Competitive balance in major league baseball.

Butler, Michael R.

I. Introduction

A number of economists have previously addressed the issue of competitive balance in major league baseball, in particular, the effects of the reserve clause and free agency on competitive balance. While there is general agreement that competitive balance in major league baseball has improved over time, there is no consensus as to the cause of this improvement. Among the suggested possible causes include the elimination of the reserve clause, a narrowing of market sizes among major league teams, and the compression of baseball talent. Unfortunately, the proponents of each of these possible causes have tended to test their hypotheses to the exclusion of competing hypotheses. This paper will present a model of the determinants of competitive balance which should allow the testing of each of the possible explanations.

II. Previous Research

Among those economists who have recently addressed the issue of competitive balance in major league baseball are Balfour and Porter [1991], Scully [1989], and Zimbalist [1992].

Balfour and Porter [1991] compare the variation of winning percentage for the population of teams both before and after free agency and find that that variance has been lower in the period of free agency (1977-89) than it was in the earlier period tested (1961-76). As a result, they "not only reject the hypothesis that the dispersion of winning percentage is higher with free agency, but conclude that it is indeed lower (i.e., that divisional races are closer) during the period of free agency. It appears free agency promotes competitive balance." (Balfour and Porter [1991, 16]). They go on to examine the correlation of team win percentage from year to year and find that year-to-year team win percentages are less likely to be significantly correlated during the period of free agency than in the earlier period studied. They conclude, therefore, that "the mix of wins and losses between the teams changes more rapidly with free agency than with the reserve clause." (Balfour and Porter [1991, 17]).

Scully [1989] uses the standard deviation of team win percentages as a measure of the relative quality of play in major league baseball and notes that this measure has been declining over time in both the American and National Leagues. Based on his own work, as well as that of others,(1) Scully [1989, 97] rejects the hypothesis that free agency has adversely affected league balance but argues instead that "a narrowing of the size of the market in which teams compete has contributed to competitiveness on the playing field."

Recently, Zimbalist [1992] has argued that it is the compression of baseball talent which has served as this leveling force at work in major league baseball. According to Zimbalist [1992, 97]

(i)n 1990, 0.00026 percent of the U.S. population

played major league baseball, or 35

percent less than the share who played in 1903.

At the same time, the population is increasingly

fit athletically, blacks have been allowed

in the game, Latins have entered professional

baseball in large numbers, and the availability

of baseball programs for training youth is far

more extensive today. Today's major league

ballplayers, then, are a smaller fraction of an

increasingly prepared population. The difference

between today's best, average, and worst

players is much smaller than it was twenty or

forty years ago. This results in greater difficulty

in selecting dominant players and in

greater competitive balance among the teams.

Thus, while there is general agreement that the elimination of the reserve clause and the introduction of free agency to major league baseball has not adversely affected competitive balance, there is apparently little agreement as to whether free agency has promoted competitive balance, or if other factors have been responsible for the narrowing of team performance over time--Balfour and Porter give credit to free agency, Scully suggests that it is due to a narrowing of market size, and Zimbalist argues that it is compression of baseball talent.

III. The Model and Data

There can be little doubt that "competitive balance," whether measured by the distribution of team winning percentages within a single season or by the correlation of team winning percentages across seasons, has improved over time in major league baseball. Table 1 shows the results of simple regressions of both the standard deviation of team winning percentages (WPCTSTD) and the season-to-season correlation of team winning percentages (WPCTCORR) against time for both the American and National Leagues over the period 1946-92. In all four equations, the coefficient on time is negative and statistically significant.

TABLE 1

 Dependent Variable: Dependent Variable:
 WPCTSTD WPCTCORR
 American National American National
 League League League League

Intercept 0.1071(a) 0.0898(a) 0.8458(a) 0.7692(a)
 (21.09) (18.880) (14.720) (11.115)

Time -0.0011(a) -0.0006(a) -0.0110(a) -0.0095(a)
 (5.68) (3.376) (5.171) (3.704)

R-Square 0.4228 0.2058 0.3780 0.2377

Absolute value of t-statistic in parentheses

(a)-statistically significant at .01 level

(b)-statistically significant at .05 level

(c)-statistically significant at .10 level

What is less certain, however, is why this leveling has occurred. Is it due to the elimination of the reserve clause and the advent of free agency as argued by Balfour and Porter? Or to the narrowing of market sizes as suggested by Scully? Or perhaps to the compression of baseball talent as argued by Zimbalist? The remainder of this paper will seek to estimate the determinants of both the distribution of team winning percentages within seasons and the correlation of team winning percentages from season-to-season.

