Shirking or stochastic productivity in major league baseball: reply.

In my earlier paper in this Journal [9], I attempted to illustrate how the stochastic nature of an input's productivity might help explain the popular perception that Major League Baseball players shirk after receiving a longterm contract. What always made this argument hard for me to swallow is that a player's reputation for being such an unduly contributor would hardly enhance his ability to sign on with another team after the contract expired. At the least, such a position implies a very large discount rate on the part of the player.

What this debate has ignored is the tremendous variability of players' productivity. Table I, replicated below, illustrates the variation in mean (career) slugging averages (SA) of a sample of present and future Hall of Famers [9, 963]. Note the sizable variation among both players' mean performances and standard errors, as well as the considerable variation across time of a particular player's performance.

Table I. Variability of Players' Performances

Name            Career SA   Std. Err.   Minimum SA   Maximum SA

Tony Perez        .460        .051          .372         .589
Carlton Fisk      .473        .056          .361         .551
Mickey Mantle     .554        .089          .398         .705
Reggie Jackson    .486        .068          .340         .608
Rod Carew         .436        .059          .347         .570
Pete Rose         .407        .058          .386         .512
Babe Ruth         .691        .095          .537         .847

If all players' productivity came from the same population, then one could test the disincentive effect of longterm contracts by aggregating together all players and seeing if there is a significant dropoff from the (common) mean in the period following the new contract. This is, in essence, the methodology proposed by Professor Scoggins in the preceding comment [14].

Even a cursory examination, however, of Table One would lead one to seriously question the reality of the author's assumption of identical distributions-simply said, ability is too heterogeneous to tolerate aggregating all players together. What I proposed was that we treat each player separately, basing our analysis on individual-specific distributions. Admittedly, one cost of such an approach is making inferences on small samples, sometimes as low as 4 or 5 observations on a player's past performances. For this reason I reported the number of occurrences in which a player's performance fell off in the subsequent period, both in a statistical sense (which is more sensitive to sample size) as well as in an nonparametric sense.(1) In the first case, I found only 2 of 110 players having statistically below-average performances, a proportion which is not significantly different from zero. Further, under the null hypothesis of no shirking we would expect about 50 percent of the players to fall below (and 50 percent to be above) their means in the subsequent period. In fact, I found only 36 percent had below-average performances! In neither case would one want to conclude that the evidence favors the shirking hypothesis.

Professor Scoggins [14] suggests that measuring performance with the player's slugging average would not properly measure shirking for it ignores the days spent on the disabled list. As most "sports economists" know, the debate about which statistic (or index) best measures productivity is far from resolved. Some analysts prefer career batting average [10], Run Production Average [6], a weighted average of many statistics [3; 8], runs scored [7; 13; 17], but the most common continues to be slugging average [1; 2; 4; 5; 15; 16; 17]. One item that is generally agreed upon, however, is that all of these statistics do an adequate job of measuring the contribution of the player to team winning-the correlation between these measures and the team winning percentage typically ranges between 0.8 and 0.95.

Professor Scoggins [14] has suggested a better measure of productivity, total bases, which he feels will more closely reflect the disincentive effect associated with the propensity to going on the disabled list following a longterm contract [11; 12]. Aggregating together all players, the author regresses total bases (BASES) against a dummy variable (LT) equal to one if the player signed a longterm contract in the previous period.2 Finding a significantly negative coefficient on LT leads him to reject the hypothesis that shirking does not occur, suggesting that my results are quite sensitive to the performance measure used.

To examine whether using a different performance measure would lead me to starkly different conclusions, I recalculated my model using total bases instead of slugging average. Because of the heterogeneity issue discussed above, I continue to base inferences on player-specific distributions. Under the null hypothesis of no shirking, we would expect no more than 5 percent of the sample to have realizations of performance lying below the lower limit of the forecast interval due to purely stochastic reasons. Using BASES as the productivity measure I found 6 such outliers, or 5.4 percent of the sample. Further, if the series is stationary, we would expect about 50 percent of the players to have realizations below their career average in any period, including the subsequent one. Of the 110 players, 40 percent experienced below-average realizations, about the same proportion as in the original study. As before, I hardly believe the evidence favors the shirking hypothesis.

I suspect the seemingly conflicting results obtained by Scoggins are due to his assumption that players' performances are derived from the same population. As both a scientist and a fan of the game, I have a very hard time accepting such an assumption.

References

[1.] Bruggink, Thomas H. and David R. Rose, Jr., "Financial Restraint in the Free Agent Labor Market for Major League Baseball- Players Look at Strike Three." Southern Economic Journal, April 1990, 1029-43. [2.] Cassing, James H. and Richard W. Douglas, "Implications of the Auction Mechanism in Baseball's Free Agency Draft." Southern Economic Journal, July 1980, 110-20. [3.] Chelius, James R. and James B. Dworkin, "Free Agency and Salary Determination in Baseball." Labor Law Journal, August 1982, 539-48. [4.] Cymrot. Donald J., "Migration Trends and Earnings of Free Agents in Major League Baseball: 1976-1979." Economic Inquiry, October 1983. 545-56. [5.] _____ and James A. Dunlevy, "Are Free Agents Perspicacious Peregrinators?" The Review of Economics and Statistics, February 1987, 50-58. [6.] Dworkin, James B., "Collective Bargaining in Baseball: Key Current Issues." Labor Law Journal, August 1988,480-86. [7.] Hill, James R. and William E. Spellman, "Professional Baseball: The Reserve Clause and Salary Structure." Industrial Relations, Winter 1983, 1-19. [8.] James, William. "Introduction for Old Readers," in The Bill James Baseball Abstract. New York. Ballentine Books,1986. [9.] Krautmann, Anthony C., "Shirking or Stochastic Productivity in Major League Baseball?" Southern Economic Journal, April 1990, 961-68. [10.] Krohn, Gregory A., "Measuring the Experience-Productivity Relationship: The Case of Major League Baseball." Journal of Business and Economic Statistics, October 1983. 273-79. [11.] Lehn, Kenneth M., "Property Rights, Risk Sharing, and Player Disability in Major League Baseball." Journal of Law and Economics, October 1982, 341-66. [12.] _____, "Information Asymmetries in Baseball's Free Agent Market." Economic Inquiry, January 1984, 37-44. [13.] Medoff, Marshall H., "On Monopsonistic Exploitation in Professional Baseball." Quarterly Review of Economics and Statistics. Summer 1976, 113-2 1. [14.] Scoggins, John F., "Shirking or Stochastic Productivity in Major League Baseball: Comment." Southern Economic Journal, July 1993. [15.] Scully, Gerald W., "Pay and Performance in Major League Baseball." American Economic Review, December 1974,915-30. [16.] _____. The Business of Major League Baseball, Chicago: University of Chicago Press, 1989. [17.] Sommers, Paul M. and Noel Quinton, "Pay and Performance in Major League Baseball: The Case of the First Family of Free Agents." Journal of Human Resources, 1982, 426-35.

(1.) That is, just counting the number of occurrences in which the subsequent performance fell below the mean. (2.) Interpreting the author's model is difficult since inclusion into the sample requires that the player just signed a longterm contract, meaning every observation MUST have a I assigned to LT. Somehow another observation On each player was included; unfortunately, the author is cryptic about this aspect of his sample.