.
Each of these changes is statistically significant according to standard
Student t-tests.(11) The impact of the introduction of the amateur draft
follows similarly. (12)
These last results seem inconsistent with the arguments of
Rottenberg and Coase. However, an alternative explanation for the
observed changes are not considered. In essence, most studies examining
free agency and the amateur draft begin with the supposition that these
institutions would alter the level of competitive balance. On observing
changes in the distribution of wins, these studies then conclude that
the institution examined is the cause of the observed changes. The works
of Gould (1986; 1996) and Zimbalist (1992), however, suggest that
another factor may be at work: an expanding labor population.
IV. INCREASING THE GLOBAL SEARCH FOR PLAYING TALENT
The breaking of the color line by Jackie Robinson of the Brooklyn
Dodgers in 1947 changed the racial composition of Major League Baseball.
Prior to this date, the typical Major League Baseball player had been a
white American. After 1947, Major League Baseball teams realized that a
global search for talent was necessary if the team wished to remain
competitive. (13)
Globalization of baseball is now evident on the playing fields in
the United States. Players still hail from the traditional areas of
recruitment, such as the United States, Dominican Republic, Puerto Rico,
Venezuela, and Cuba, but many players from Mexico, Australia, Japan, and
Korea also play in the Major Leagues. Even such countries as Spain,
Belgium, the Philippines, Singapore, Vietnam, the United Kingdom,
Brazil, Nicaragua, and the Virgin Islands have produced professional
baseball players. In 2000, the number of foreign-born players on Major
League Baseball rosters was 312, constituting 26% of all players (Levin
et al., 2000).
The impact of the game's globalization on competition in
baseball has recently been highlighted in the writings of Gould (1986;
1996) and Zimbalist (1992a; 1992b). Gould (1986), for example, applied
the nature of biological evolution to the inability of Major League
Baseball players to hit for a 0.400 average after Ted Williams last
accomplished this feat in 1941. In contrast to reports that the
inability of modern players to approach this level of performance
represented a decline in the abilities of today's athletes, Gould
suggested that this change actually represented an improvement in the
average skills of the modern baseball player.
Gould argued that the distribution of athletic talent in a
population should follow a normal curve. At the right tail of this
distribution lay the people with the greatest level of athletic ability.
Given that there is a biomechanical limit to the ability of humans, the
athletes in the far right tail tend to be relatively equal or, in other
words, fairly close to the biological limit. At the beginning of the
20th century, when the people playing Major League Baseball were only
white Northeastern American males, the population baseball could draw
from was relatively small. Consequently, although baseball employed the
most talented players available, the population consisted of players
close to the biomechanical limit and many others from further away.
When the population of players exhibits such diversity in talent, a
truly skilled player can achieve a level of performance far beyond that
of the average player. As the population of available players expanded,
due to both racial integration and the expanding global search, the
number of players approaching the limit of athletic ability increased.
Consequently, large deviations from the mean performance were no longer
observed, and therefore the 0.400-hitter disappears. This argument was
largely echoed in Zimbalist (1992a; 1992b). Zimbalist noted that
competitive balance had improved following the institution of
free-agency, but such improvement was most likely due to the
"compression of baseball talent."
As a precursor to our analysis, Figure 2 reports the behavior of
the mean and standard deviation of hits per at-bat, that is, batting
average, for Major League Baseball. Consistent with Gould's
hypothesis, there has been little change in the mean batting average
across time, particularly if one excludes the 1920s and 1930s. In
contrast, the variance of batting averages has declined.
[FIGURE 2 OMITTED]
Following Chatterjee and Yilmaz (1991), this argument may be
extended to competitive balance. Specifically, because player
performance will converge on the mean when the population of players
more frequently consists of those close to the biological limit of
human, teams (which consist of these more similar players) should also
be converging on the mean winning percentage. (14) In other words, as
the number of players close to the biological limit expands, the talent
each team has access to will increase, making the game itself
increasingly competitive. To test the aforementioned hypothesis,
Chatterjee and Yilmaz (1991) examined the variability of winning
percentage in Major League Baseball. Similar to the evidence offered in
Figure 1 and Table 1, these authors found baseball to be increasingly
competitive over time.
Along similar lines, if competitive balance was dictated only by
the underlying population of potential athletes and not by league
institutions, then one should see similarities in the level of
competitive balance within different leagues in the same sport, yet
differences across sports. (15) We examine this hypothesis by
investigating the level of competitive balance in five different sports
(baseball, basketball, American football, hockey, and soccer) and the
following leagues: the American and National League in baseball, the
National Basketball Association (NBA) and American Basketball
Association (ABA); the National Hockey League (NHL) and World Hockey
Association (WHA); the National Football League (NFL) and the American
Football League (AFL); and the Bundesliga, North American Soccer League (NASL), and Major League Soccer (MLS). To facilitate comparison, only
years for which leagues simultaneously existed in the sport are
examined.