The models to be estimated take the form

(1) WPCTSTD = f(AMDRAFT,

EXPNSNnn,

FRAGENCY,

COVARPOP,

POPPPLYR),

(2) WPCTCORR = f(AMDRAFT,

EXPNSNnn,

FRAGENCY,

COVARPOP,

POPPPLYR),

where WPCTSTD = the standard deviation of team winning percentages in each league for each season from 1946-91;

WPCTCORR = the correlation between each team's winning percentage in years t and t - 1 for each season from 1947-91;

AMDRAFT = 1 for each season from 1965-91 and zero otherwise (included to capture the effects of the introduction of the reverse-order amateur draft in 1965);

EXPNSNnn = 1 for an expansion season (1961, 1969, and 1977 for the American League; 196,2 and 1969 for the National League) and zero otherwise;

FRAGENCY = 1 for each season from 1977-91 and zero otherwise (included to measure the effects of the introduction of free agency in 1977);

COVARPOP = the coefficient of variation (standard deviation divided by the mean) of the population of the urbanized areas associated with each U.S.-based team in each league; and

POPPPLYR = U.S. resident population (in thousands) per player in the major leagues.(2)

Estimation of equations 1 and 2 should allow the testing of the competing hypotheses regarding the leveling of team performance in major league baseball over the post-war period. Negative and significant coefficients on FRAGENCY would provide support for the Balfour-Porter position, positive and significant coefficients on COVARPOP would provide support for the Scully position, while negative and significant coefficients on POPPPLYR would provide support for the Zimbalist position.

IV. Results

The results of the estimation of equation (1), in which the dependent variable is the standard deviation of team winning percentages are contained in column (1) of tables 2 and 3(3). The coefficients on AMDRAFT are negative and significant in both estimated equations, indicating that the introduction of the reverse-order amateur draft in 1965 served to promote competitive balance in both the American and National Leagues. The coefficients on EXPNSN62 and EXPNSN69 in the National League equation are both positive and significant, indicating that National League expansion had a short-term positive effect on the dispersion of team winning percentages.(4) The coefficients on the expansion year dummy variables in the American League equation were all positive, but not significantly different from zero.

TABLE 2
American League Dependent Variable: WPCTSTD

 (1) (2) (3)

Constant 0.2831(b) 0.2444(b) 0.16798
 (2.597) (2.347) (2.760)
AMDRAFT 0.0291(a) -0.0252(b) -0.0281(a)
 (2.964) (2.598) (2.816)
EXPNSN61 0.0165 0.0171 0.0204
 (1.047) (1.113) (1.315)
EXPNSN69 0.0070 0.0119 0.0003
 (0.408) (0.752) (0.020)
EXPNSN77 0.0254 0.0277(c) 0.0232
 (1.542) (1.730) (1.411)
FRAGENCY -0.0003 0.0006 -0.0029
 (0.030) (0.060) (0.289)
COVARPOP -0.1325 -0.1507
 (1.252) (1.425)
POPPPLYR -0.0001 -0.0002
 (0.925) (1.175)
Adj R-Sq. 0.4560 0.4329 0.3939

Absolute value of t-statistic in parentheses

(a)-statistically significant at .01 level

(b)-statistically significant at .05 level

(c)-statistically significant at .10 level

TABLE 3
National League Dependent Variable: WPCTSTD

 (1) (2) (3)

Constant 0.0878 0.0437 0.1419(a)
 (1.165) (1.579) (3.043)
AMDRAFT -0.0168(b) -0.0155(b) -0.0151(c)
 (2.210) (2.095) (2.001)
EXPNSN62 0.0303(b) 0.0306(b) 0.0328(b)
 (2.190) (2.234) (2.440)
EXPNSN69 0.0333(b) 0.0361(a) 0.0327(b)
 (2.377) (2.722) (2.363)
FRAGENCY -0.0044 -0.0033 -0.0068
 (0.589) (0.432) (0.941)
COVARPOP 0.0328 0.0442
 (0.917) (1.1445)
POPPPLYR -0.0001 -0.0001
 (0.632) (1.263)
Adj R-Sq. 0.4043 0.4133 0.4069

