## Simple Adjustment of Our Pitching Staff for Team Defense

There are many ways to slice the same pie.  I was playing around on Fangraphs when I should have been working or sleeping and eventually had a bunch of numbers and an idea.  Its an idea which I'm sure has been done before but I think its useful just because I think it will show how much of an impact defense can have on a pitcher's stats.

The basics behind the idea is that we know a pitcher's R/9 which is easy and straightforward.  We also know how valuable our infield defense and outfield defense is.  Finally, we know the batted ball profile of each pitcher.  Using the team defense numbers and the batted ball profiles we can adjust a pitcher's R/9 to make it defense neutral.  Its simple and doesn't require DIPS theory like most other stats.  I am about 99% sure I have seen this done before but I was curious and went ahead and calculated the Mariners adjusted R/9 (I'm gonna call it xR/9).

Working from numbers from Fangraphs, I went through some simple math and divided up the defensive impact.  I'll try to just state what I did right here.  If its boring, skip it and go to the stuff later on.

From Fangraphs I was able to compute UZR runs per BIP for the OF and IF.  The Mariners OF was +62.1 runs and IF was +23.4 runs or 0.036 runs/BIP and 0.013 runs/BIP.  Then I could just look at how many GB and FB were  allowed by each pitcher to figure out how to divide up the defensive contribution.  The final equation looked something like this:

xR/9 = 9*(Runs Allowed - xFB - xGB)/IP

xFB = (FB BIP) * (team OF UZR / team FB BIP) [runs saved on flyballs by defense]

xGB = (GB BIP) * (team IF UZR / team GB BIP) [runs saved on groundballs by defense]

Its pretty simple.  Basically all we are doing here is saying that a pitcher benefits from a defense based on how many balls in play he allows and where these balls in play go.  I ignored line drives basically because it was hard and not totally clear how to treat them.  Lets say I'm ignoring line drives because they usually go for hits even for good defenses (this might be false).

The other simple thing I tried was regressing each player's HR/FB numbers to the team average.  Then I could use the linear weights value for a home run to correct the pitcher's total runs allowed for the number of home runs they should have allowed.  Since I lack much creativity, I'm going to call this xR*/9.  I don't want to say xR/9 is equivent to FIP but if xR/9 was FIP then xR*/9 is like xFIP.

Now to the results.

The Mariners benefited from some great defense last year.  The Mariners outfielders were freaking amazing though being 62.1 runs above average compared to the Mariners infielders who were more good than divine at +23.4 runs.  The question is how much did this defense help our pitchers' numbers and who did it help the most.  If the defense helped all pitchers equally, each pitcher should see their R/9 decrease by 0.53 runs (11%).  We know that defense doesn't benefit all pitchers equally though because some pitchers limit balls in play and others don't.  Obviously Felix Hernandez with high strikeout and groundball rates will benefit less than Jarrod Washburn with low strikeouts, walks and high flyball totals.

I know its a big chart so I also posted a shortened chart and graph below to try to pick out the major pitchers you are probably interested in.  I just wanted to point out the column labeled "tdiff" is how the pitcher's xR/9-R/9 differs relative to the team average.

The major thing I think jumps out to me is that almost all pitchers affected relatively evenly by a good defense.  Although Washburn is a contact hitter and others aren't they all roughly benefit by around the same amount.  Only looking at the major pitchers on the team, Ryan Rowland-Smith appears to have been helped the most and either Felix Hernandez or Erik Bedard were helped the least by the defense.

I think I like this approach of looking at how defense affects a pitcher's R/9 because its fairly simple although it definitely isn't as useful as metrics like FIP.  I think its mostly just an interesting way to quantify how much defense can help different types of pitchers.  If you would have asked me, I would have guessed Washburn would have been helped much more than Felix but its really only a tenth of a run between the two.

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