Table 2 reports the average level of competitive balance in each of
these leagues. (16) The dispersion of wins within leagues in baseball,
basketball, football, and soccer are statistically similar. (17) The
lone exception is hockey, the sport with the smallest sample of
simultaneously existing leagues. (18) The level of competitive balance,
in contrast, achieved by each sport is quite different. The most
competitive is soccer, the sport with the largest underlying population
of athletes. The least competitive sport is professional basketball,
which extensively draws its talent from the small pool of tall athletes.
(19)
V. EMPIRICAL METHODOLOGY AND RESULTS
For the past century, Major League Baseball has taken a variety of
steps designed, according to baseball's hierarchy, to alter the
level of competitive balance in the sport. These innovations include
changing how the rights to players were distributed as well as expanding
the pool of available talent. The purpose of this inquiry is to examine
if either of these actions is the primary cause of the observed changes
in the distribution of wins.
Our efforts begin with Figure 3, where two separate measures of
baseball's larger player pool are offered. The first (a) represents
the percentage of Major League Baseball players that were foreign-born,
and the second (b) represents the percentage that is black. (20) Both
measures suggest that increased diversification of Major League Baseball
players is a characteristic of the industry. To examine the impact an
expanding population has on competitive balance, we take advantage of
the time series characteristics of the C[B.sub.t] and player-composition
measures. Specifically, we examine whether the series have a long-run
relationship, that is, whether they are cointegrated. Furthermore, we
examine whether competitive balance responds to changes in the make-up
of players.
[FIGURE 3 OMITTED]
Empirical Methodology
In their seminal treatment of cointegration, Engle and Granger
(1991) describe the process of cointegration as that of attraction--two
(or more) cointegrated series are held together through time.
Specifically, although the (2) series may deviate from each other, there
exists a process(es) that return the series to their defined
equilibrium. In the present case, Gould's theory suggests that
competitive balance and the population pool may be related across time.
Furthermore, if the two are related, Gould's supposition would
suggest that the attraction should flow from the increased population
toward competitive balance, that is, an increased player search should
Granger cause increased competitive balance.
To examine the long-run properties of the set of variables, the
present paper opts for the Johansen maximum likelihood estimation (MLE)
approach rather than the Engel-Granger two-step method preferred by
some. The choice is motivated by the recent findings of Gonzolo (1994)
demonstrating that the Johansen MLE approach has stronger small sample
properties. In addition, Gonzolo has shown that the Johansen MLE
approach is less sensitive to the choice of lag structure. As has been
highlighted within the literature, the estimation of both long- and
short-run estimates can be sensitive to such a choice. (21)
In brief, the Johansen MLE approach integrates both of the long-
and short-run responses. The approach maybe summarized by the following
general k-order VAR model (see Johansen, 1988; 1992a; 1992b):
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [X.sub.t] is a vector of I(1) variables at time t, the
[[GAMMA]sub.i[DELTA]x.sub.t-i] terms account for the stationary
variation related to the past history of the variables, and the [PI]
matrix contains the cointegrating relationships. Furthermore the H
matrix may be separated into two components, such that [PI] =
[alpha][beta]', where the cointegrating parameters--that is,
equation (1)--are contained within the [beta] matrix and the a matrix
describes the weights with which each variable enters the equation, that
is, equation (2). Cointegration, then, requires that the [beta] matrix
contain parameters such that [Z.sub.t], where [Z.sub.t] = [beta]'
[X.sub.t], is stationary. Finally, the [alpha] matrix is thought to
represent the speed with which each variable changes to return the
individual vectors to their respective long-run equilibrium. Such a
matrix may be estimated from the error correction equations.
In terms of directional causality, the use of cointegration
techniques presents a difficulty because all of the included variables
are assumed to be endogenous and therefore cannot provide direct
information on the exogeneity of the variables. Crowder (1998), though,
offers straightforward tests for exogeniety through examination of the
[GAMMA] [sub.i] and [alpha] estimates. Specifically, if
[[DELTA]X.sub.it] fails to respond to the defined long-run
disequilibrium, that is, [[alpha]sub.i] = 0, then [X.sub.it] is said to
be weakly exogenous.(22) In addition to weak exogeneity, strong
exogeneity requires that [[DELTA]X.sub.it] fail to respond to the
incorporated (k) lags of [[DELTA]X.sub.j], that is,
[[SIGMA][GAMMA]sub.i] = 0.
