Dan Seligman

Dan Seligman

11/15/1999 @ 12:00AM

The Baseball Enigma

IF YOU ARE A COMPENSATION CONSULTANT, you call it pay-for-performance; if you have an economics dictionary in front of you, “marginal productivity” pops into view. Whatever the catch phrase, the point is that pay should bear some relation to a worker’s output. Neoclassical economic theory says that optimum results are achieved when the relation is close. All of which makes the information about baseball players’ performances and salaries a little unsettling. There, the relationship is not close.

Unlike the tasks accomplished by secretaries or vice presidents for media relations, the records of ballplayers are captured in incredible detail and made public (at usatoday.com, for instance). You can access an avalanche of ratios capturing the probabilities of batting, pitching and fielding events, and every imaginable influence on them. On cbssportsline.com, you can also download the unofficial, but widely accepted, player salaries.

How bad is the pay-performance disparity? Boldly risking carpal tunnel syndrome, I recently created a huge spreadsheet with salaries and detailed regular-season performance records of two sizable representative samples of 1999 major-leaguers–100 batters and 100 pitchers–to which I was steered by the Lotus 1-2-3 random-number generator. Even before running any statistical tests on the two samples, I discerned that pay-performance anomalies abound far more than in the secretarial world.



The science of statistics tells us that positive correlations range from 0.0 to 1.0. Batting average and salary correlate only 0.42. To make that figure meaningful, you would square it and come up with the so-called coefficient of determination–in this case 0.18–which tells us that only 18% of the variability in batters’ pay is explained by differences in their batting averages. The correlations that most affect pay are those featuring numbers of home runs (0.62) and total runs driven in (0.66). Taking a whole raft of batting indicators all together–batting average, on-base average, number of times at bat, home runs, RBIs, and player age (a proxy for major-league experience)–you still can’t push the correlation with salary beyond 0.74. When you square that figure, you get 0.55, essentially delivering a message that the reams of published, endlessly analyzed batting data together explain only a shade more than half of the variance in salaries.

Negative correlations range from 0.0 to -1.0. You would expect strong negative correlations between a pitcher’s pay and the collective batting average generated in the at-bats against him. The correlation is negative, but strangely weak, at -0.10. ERA, arguably the single best guide to how well a pitcher is doing his job, also generates weak negative correlations–in this case just -0.20. Incredible bottom line: Only 4% (the square of -0.20) of the variability in pitcher pay reflects their varying ERAs.

More meaningful for pitcher pay is a quite different figure: total number of strikeouts. Correlation with pitchers’ salaries: 0.61.





Comments are turned off for this post.