Absolute value of t-statistic in parentheses

(a)-statistically significant at .01 level

(b)-statistically significant at .05 level

(c)-statistically significant at .10 level

Of primary interest, of course, are the coefficients on the variables FRAGENCY, COVARPOP, and POPPPLYR. None of these coefficients, in either league, are significantly different from zero. Since the COVARPOP and POPPPLYR variables were found to be fairly highly collinear,(5) equation (1) was re-estimated with each of these variables entered individually. These results appear in columns (2) and (3) of tables 2 and 3. In no instance do the coefficients on either COVARPOP or POPPPLYR achieve statistical significance. In addition, a joint F-test of the hypothesis that the coefficients on these two variables are simultaneously equal to zero was unable to reject the null hypothesis. In summary, then, the evidence presented in tables 2 and 3 provide no support for any of the three competing hypotheses. The only significant variable explaining the long-term downward trend in the dispersion of team winning percentages is the dummy variable for the introduction of the amateur draft in 1965. This is consistent with Zimbalist's [1992, 96] observation that "the end of baseball's dynasties dates back more accurately to 1965, the year the amateur draft was introduced, not to 1976. . . . The amateur draft, mandating a selection in reverse order of finish, made it impossible for wealthier clubs to dominate the signing of top amateurs; . . . ."(6)

Table 4 contains the results of the estimation of education 2 above, in which the season-to-season correlation of team winning percentages is the dependent variable. The first column of table 4 presents the OLS estimates from the American League. The coefficient on AMDRAFT is again negative and significantly different from zero, as expected. Of the expansion year dummy variables, the coefficient for the 1969 dummy is negative and significant, while those for 1961 and 1977 are insignificantly different from zero. The coefficients on FRAGENCY, COVARPOP, and POPPPLYR are all of the expected sign and are all significantly different from zero, despite the collinearity between COVARPOP and POPPPLYR.

TABLE 4
Dependent Variable: WPCTCORR

 American League
 (1) (2)

Constant -0.4733 1.0610
 (0.521) (1.291)
AMDRAFT -0.2677(a) -0.1119
 (3.325) (1.461)
EXPNSN61 0.0920 -0.1012
(NL = 62) (0.493) (0.481)
EXPNSN69 -0.3476(c) -0.4875(b)
 (1.788) (2.279)
EXPNSN77 -0.1748
 (0.913)
FRAGENCY -0.1788(b) -0.2532(a)
 (2.400) (3.626)
COVARPOP 2.6613(a) 0.5014
 (2.871) (1.310)
POPPPLYR -0.0035(b) -0.0021
 (2.624) (1.507)
Adj R-Sq. 0.4272 0.3660

 National League
 (3) (4)

Constant -0.1118 1.9490(a)
 (0.382) (4.159)
AMDRAFT -0.0711 -0.0968
 (0.943) (1.267)
EXPNSN61 -0.0464 -0.1139
(NL = 62) (0.218) (0.537)
EXPNSN69 -0.4524(a) -0.4998(b)
 (2.803) (2.318)
EXPNSN77

FRAGENCY -0.2255(a) -0.2896
 (3.184) (4.482)
COVARPOP 0.8497(b)
 (2.610)
POPPPLYR -0.0032(a)
 (2.795)
Adj R-Sq. 0.3474 0.3543

Absolute value of t-statistic in parentheses

(a)-statistically significant at .01 level

(b)-statistically significant at .05 level

(c)-statistically significant at .10 level

Column 2 of table 4 presents the estimates of equation 2 for the National League.(7) The coefficient on AMDRAFT remains negative, but is insignificantly different from zero in this equation. As in the American League equation, only the coefficient on the 1969 expansion year dummy is significant. Of the three variables of primary interest, the coefficient on FRAGENCY is negative and significant, while the coefficients on COVARPOP and POPPPLYR are positive and negative, respectively, but not significantly different from zero. As in the estimation of equation (1), however, the intercept term and the COVARPOP and POPPPLYR variables are highly collinear.(8) An F-test of the joint significance of the coefficients on COVARPOP and POPPPLYR rejects the null hypothesis (at the .10 level of significance) that both are simultaneously equal to zero. When equation (2) is estimated with COVARPOP and POPPPLYR entered individually (columns 3 and 4 of table 4), each of the coefficients takes on its expected sign and is significantly different from zero. Summarizing the results from the estimation of equation (2), then, it appears that the introduction of free agency, the narrowing of market sizes and the compression of baseball talent have all contributed to reductions in the season-to-season correlation of team winning percentages and have thus promoted competitive balance.

V. Summary and Conclusions

Previous research concerning the issue of competitive balance in major league baseball has demonstrated a downward trend both in the dispersion of team winning percentages within single seasons and in the season-to-season correlation of team winning percentages. Various researchers have previously attributed this improvement in competitive balance to the introduction of free agency, a narrowing of team market sizes, and a compression of baseball talent. This paper has set out to test the validity of these competing hypotheses by presenting and estimating models of competitive balance.

