Thursday, December 29, 2005

Win Shares Walkthrough, pt. 5

Distributing Pitching Win Shares to Individuals

The main component of the individual pitcher’s “Claim Points” formula is very similar to that of the only criteria for batters: Marginal Runs. For pitchers, we also consider W, L, and SV, something called “Save Equivalent Innings”, and the sub-marginal batting performances of pitchers.

We start by calculating the zero-level. This is simply the 152% of the league rate of runs/ 9 innings:
ZL = LgRA*PF(R)*1.52
The 1993 NL RA was 4.521, the Braves PF(R) is .998, and so the ZL for the Braves is 4.521*.998*1.52 = 6.858. But this is the zero-level for the defense as a whole; it includes fielders and pitchers. So we find the PZL, or Pitcher ZL, as:
PZL = ZL - (ZL - RA)*Field%
The Braves’ RA was 3.458, and the Field%(Field% is not the team Fielding Percentage, although I can see why the abbreviation I chose might make some think that. It is the percentage of defensive win shares that has been assigned to the team’s fielders) was .297, so the PZL is 6.858 - (6.858 - 3.458)*.297 = 5.848. So Braves pitchers will get credit for their marginal runs saved compared to a 5.848 RA pitcher.

In WS, unearned runs are counted as one half for the purpose of calculating RA. So ER + .5(R - ER) simplifies to (R + ER)/2, which allows us to write this formula:
PCL-1 = IP/9*PZL - (R + ER)/2
We’ll run through these steps for a starter and a reliever. Steve Avery pitched 223 innings and allowed 81 R and 73 ER, so his PCL-1 is 223/9*5.848 - (81+73)/2 = 67.90. Mike Stanton pitched 52 innings allowing 35 R and 27 ER, for a PCL-1 of 52/9*5.848 - (35+27)/2 = 2.78.

The second criteria used for pitchers is a combination of W, L, and SV:
PCL-2 = (3*W - L + SV)/3
Avery was 18-6 with no saves, for (3*18-6)/3 = 16, while Stanton was 4-6 with 27 saves for (3*4-6+27)/3 = 11.

The third criteria is for “Save Equivalent Innings”. This is designed to give extra credit to relief pitchers for the high leverage value of their innings. SEI = 3*SV + HLD, with the caveat that this figure cannot be greater then 90% of the pitcher’s actual IP. Avery had no saves or holds, and therefore has 0 SEI and will get 0 PCL-3. Stanton had 27 saves and 5 holds, which is 3*27 + 5 = 86 SEI. This is greater then 90% times his 52 innings, by a longshot, so he only gets credit for .9*52 = 46.8 SEI.

Then claim points are given by the marginal runs saved, over your SEI, based on RAC(discussed above):
PCL-3 = (PZL - RAC)*SEI/9
For Stanton this is (5.848 - 4.64)*46.8/9 = 6.28
(This is one case where my input numbers will differ from reality, because I do not have hold data for Steve Bedrosian or Jay Howell in 1993, but I do for the other Braves relievers.)

The final criteria for pitchers is their hitting performance, if it was sub-marginal. This is PCL-4. Marginal Runs hitting was already calculated when we distributed OWS to individuals. But we zeroed out negative MR; here we count them against pitchers. Mike Stanton did not bat in 1993 and therefore has 0. Steve Avery created 3.83 runs while making 72 outs. A marginal player making 72 outs would have created 8.32 runs, so Avery is -4.49 runs. This is PCL-4.

We then sum PCL-1 through PCL-4 for all players, zeroing out negative numbers. Stanton has 2.78+11+6.28+0 = 20.06 claim points, while Avery has 67.90+16+0+-4.49 = 79.41 claim points. The team total is 527, and the team has 128 PWS to give out. So Stanton is credited with 20.06/527*128 = 4.87 PWS, while Avery has 79.41/527*128 = 19.29 PWS.

