Shirking or stochastic productivity in major league baseball: reply.

• Author: Krautmann, Anthony C.

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...