THE BOOK--Playing The Percentages In Baseball

Thursday, July 22, 2010

Simple PZR

Moons ago, I talked about PZR, which is the flip-side of UZR, and, when you add in PZR with UZR, it should match, exactly, park-and-opponent-adjusted runs allowed. PZR is a bear.  MGL published it a few times, but he’s always had some issue with it that he didn’t care for.  It’s been a hard topic for the two of us to try to wrap ourselves around.

So, the idea is to do a simple version of PZR.  Chris looks like he’s on the right track here, but he makes one mistake (I think):

1. Take the teams ZR chances and Plays Made.  This represents the responsibility of the fielders, NOT THE PITCHER.  That isn’t a perfect nor completely correct assumption, but we’ll talk about that later.
...
Back to the pitcher being responsible part.  A key theory for DIPS and FIP is that the pitcher isn’t responsible for HBIP (much).  Therefore, all plays fielded are the responsibility of the fielders, and the pitcher gets zero credit.  Or, as I noted last year, the pitcher is responsible for about 70% of plays made.  That’s the bare minimum anyone playing gets to make.  I referenced it the other day - scroll to post #30 for the dirty details.

But that’s not true.  The pitcher is responsible for the FREQUENCY, and the fielder is responsible for the SUCCESS.

Anyway, it’s easy enough to do a simple-PZR:
1. Split all the BIP into BIZ and BOZ (balls in zone, and balls out of zone).
2. Figure out the average run value for BIZ and BOZ.  Ideally, you would split it by location on the field, but for now, let’s make it simple (hence, Simple PZR). 

For the purposes of illustration ONLY, I’m going to say that 80% of all BIP are BIZ and 20% are BOZ.  For more illustration, I’m also going to say that the run value for a BIZ is -.15 runs, and the BOZ is +.40 runs.  It’s an illustration.  You guys with a database available during the day time can give me the real numbers.

3. Figure out the FREQUENCY of BIZ and BOZ, since that is what the pitcher IS responsible for.

4. Multiply the figure from 2 to the figure from 3.  As an illustration, let’s say Steve Rogers has 450 BIZ and 50 BOZ.  The run value of his BIP distribution is 450 x -.15 + 50 x +.40 = -47.5 runs.  An average pitcher would be 400 x -.15 + 100 x +.40 = -20 runs.

That makes Steve Rogers’s Simple PZR as 27.5 runs better than average.

We can worry about adjustments etc later.  Right now, this is the basis, and I think this might intersect with what Chris is doing.

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I just know someone does want to talk about adjustments.  Ok.  Instead of BIZ, you want BIZ1, BIZ2, BIZ3 ... BIZ9.  That is, the frequency of BIZ for the 9 fielding spots, as well as the run value of those zones. 

For BOZ, you probably won’t have the hit location, but, that’s fine.  We’ll live with that.  If you insist, then you have to figure out the “no man’s land” (NML zones.  So, the NML567 for the balls that go between 3B, SS, and LF.  The NML78 for the balls that go between LF and CF.  ETc, etc, etc.  But, adjustments is for a later discussion.

Focus on the simple.