DePodesta and OPS

In Michael Lewis' book Moneyball the following passage can be found

"... OPS was the simple addition of on-base and slugging percentages. Crude as it was, it was a much better indicator than any other offensive statistic of the number of runs a team would score. Simply adding the two statistics together, however, implied that they were of equal importance. If the goal was to raise a team's OPS, an extra percentage point of on-base was as good as an extra percentage point of slugging.

Before his thought experiment Paul (DePodesta) had felt uneasy with this crude assumption; now he saw that the assumption was absurd. An extra point of on-base percentage was clearly more valuable than an extra point of slugging percentage -- but by how much? He proceeded to tinker with his own version of Bill James's "Runs Created" formula. When he was finished, he had a model for predicting run production that was more accurate than any he knew of. In his model an extra point of on-base percentage was worth three times an extra point of slugging percentage."

For some time now analysts have known that an additional point of on base percentage was worth more than an additional point of slugging percentage if for no other reason than slugging percentage is based on a four point scale whereas on base percentage is measured on a scale of 0 to 1. So for example, it is clear that if you have two players who both have an OPS (on base + slug) of 800:

Player A: OBP .330 SLUG .470
Player B: OBP .350 SLUG .450

Player B is the more valuable since his 20 points of on base percentage represent more than Player A's 20 points of slugging percentage. That difference has usually been estimated to be 1.4 to 1.5 and so some have taken to calculating OPS as:

OPS' = (OBP*1.5)+SLUG

But the question is, is DePodesta correct, that each incremental point of OBP is worth three times that of slugging percentage?

Recently, in the sabermetric community some research has been done by Phil Birnbaum of SABR's Statistical Analysis Committee and published in the May 2005 issue of the committee's newsletter By The Numbers. Using aggregate data from 1987 and a method where he creates batting lines with one additional point of OBP or SLUG and then uses linear weights to determine how many runs this translates into. He does this for three different cases and comes to the conclusion that an additional point of OBP is worth 1.2 times that of SLUG. He has since corrected this to 1.7 due to a calculation mistake - still short of the 3.0 that DePodesta talks about.

Last year at SABR's convention in Cincinnati Mark Pankin presented the results of his study on this question as well. His more sophisticated approach using Runs Created and a Markov Model to test the impacts at various positions in the batting order concluded that the relative value of OBP versus slugging percentage varies with team and lineup position but that overall the extra point of OBP is worth about twice that of SLUG. For some lineup positions, such as those in front of power hitters (2,3,4) the number is also much higher. He also presented his own version of an "improved OPS" based on his research:

OPS'' = OBP + SLG + (OBP - 0.340)

Below I've compared these two formulas for a series of OBP and SLUG values that range from .300 to .500.

    OBP     SUG    OPS'   OPS''     OPS
   0.300   0.500   0.950   0.760   0.800
   0.310   0.490   0.955   0.770   0.800
   0.320   0.480   0.960   0.780   0.800
   0.330   0.470   0.965   0.790   0.800
   0.340   0.460   0.970   0.800   0.800
   0.350   0.450   0.975   0.810   0.800
   0.360   0.440   0.980   0.820   0.800
   0.370   0.430   0.985   0.830   0.800
   0.380   0.420   0.990   0.840   0.800
   0.390   0.410   0.995   0.850   0.800
   0.400   0.400   1.000   0.860   0.800
   0.410   0.390   1.005   0.870   0.800
   0.420   0.380   1.010   0.880   0.800
   0.430   0.370   1.015   0.890   0.800
   0.440   0.360   1.020   0.900   0.800
   0.450   0.350   1.025   0.910   0.800
   0.460   0.340   1.030   0.920   0.800
   0.470   0.330   1.035   0.930   0.800
   0.480   0.320   1.040   0.940   0.800
   0.490   0.310   1.045   0.950   0.800
   0.500   0.300   1.050   0.960   0.800

And graphed them....

You can see that Pankin's version (OPS'') has a greater slope since his puts a greater weight on OPS whereas the more traditional version climbs more slowly.


Update 8/10: I learned yesterday that there was also a study done by Jahn K. Hakes and Raymond D. Sauer of Clemson University titled "An Economic Evaluation of the Moneyball Hypothesis" where the authors use a couple different techniques and come to the conclusion that the ratio between OBP and SLUG is around 2.0.