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Does "Better" Pitching Cause the Batting Average on Balls in Play to Fall? (Update)

What I do this week is report on analysis that was suggested by a commentor on last week's post. The original idea then was to see if pitchers did better in the defense independent stats, did that affect the batting average on balls in play that they allowed? I think I found something interesting even if I could not really explain what it meant.

Here is what Guy M suggested:

"This is an interesting way to look at BABIP's relationship to other skills. Obviously, limiting the study to 20 of the greatest pitchers in history is a real limitation, but still interesting. One way Cyril could vastly expand the sample would be to normalize each variable for a pitcher, compared to his career rate. So in a given year a pitcher might be, say, 107 K+, 98 BB+, 113 HR+, and BABIP 102+ (all compared to his career rate). Then you could include hundreds or thousands of pitcher seasons in your analysis, including a range of abilities, and see what the relationship looks like."

So I found all the pitching seasons from 1996-2005 with 200+ IP. Then I did exactly as suggested. There were 370 such seasons. But when I ran the regression, the r-squared was just about 0. That implies that better pitching as measured by DIPS stats does not affect BABIP.

This is different than what I found for regressions that were done for each individual pitcher. Some had a fairly high percentage of their yearly variation in BABIP explained by their DIPS stats. But one of the strange things I found was that the signs on the coefficients were not always as expected. For example, I exptected that If a pitcher had a lower HR% allowed then his BABIP would be lower. That was not always true. In some cases BABIP fell as HR% allowed went up. I also expected that BABIP would fall as SO% went up. That was not always true, either.

But I did find that the average r-squared was about .20. This is a different result from what I found this week. I don't know why this is true. Maybe pitchers are idiosyncratic-what means better pitching for one is not the same for another. I think one thing I should try is what I did last week but with more pitchers, maybe lower the number of years with 100+ IP to 15. That would give me more observations.