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Friday, April 25, 2008
How much of an NL starter’s hitting is tied up to his value?
This is what I did:
1. Looked at all years since 1955.
2. Selected all pitchers who had a career of at least 150 PA (AB+BB-IBB+HBP+SF). That’s 619 pitchers.
3. Figured out the batting Linear Weights (LWTS), using a floating value for the out, per year, based on all pitchers (regardless of league) hitting in that year. 1955 is -.141, 1995 is -.115, etc.
4. Figured out the pitching LWTS, using league Runs allowed per IP as the baseline.
5. Figured the pitching LWTS per 800 BFP, and hitting LWTS per 65 PA. That would correspond to roughly a full season. (Greg Maddux had 12.4 BFP per PA, and 800/65 is 12.3.)
6. I did it two ways, one the easy way, and the other the hard way. a. is easy, and b. is hard.
a. Calculate the standard deviation of the two LWTS. The pitching LWTS was 9.5 runs (in 800 BFP), and the hitting LWTS was 1.8 (per 65 PA). That makes the spread 5.3 times wider for pitching, making the “split” 16% hitting, and 84% pitching.
b.i) Figure out how many SD each pitcher is from the league mean in both categories (his z-score). Pedro is +12 SD from the league mean with his pitching. Don Newcombe is +11 SD from the league mean with his hitting.
b.ii) Find the standard deviation of all these z-scores. The pitching one is 2.24, and the hitting one is 1.76. From this, we can figure out the reliability of each stat. For pitching, that’s 1-1/2.24^2 = .80. For hitting, that’s .68. (Note: this probably corresponds to the intraclass correlation that Pizza Cutter likes to do. I like to do this too. I just don’t know what it’s called. For all I know, it IS the intraclass correlation.)
b. iii) Figure out the average number of BFP and PA for each pitcher. That’s 6658 and 405, respectively.
b. iv) Figure out the regression equation as:
r=6658/(6658+x)=.80, making x=1653. For hitting, x=194.
b. v) Regress each player’s stats by using:
regression = 1653/(1653+BFP) and 194/(194+PA)
b. vi) Take the standard deviation of the regressed figure. That’s 7.25 runs per 800 BFP for pitching, and 1.15 runs per 65 PA for hitting. That makes pitching over 6 times wider than the hitting in terms of impact. And that makes the hitting split 14%, and pitching split 86%.