Once stationarity has been established, it is precisely the
[[GAMMA]sub.i] and [alpha] estimates that are of interest. Shocks that
alter the defined long-run equilibrium, [Z.sub.t] =
[[beta]'X.sub.t], by creating a wedge between the cointegrated
variables require some adjustment by the included variables to re-attain
the defined equilibrium. In the present case, the policy prescription of
increasing the labor search would, hypothetically, increase the labor
pool and therefore alter the makeup of players. The question is,
therefore, to what extent do the individual cointegrated variables, that
is, competitive balance measures, move to clear the disequilibrium
created by the shock, [[GAMMA]sub.i] and [alpha]. We recognize that
although the Coase theorem may suggest that institutional factors, such
as free agency, fail to influence competitive balance measures, that is,
[X.sub.t], these factors may still have an impact and therefore could
bias the estimated results (Johansen and Juselius, 1992). For example,
high transactions costs or restrictions on the sale of players would
limit the applicability of the theorem. Daly (1992), among others, has
argued that the sale of players was significantly restricted prior to
free agency.
Therefore, we included several of these factors as conditioning
variables. Conditioning variables are generally incorporated to
eliminate unwanted influences that might affect the estimates of the
cointegrating vectors, but because they are not in any hypothesized
vectors, it would be inappropriate to include them in the system. These
variables, though, may be influential, and their effects would need to
be included. Consequently we chose to include dummy variables (for
expansion in each league, the institution of free agency, and the
reverseorder draft). Specifically, we included the conditioning vector
[C'.sub.t], where [C'.sub.t] = (Expansion, Free Agency, and
Draft Dummies). In terms of specification, a pure pulse specification
for the dummy variables would clearly be inappropriate, hence we
introduced the variables as unity for the entire postinstitutional
change period, that is, the dummy for free agency is (1) from 1976 to
the conclusion of the study. Finally, it is possible (perhaps even
likely) that significant multicollinearity exists between the dummy
variables. Therefore, in the final estimation we replaced the individual
dummy representation with the sum of the variables, dummy-all.
Empirical Results
A starting point for any long-run analysis involves investigation
of the integrated level of the incorporated data. To examine the
stationarity of the variables, both augmented Dickey-Fuller and
Phillips-Perron analysis were performed. As noted in Table 3, both test
results confirm the presence of a unit root in competitive balance and
player diversity measures.
Given the I(1) nature of the data, the variables are introduced in
levels and may therefore be cointegrated. In addition, a lag structure
must be selected for the Johansen MLE procedure. To determine the
appropriate number, we examined the Hannan-Quinn, AIC, and SBC tests on
various lag options. Overall, these tests suggest that the two-variable
VARs have different lag structures. Specifically, though the
(C[B.sub.t][NL]--% foreign born) VAR selects a lag of (4), the AL
version opts for (2). Both AL and NL versions of the % Black VAR chose a
lag of (l). Finally, to examine the sensitivity of the choice, the
following was replicated using the alternative lag lengths, that is,
(I),... (4). The results from these were qualitatively similar to those
presented later.
A final issue in the analysis is whether to include intercept and
trend variables. Such tests may be sensitive to this choice. To address
these issues, Johansen (1992a; 1992b) maintains that an examination of
cointegration should begin with as general an approach as possible.
Therefore, we examined the restricted results with both constant and
trend terms to assess their relative importance. In the majority of
cases, both trend and constant terms were significant; therefore, the
cointegrating equations were estimated with both.
With the use of Johansen and Juselius's (1992) procedure, it
is possible to obtain the estimated cointegrating coefficients, that is,
the estimated [beta]'s, and to test the hypothesized unity
restriction. The identifying procedure, though, requires a normalizing
restriction. In the present context, the relation is normalized on the
league C[B.sub.t] competitive balance measure. Table 4 reports the
results of applying Johansen and Juselius likelihood ratio tests to the
two-variable VARs. All tests fail to reject the unity restriction at
conventional levels. Though these tests suggest that the variables are
cointegrated and tied together through time, it does little to guarantee
how the variables maintain their equilibrium. Therefore, a final step in
a cointegration analysis is to ascertain these responses.
The endogenous responses of competitive balance to changes in
population may provide important information for sports league participants. Exogenous shocks that create a wedge between the
cointegrated variables require one and/or more of the variables to move
to re-attain the prescribed equilibrium. Such responses, though, may be
an outgrowth of either deviations from the defined long-run equilibrium,
the disequilibrium gap, or from the incorporated lags.
Specifically, the disequilbrium error term, [[epsilon]sub.t],
represents the deviation away from the defined long-run equilibrium.
