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# dXRAAR+

As NRAA and mOPS and EPL have been floating around the site, I was working on a "pitching" stat to evaluate pitchers in a slightly different way.

It's a combination of the work of Keith Woolner, Jim Furtado, and Voros McCracken, all put together into a formula that uses the XR framework, BABIP, and the concept of "replacement level."

This is still in formation and doesn't really say anything that other stats don't, but it came together nicely over the last few days, and I'd like to submit my work for peer review. Assault this, please.

dXRAAR, or, as it will be affectionately known as, DEXTER, is a complicated evaluation of the extrapolated runs above replacement level that a pitcher gave up when adjusted for BABIP.

Seems like a mouthful, right? Well, if you keep it in stages, it's not too complex.

1. Calculate the XR that the pitcher allowed.

XRA=(0.5*(H-2B-3B-HR)) + (0.72*2B) + (1.04*3B) + (1.44*HR) + (0.33*(BB+HBP)) + (0.04*SH) + (0.37*SF) + (-0.37*DP) + (-0.09*(AB-H-K)) + (-0.098*K) + B

Very few sources have at bats for pitchers, but it's easy to derive. Just divide hits by batting average and round that to a whole number.

2. The B-term is the adjustment for stolen bases. Stolen bases are taken from the team and then the pitcher's component is assessed from the difference in the team's steals-prevention ability as is dependent on the pitcher.

B = (0.18*(SB-C))+(-0.32*(CS-C))
C = (SB+CS)*((TSB-SB)/(TSB-SB+TCS-CS))

I think I did this part right; it was probably the toughest part of the whole equation. The C term is the success on stolen base attempts that the other team would be expected to have, and the B term is the difference in that for that specific pitcher.

3. You can calculate the XRAAR for the pitcher at this point.

XRAAR = (((LXRAAR*9/LIP)+1)/9) - XRA

This establishes a "replacement level" at 1 run higher than the league average.

1. We're not done yet. Now it's time to DIPSify it. The underlying assumption, at this point in the stat, is that a pitcher has no significant quantifiable control over balls hit in play, or that the ability to limit line drives is insignificant at the major league level, or something similar. If you disagree with this point, you can use XRAAR+, which is just a simple park adjustment away. Skip to Step 16 at this point if you'd like to avoid the DIPS adjustments.
2. Calculate the pitcher's "Balls in Play," using this formula:
BIP = AB-HR-K
1. Calculate the frequency of all occurances for a pitcher: strikeouts, walks, balls in play, home runs, sacrifices, and double plays. This can be done by simply dividing the # of an event by the BFP or TBF. These will be necessary to calculate the new values.
2. Mutliply BIP*LBABIP.
3. Subtract this figure from the original hits total. Record this new number as "Less Outs."
4. Add Less Outs to BFP. You now have the new "expected batters faced."
5. Using this new figure and the ratios calculated from step 6, simply calculate the expected number for every single category involved. Essentially, multiply K/BFP by the new BFP figure, and so on and so forth.
6. Repeat this step for "Balls in Play." Recalculate the expected hits on balls in play, and that's the number. (For this, just multiply BIP*LBABIP again.)
7. Get the league total for the number of hits on balls in play.
LH-HR = LH - LHR

Easy, right?

13. Now we break it down into singles, doubles, and triples. Using league totals, determine the percentage of balls in play that are extra base hits. With these percentages, calculate the pitcher's expected hits distribution.

ex1B = L1B/LH-HR * exH-HR
ex2B = L2B/LH-HR * exH-HR
ex3B = L3b/LH-HR * exH-HR

Save these numbers.

Now we bring it all together.

1. Using the new BABIP-adjusted numbers, recalculate the XR formula.
2. You can now calculate the pitcher's dXRAAR+.
dXRAAR = (((LdXRAAR*9/LIP)+1)/9) - dXRA

16. Park adjust and serve with a grain of salt.

For 2004, I only calculated the stat for qualifiers, but any pitcher works. Peter Gammons references VORP with some frequency in his columns and he likes to cite it as a value of quality and quantity. This is similar. Brad Lidge would not be at the top of this list, but he would be on it.

So the Top 10 dXRAAR+ values for the 2004 season, among starting pitchers, were:

1. Randy Johnson - 75.9
2. Ben Sheets - 65.7
3. Johan Santana - 62.3
4. Roy Oswalt - 58.2
5. Jason Schmidt - 55.0
6. Curt Schilling - 54.6
7. Roger Clemens - 49.6
8. Carlos Zambrano - 43.1
10. Oliver Perez - 40.6
And the Bottom 10:
1. Jamie Moyer: -14.6
2. Ismael Valdez: -11.3
3. Jose Contreras: -9.7
4. Eric Milton: -7.7
5. Darrell May: -6.1
6. Brian Anderson: -5.1
7. Esteban Loaiza: -4.4
8. Brett Myers: -3.7
9. Ryan Franklin: -1.0
10. Kazuhisa Ishii: -0.3
Tim Wakefield was also among the Bottom 10, but I removed him because of the standard DIPS formula's caveat about knuckleballers.

[on edit]: I just ran Brad Lidge through, and he had a 33.3 figure, which ranked him right between Pedro Martinez and Jake Peavy from 2004. But he was not in the Top 10. [on further edit]: I'm unsure about the inclusion of a pitcher's XBH rate or at least a partial weighting of a pitcher who gives up a lot of doubles or triples. I'm still playing around with that, but, as of now, it is not included. If anyone has any ideas on that, please let me know.