The results of the estimation of these models leads to a rather curious conclusion. If the distribution of team winning percentages is taken as being the appropriate measure (indicative of greater competitiveness within seasons) of the nature of competitive balance, then none of the competing hypotheses is supported. Only the introduction of the amateur draft is found to have significantly promoted within season competitiveness. On the other hand, if the season-to-season correlation of team winning percentages is used to measure competitive balance (indicating greater competitiveness across seasons), then the results presented above support all three of the competing hypotheses--free agency, a more narrow distribution of market sizes, and a compression of baseball talent have all served to promote competitiveness across seasons.

In conclusion, then, if one's preference is to measure competitiveness within a season, Balfour and Porter, Scully and Zimbalist are all wrong; if one's preference is to measure competitiveness across seasons, they are all right.

Notes

(1.) See, for example, Drahozel [1986] and Noll [1988].

(2.) Team winning percentages were taken from The Baseball Encyclopedia [1993]. U.S. Resident population for the years 1946-91 was taken from U.S. Bureau of the Census [1992]. Population of urbanized areas was taken from U.S. Bureau of the Census [1953, 1961, 1979, 1984, and 1992] for the census years 1950-90 and was interpolated between census years assuming a constant rate of population growth for each urbanized area. The 1950-60 growth rates were used to extrapolate back to 1946; the 1980-90 growth rates were used to estimate 1991 urbanized area populations.

(3.) Since each of the ordinary least squares estimates of equation (1) suffered from positive autocorrelation, the estimated coefficients reported in tables 2 and 3 were obtained using weighted least squares.

(4.) Coefficients on dummy variables for the years immediately following league expansion were consistently insignificantly different from zero.

(5.) The condition indexes from the American League equation were 46 and 95 and from the National League equation were 23 and 79, indicating a high degree of collinearity between COVARPOP, POPPPLYR, and the intercept term.

(6.) Later, Zimbalist [1992, 99-100] suggests that "(t)he end of the Yankee dynasty probably had as much to do with the team losing its major league farm club (described as a "hand-in-glove" relationship between the Yankees and the Kansas City Athletics) as with the introduction of the 1965 amateur draft." The fact that the coefficients on AMDRAFT in the American League equations are consistently larger (in absolute value) than those in the National League is consistent with this suggestion.

(7.) All three of the estimated equations for the National League were obtained using weighted least squares to correct for an autocorrelation problem.

(8.) Condition indexes of 23 and 82.

References

Balfour, Alan and Philip K. Porter. "The Reserve Clause and Professional Sports: Legality and Effect on Competitive Balance." Labor Law Journal 42(1), 1991, 8-18.

The Baseball Encyclopedia: the Complete and Definitive Record of Major League Baseball (9th ed.). New York: Macmillan, 1993.

Drahozel, Christopher R. "The Impact of Free Agency on the Distribution of Playing Talent in Major League Baseball." Journal of Economics and Business 38(2), 1986, 113-21.

Noil, Roger G. "The Economics of Sports Leagues." In The Law of Professional and Amateur Sports, Gary A. Uberstine, ed. New York Clark Boardman, 1988.

Scully, Gerald W. The Business of a Major League Baseball. Chicago: University of Chicago Press, 1989.

U.S. Bureau of the Census. 1990 Census of Population and Housing. Summary Population and Housing Characteristics, United States. Washington: U.S. Government Printing Office, 1992.

--. Statistical Abstract of the United States: 1992 (112th edition). Washington: U. S. Government Printing Office, 1992.

--. Supplementary Report, 1970 Census of Population, "Population and Land Area of Urbanized Areas for the United States and Puerto Rico, 1970 and 1960." Washington: U.S. Government Printing Office, 1979.

--. Supplementary Report, 1980 Census of Population, "Population and Land Area of Urbanized Areas for the United States, 1980 and 1970." Washington: U.S. Government Printing Office, 1984.

--. U.S. Census of Population: 1950. Vol. II, Characteristics of the Population, Part 1, United States Summary. Washington: U.S. Government Printing Office, 1953.

--. U.S. Census of Population: 1960. Vol. I, Characteristics of the Population. Part A, Number of Inhabitants. Washington: U.S. Government Printing Office, 1961.

Zimbalist, Andrew. Baseball and Billions: A Probing Look Inside the Big Business of Our National Pasttime. New York: Basic Books, 1992.

Michael R. Butler, Associate Professor, Department of Economics, Texas Christian University, Fort Worth, TX 76129