Given the normalization on the competitive balance measure, if
[[epsilon]sub.t] > 0, the adjustment back to equilibrium would
require that the C[B.sub.t] measure to fall and/or for the population
measure to rise. Theoretically, any combination of the two will clear
the relationship. For [[epsilon]sub.t] < 0, the opposite responses
are available. Therefore, the C[B.sub.t] measure should respond
negatively to [[epsilon]sub.t], and the population measure should move
positively.
These results are presented in Table 5. In general, the results are
consistent with the theories of Gould because the competitive balance
measures do respond endogenously to changes in the population pool. (23)
Specifically, although the C[B.sub.t] measures all respond negatively
and significantly to the associated disequilbrium, none of the
population measures provide a significant response. Furthermore, the
competitive balance response values are relatively close to (1) and
therefore suggest that adjustment occurs relatively quickly.
The analysis does allow us to investigate the impact of
institutional changes on competitive balance. In support of
Rottenberg's position, the vast majority of the individual dummy
variables are insignificant within the VECs. There is, however, one
exception: the response to the free agency (1976) dummy variable within
the % Black equations. These responses support the owner's position
that the introduction of free agency would create greater competitive
imbalance.
Significant multicollinearity, though, may exist between the dummy
variables. Therefore, we replaced the individual dummy variables with an
aggregate measure of institutional change. Specifically, dummy-all
represents a simple sum of the individual dummy variables in Table 5.
The estimated responses within the VECs are reported under the column
dummyall.(24) Although significant C[B.sub.t] responses exist within
both league equations and within both population measures, all are quite
small in magnitude. Moreover, the population measures suggest different
responses, with the % Black equations producing greater competitive
imbalance and the % Foreign equations suggesting greater competitive
balance.
Finally, the significant response of our population series to
institutional changes, particularly the National League response, is
consistent with the arguments recently raised in Shepherd and Shepherd
(2002). The authors suggest that the stricter hiring requirements
imposed on domestic players, specifically, the reverse-order player
draft and minimum age requirements, reduced the potential benefits of
signing and developing domestic players. Teams, therefore, have sought
out alternatives where such limitations do not exist. In which case, the
imposition of these institutional changes should produce a positive
response in our population series.
VI. CONCLUDING OBSERVATIONS
The literature examining the economics of professional baseball has
generally focused on the impact various institutions have on the level
of competitive balance. A difficulty with this literature is that
alternative causal factors have not been regularly addressed.
Consequently, the applicability of the Rottenberg (Coase) theorem could
not be clearly ascertained.
The empirical method employed herein examined both the impact of
league institutions as well as the Gould hypothesis, which asserts that
the distribution of wins in Major League Baseball is primarily a
function of the size of the underlying population of talent. In general,
the reported findings support both the work of Rottenberg and Gould.
Although competitive balance has improved over time in Major League
Baseball, the observed changes appear to be consistent with changes in
the available talent pool, not changes in the institutions Major League
Baseball has utilized to distribute the rights to playing talent.
Such results stand at variance with the position adopted by Major
League Baseball Commissioner Bud Selig.(25) Selig contends that baseball
at the dawn of the 21st century has a competitive balance problem.
Furthermore, this problem can be at least partially addressed by
altering the institutions governing the game. Following the work of
Coase and Rottenberg, the changes proposed by Selig would likely
increase the amount of revenue retained by the owners of Major League
Baseball teams. Such changes, though, following the reported empirical
results, would not alter the level of competitive balance.
In terms of what policies may work, it is the case that through
much of the 20th century baseball was the sport of choice among American
youths. Currently, though, sports participation by boys ages 7-17 is 8.7
million in basketball compared to 6.9 million in baseball (Fort, 2003,
p. 20). Given the work of Gould and the empirical results offered here,
the relative decline in the popularity of baseball should be of serious
concern to those concerned about the level of competition in Major
League Baseball. If young men choose not to participate in baseball, the
available talent pool will fall, and so will the level of competitive
balance. Perhaps the resources expended on resolving yet another labor
dispute would be better spent on the promotion of the sport that was
once America's pastime.
ABBREVIATIONS
ABA: American Basketball Association
AFL: American Football League
MLE: Maximum Likelihood Estimation
MLS: Major League Soccer
NASL: North American Soccer League
NFL: National Football League
NHL: National Hockey League
WHA: World Hockey Association
TABLE 1
OLS Trend Estimates for Competitive Balance (C[B.sub.t])
Sample 1911-2000
Dependent Variable Constant Time
C[B.sub.t] AL 2.72 ** -0.012 **
(0.109) (0.002)
C[B.sub.t] NL 2.439 ** -0.008 **
(0.108) (0.002)
Sample 1960-2000
Dependent Variable Constant Time
C[B.sub.t] AL 2.601 ** -0.011 **
(0.335) (0.004)
C[B.sub.t] NL 2.721 ** -0.001 **
(0.377) (0.005)
Note: ** indicates rejection of [H.sub.0] at the 1% level.
TABLE 2
Competitive Balance (C[B.sub.t]) across
Various Professional Team Sports
Average
Level of
Sport League Years C[B.sub.t]
Basketball NBA 1967-68 to 1975-76 2.59
ABA 1967-68 to 1975-76 2.60
Baseball AL 1901-2000 2.12
NL 1901-2000 2.08
Hockey NHL 1972-73 to 1978-79 2.59
WHA 1972-73 to 1978-79 1.89
Football NFL 1960-1969 1.57
AFL 1960-1969 1.58
Soccer Bundesliga 1964-95 1.32
NASL, MLS 1967-84, 1996-2000 1.34
TABLE 3
Augmented Dickey-Fuller and Phillips-Perron Unit Root Tests
ADF Statistic (p) Phillips-Perron
Statistic (1)
Sample 1901-2000
C[B.sub.t] AL -0.940 (2) -1.096 (3)
d(C[B.sub.t] AL) -8.607 (2) ** -14.382 (3) **
Sample 1911-1997
% Foreign -1.293 (2) -0.325 (3)
d(% Foreign) -8.489 (2) ** -14.327 (3) **
ADF Statistic (p) Phillips-Perron
Statistic (1)
Sample 1901-2000
C[B.sub.t] NL -0.946 (2) -1.077 (3)
d(C[B.sub.t] NL) -8.438 (2) ** -14.499 (3) **
Sample 1950-1984
% Black -2.272 (l) -2.444 (3)
d(% Black) -3.700 (1) ** -6.708 (3) **
Notes. The augmented Dickey-Fuller statistics were computed using (p)
lags. The choice of p was based on minimization of the
Schwartz-Bayesian criteria. The Phillips-Perron statistics were
computed using the AR(1) regression including a constant. The choice of
truncation lag (l) is based on Newey-West. In addition, ** represents
significance at the 99% critical level.
TABLE 4
The Cointegrating Vectors: Normalized [beta] Estimates
Normalized LR X[.sup.2] (l)
On Restriction Statistic
% Foreign C[B.sub.t] (AL) [beta] = -1.00 2.156 (0.142)
(1911-97) C[b.sub.t] (NL) [beta] = -1.00 3.352 (0.067)
Normalized LR X[.sup.2] (l)
On Restriction Statistic
% Black C[B.sub.t] (AL) [beta] = -1.00 1.476 (0.224)
(1950-84) C[b.sub.t] (NL) [beta] = -1.00 2.664 (0.103)
Notes: The (n) overidentifying restrictions are imposed on the
estimated matrix and the log-likelihood ratio tests are by the method
suggested in Johansen and Juselius (1992). The ratio test statistics
estimated x(n) p-values are reported in parentheses.
TABLE 5
Weak and strong exogeniety tests: Speed of adjustment and associated
lag Wald tests.
[summation of] [summation of]
[DELTA](NS)t-j [DELTA] (%)t-j
[[epsilon] [summation of] [summation of]
[beta] Variable .sub.t-1)] [[GAMMA].sub.i] [[GAMMA].sub.i]
= 0 = 0
% Foreign C[B.sub.t] AL -0.808 0.245 2.614
(1911-97) (0.000) (0.666) (0.235)
% Foreign 0.005 -0.007 -0.884
(0.657) (0.489) (0.000)
C[B.sub.t] NL -0.740 -0.184 6.258
(0.000) (0.997) (0.223)
% Foreign 0.009 -0.018 -2.423
(0.521) (0.418) (0.000)
% Black C[B.sub.t] AL -0.843 0.051 1.676
(1950-84) (0.000) (0.766) (0.647)
% Black 0.010 -0.008 -0.486
(0.339) (0.360) (0.010)
C[B.sub.t] NL -1.361 0.342 2.078
(0.000) (0.089) (0.089)
% Black 0.014 -0.020 -0.481
(0.311) (0.038) (0.005)
[beta] Variable Dummy-1961 Dummy-1962 Dummy-1965 Dummy-1969
% Foreign C[B.sub.t] -0.156 -- -0.276 0.171
(1911-97) AL (0.487) (0.364) (0.524)
% Foreign -0.020 -- 0.029 -0.018
(0.211) (0.159) (0.323)
C[B.sub.t] -- 0.408 -0.594 0.217
NL (0.147) (0.111) (0.430)
% Foreign -- -0.005 0.009 -0.015
(0.809) (0.726) (0.413)
% Black C[B.sub.t] 0.347 -- -0.012 0.627
(1950-84) AL (0.173) (0.968) (0.032)
% Black 0.009 -- -0.007 -0.031
(0.479) (0.613) (0.033)
C[B.sub.t] -- 1.293 -0.429 0.721
NL (0.002) (0.161) (0.008)
% Black -- 0.001 -0.008 -0.028
(0.950) (0.601) (0.031)
[beta] Variable Dummy-1977 Dummy-all Diagnostic Tests
% Foreign C[B.sub.t] AL -0.045 -0.060 JB(2): 0.298 (0.862)
(1911-97) (0.808) (0.000) W(4): 1.477 (0.148)
G(4): 0.227 (0.797)
R(1): 0.011 (0.919)
% Foreign 0.022 0.003 JB(2): 4.732 (0.090)
(0.087) (0.147) W(4): 0.833(0.632)
G(4): 6.981 (0.010)
R(1): 0.087 (0.769)
C[B.sub.t] NL -0.021 -0.053 JB(2): 0.292 (0.864)
(0.910) (0.054) W(4): 1.293 (0.218)
G(4): 1.475 (0.236)
R(1): 0.165 (0.686)
% Foreign 0.026 0.003 JB(2): 3.367 (0.186)
(0.034) (0.103) W(4): 1.001 (0.474)
G(4): 0.353 (0.704)
R(1): 0.128 (0.721)
% Black C[B.sub.t] AL 0.840 0.173 JB(2): 0.373 (0.830)
(1950-84) (0.004) (0.002) W(4): 0.920 (0.622)
G(4): 1.227 (0.309)
R(1) 0.321 (0.576)
% Black -0.017 -0.001 JB(2): 1.984 (0.371)
(0.221) (0.979) W(4): 1.933(0.100)
G(4): 1.921 (0.160)
R(1): 0.167 (0.684)
C[B.sub.t] NL 1.024 0.317 JB(2): 0.124 (0.947)
(0.001) (0.002) W(4): 0.834 (0.593)
G(4): 1.849 (0.178)
R(1): 0.223 (0.641)
% Black -0.021 -0.013 JB(2): 3.086 (0.214)
(0.149) (0.004) W(4): 1.522 (0.199)
G(4): 5.081 (0.040)
R(1): 1.271 (0.260)
Notes: The [[epsilon].sub.t-1], was computed from the results presented
in Table 4. Each equation includes a constant. The coefficients are
reported with their associated t-statistic for the null hypothesis that
the estimated value is equal to zero. G(q) reports the Breusch-Godfrey
statistic for serial correlation within the residuals obtained from the
estimated model, with lag order of q. JB(q) reports the Jarque-Bera
statistic for normality of the residuals obtained from the estimated
model, with lag order of q. W(q) reports Whites statistic for
heteroscedastic errors within the residuals obtained from the estimated
model, with lag order of q. R(n) reports the Ramsey RESET statistic for
functional form of the estimated model. p-values are in parentheses.
(1.) Rottenberg (1956, 255) further states, "It seems, indeed,
to be true that a market in which freedom is limited by a reserve rule
such as that which now governs the baseball labor market distributes
players among teams about as a free market would."
(2.) of course, if teams are not concerned with profit
maximization--that is, if they are concerned with win
maximization--institutional arrangements may matter.
(3.) Average winning percentage is typically 0.500. With respect to
Major League Baseball, two exceptions to this general condition are
possible. First, the introduction of interleague play in t997 allowed
for each league's ([mu]) to differ from (0.5). A divergence from a
mean of (0.5) also was possible prior to interleague play. Major League
Baseball has traditionally not played games between noncontenders toward
the end of the season postponed due to inclement weather. When this
happens, the number of games played for each team can differ. Given
these possibilities, we used the actual mean winning percentage in the
calculation of the idealized standard deviation rather than the assumed
value of (0.5).
(4.) A variety of alternative competitive balance measures have
been offered in the literature. These include the dispersion and
season-to-season correlation of team winning percentages (Butler, 1995;
Quirk and Fort, 1992; Balfour and Porter, 1991), the relative entropy approach (Horowitz, 1997), the Gini coefficient (Schmidt, 2001; Schmidt
and Berri, 2001), and the Herfindahl-Hirschman index (Depken, 1999) Each
of these measures indicate that competitive balance did improve in the
latter half of the 20th century in Major League Baseball.
(5.) Bud Selig, the commissioner of Major League Baseball, argued
during the 2002 season that the lack of competitive balance has had such
a detrimental effect that six to eight teams would be bankrupt by the
end of 2003. Pappas (2002), though, in an analysis of Major League
Baseball's own financial data, disputed such an interpretation.
(6.) The Commissioner's Blue Ribbon Panel on Baseball
Economics was convened by Major League Baseball to investigate the
issues of competitive balance and economic health. Specifically, the
panel's stated purpose was to "examine the question of whether
Baseball's current economic system has created a problem of
competitive imbalance in the game" (Levin et al., 2000).
(7.) The panel also advocated eliminating the compensation pick
awarded to clubs who lose players to free agency, noting that many
players on the verge of free agency are traded midseason to clubs with
better records, who then get the draft pick.
(8.) The usual requirements of low transaction costs and lack of
restrictions on players sales applies.
(9.) We would be remiss if we did not acknowledge the role that
Curt Flood played in free agency. Though his on-field accomplishments
were substantial (he was a key player on the St. Louis Cardinals, a team
that went to three World Series during his tenure), Flood's
greatest impact on the game came off the field. Alter being traded to
the Phillies following the 1969 season, Flood refused to accept the
transfer. He argued that baseball's reserve clause illegally
prevented him from practicing his trade as he chose. The case eventually
was decided by the Supreme Court. Despite the fact that he lost the
case, Flood's stand paved the way for the eventual success of the
players' union in establishing the right of free agency.
(10.) In the ten years prior to free agency, competitive balance
according to the CB measure averaged 1.74 in the American League and
1.76 in the National League. After free agency, competitive balance in
the American League worsened, averaging 1.83 from 1977 to 1986. Over the
same time period, competitive balance improved in the National League to
1.63. To test whether these differences are statistically significant, a
standard Student t-test was employed. The results rejected (at the 5%
level of significance) the hypothesis that the average level of
competitive balance changed in the ten years before and after free
agency. Such a result is consistent with the work of Fort and Quirk
(1995).
(11.) Such a result is consistent with the work of Eckard (2001).
Although Eckard utilized alternative measures of competitive balance,
specifically the variance in league winning percentage and the
concentration of league pennant winners, he found competitive balance to
improve in the years after free agency. Eckard reached this conclusion
via a simple examination of the level of competitive balance both before
and after the institution of free agency in 1976. As with each study
reviewed, no other hypothesis for the observed changes was considered.
(12.) Although the reserve clause effectively tied a player to one
team, a free market for players who had never signed a contract did
exist until 1964. In that year, following the lead of the NFL and the
NBA, Major League Baseball introduced a reverse-order amateur draft.
Like the reserve clause, the stated intention of the draft was to
promote the level of competitive balance. The draft is organized so that
the teams that finish last in the prior season are able to choose the
top amateurs the following spring. Once an amateur player is drafted by
a team, that team then has one year to sign the player. In that year, no
other team is able to negotiate with the player. Again, following the
Rottenberg theorem, if teams can buy and sell playing talent, one would
still expect a team in a smaller market to be willing to sell its most
talented drafted players to teams located in larger markets. The work of
Fort and Quirk (1995), however, offered evidence that competitive
balance improved after the institution of a player draft, specifically
with respect to the American League. The work of La Croix and Kawaura
(1999) also found an amateur draft to have a positive impact on
competitive balance in Japanese baseball.
(13.) Goff et al. (2002) offered evidence that the integration of
Major League Baseball was first undertaken by historically successful
teams. Competitive pressure eventually led all team to integrate by the
1960s. The globalization of America's pastime extended beyond a
simple search for talent to a search for additional markets. The search
for new markets began in 1953 with the first east-to-west franchise
relocation and the arrival of Hank Aaron in Milwaukee with the Braves, a
club that had moved from Boston the previous winter. The more celebrated
and excoriated movements of the New York Giants and the Brooklyn Dodgers
to San Francisco and Los Angeles, respectively, set the stage for the
expansion of baseball franchises that occurred in the 1960s. Certainly
the expansion in the population Major League Baseball used to find
talent was tied to the expansion in markets observed in the 1950s and
1960s.
(14.) An intermediate step is required. Specifically, the Gould
hypothesis suggests that all players, below and above average, approach
a biomechanical limit. However, because below-average players are
farther away, they approach the limit at a faster pace, at least in
percentage terms, than above-average players. Furthermore, one would
suspect that the probability of winning is an outgrowth of the caliber
of individual players a team has to choose from, particularly in
baseball. The Gould hypothesis, therefore, argues that as the talent
pool rises, greater player homogeneity should be observed. Given no
change in the way players are distributed, the probability of a poor
team, now stocked with players closer in talent to those of the stronger
team, must rise relative to stronger teams. This provides another reason
for including the dummy variables: these variables capture changes in
the way players are distributed. Finally, this is precisely the issue
that Chatterjee and Yilmaz (1991) examined. These authors found that
variability in winning percentages in both the National and American
League has been declining over time.
(15.) Much of this argument follows from the work of Berri and
Vicente-Mayoral (2001).
(16.) Berri and Vicente-Mayoral (2001) examined 13 leagues, as
opposed to the 11 we report in Table 2. With respect to American
football, we only report the data from the NFL and AFL. Berri and
Vicente-Mayoral also reported the level of competitive balance in the
Canadian Football League and the Arena Football League. The results were
consistent with the theoretical extension of Gould's work, that is,
leagues drawing from the same populations did exhibit similar levels of
competitive balance.
(17.) Berri and Vicente-Mayoral (2001) tested whether or not the
reported means are statistically equivalent via the standard Student
t-test. The t-statistic was calculated by these authors for the
following league pairs: The NBA and ABA from 1967-68 to 1975-76; the NHL
and WHA from 1972-73 to 1978-79; the Bundesliga and NASL from 1967-84;
the NFL and AFL from 1960-69; and the NL and AL from 1900-2000. Except
for the NHL and WHA, Berri and Vicente-Mayoral report that every league
pair was found to have a statistically equivalent average level of
competitive balance.
(18.) As reported by Berri and Vicente-Mayoral (2001), the level of
competitive balance achieved in the brief history of the WHA was quite
similar to the level achieved in the history of the NHL.
(19.) The size of an athlete is a significant resource in both
basketball and football. However, what is meant by size and the nature
of the restriction differs across the two sports. In football,
substantial weight may help when playing certain positions. Such weight,
though, may be manufactured via diet and exercise. For professional
basketball, where height is the predominant physical characteristic,
diet and exercise are not of much assistance. As is frequently noted by
people employed in the sport, one cannot teach height. In other words,
no amount of diet or exercise will make an athlete who is six feet tall
into a seven-footer. Hence, professional basketball faces a much more
rigid restriction relative to professional football. Consequently, we
would argue that only in basketball does the size requirement
substantially limit the pool of available talent. For other factors that
may influence competitive balance, see Sanderson (2002). The work of
Sanderson was a part of a special issue of the Journal of Sports
Economics devoted to the topic of competitive balance in sports.
(20.) We would like to thank Scan Lahmen, author of the Baseball
Archive (www.baseball l.com) for the data on the number of foreign-born
players in Major League Baseball. We also thank Andrew Hanssen for
providing the data on racial integration. The latter data have
previously been utilized in a study of discrimination in Major League
Baseball (Hanssen, 1998). Given that some players would fall into both
categories, that is, foreign-born blacks, there is some degree of
overlap between the two series. However, both provide separate and
distinct tests. One group examines an increasing search due to racial
integration, the majority of which came (at least initially) from within
the nation and probably was responsible for an initial increase in the
talent pool, The second group examines a increasing search globally
regardless of race or color and likely was responsible for later
increases.
(21.) Specifically, a lag structure that is too high may
overparameterize and may thus reduce the power of the cointegration
tests. However, a lag structure that is too low may not produce
residuals that are Gaussian.
(22.) The use of strong and weak exogeneity follows the definitions
presented in Engel et al. (1983).
(23.) To examine whether the equations are properly specified,
Godfrey's LM test for serial correlation, Ramsey's RESET test
for functional form, a JarqueBera test for normality, and White's
test for heteroscedasticity are reported. Overall, the results indicate
that the system of equations are well behaved.
(24.) Because none of the other responses deviated significantly,
we do not report these. These are available from the authors on request.
(25.) Of course, it is possible, even likely, that the position of
the commissioner has little to due with competitive balance and more to
due with capturing rents for owners, In which case. his position would
be consistent. We thank an anonymous referee for raising the issue.
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MARTIN B. SCHMIDT and DAVID J. BERRI *
* We have benefited from helpful comments from the editor and two
anonymous referees. All remaining errors remain our sole responsibility.
Schmidt: Associate Professor, Department of Economics, Portland
State University, P.O. Box 751, Portland, OR 97207-0751. Phone
503-725-3930, Fax 503-725-3945, E-mail schmidtm@pdx.edu
Berri: Assistant Professor, Department of Economics, California
State University Bakersfield, 9001 Stockdale Highway, Bakersfield, CA
93311. Phone 661-664-2027, Fax 661-664-2049, E-mail dberri@csub.edu