My take: The zeroing out issue that I railed against in the offensive section is prevalent here as well, so I will not harp on it again.

One part that I am not sure about is the use of a different Zero Level for pitchers then for the defense as a whole. We already assigned a given number of Win Shares to the pitchers based on our assessment of the percentage of defensive value attributable to the pitching staff. Then we use this Pitch/Field breakdown again to find the ZL. This may be double-counting, but I am not sure about it to be honest. The effect of this decision is to have a lower ZL, so this helps better pitchers claim more Win Shares. Great pitchers already seem to be shortchanged, so if what I thinking is true, they would do even worse. Perhaps I am wrong, or just missing something really obvious here.

Some people will question the use of actual decisions in the evaluation, because these of course are dependent on many factors beyond the pitcher’s control. However, in a value method, there is potentially some “hidden” information in there. The weight given to the decisions is much lower then the weight on marginal runs. There are pros and cons, and I am ambivalent on the issue.

The third step, giving extra credit to relievers, is justifiable in a value method because they do pitch in situations in which runs are more valuable, if you use a real-time approach to value. So while the specifics of the step seem to be a guess, it is alright. Using RAC instead of actual RA is a little confusing in a value method, but James cites the misleading nature of reliever’s ERA due to inherited and bequeathed runners. If we could use actual inherited and bequeathed runners data, this would be preferable, but we don’t have that historically, so I can swallow RAC as a stand-in.

The fourth step of subtracting credit for sub-marginal offense is baffling. First of all, lumping it in with pitching means that pitching win shares incorporates offensive performance for bad hitters and does not for good pitchers. That means PWS is not a true isolation of pitching. Even more befuddling, a full-time hitter like Alfredo Griffin in 1981 does not have his value reduced by his horrific hitting, but Steve Avery does. It would be much easier to just allow Avery to have a negative OWS but then have his PWS be truly reflective of his pitching instead of including his offense. Again, the forced zeroing out of negative marginal runs comes back to create problems in Win Shares.


  1. Just a couple of comments:

    The different zero-level baseline for pitchers is very confusing to me, too, but I've played with it a lot and it seems to logically make sense. However, I cannot explain why. :)

    I very much agree about the zeroing out and putting batting Win Shares in the pitching bucket. It skews the outcomes.

    I think the saves/holds add-on is problematic over the course of baseball history, particularly because of save "inflation" over the last few decades. I played with a formula that would adjust automatically based on the overall "save environment" of the time, though I can't find it easily. I used Tango's leveraged index as a guide.

    For THT, I essentially cut the formula in half, based on the analysis.

    I think that giving relievers credit for leveraged innings is another thing that undercuts the value of starting pitching in Win Shares. Between the fielding and reliever credits, starters really do seem to be undervalued in the system. If you believe in a "zero-sum" approach to valuing players, and you agree that fielders and relievers should get credit for their particular roles, this seems almost unavoidable to me. The only other fix is to change the offense/defense split to something more radical, like 60/40, as suggested at fanhome.

    I think another answer is the establishment of a different replacement level for starters. Another thought that just occurred to me is to raise the reliever split to a higher level. That is, don't just take their credit out of the pitching bucket, but take it out of all Win Shares before you even implement the offense/defense split. I could see an argument for the greater validity of this approach.

  2. Your point about changing the zero-line for starters and relievers is well taken and something I did not consider. We know from empirical studies that the "replacement" or "freely available" or whatever you call it line for relievers is lower(in terms of ERA) then it is for starters, so it would make sense to incorporate that into WS.

    The problem is that Bill's zero lines are not based on a concept of "replacement level", but rather on the mathematical consequences of his W% estimator(ie 152% equals no marginal runs allowed equals zero value). So making a change in this area would kind of violate the "spirit" of Win Shares. I think you mentioned in one of our other posts or on your blog about pondering how many changes you could make and still call it Win Shares. This would seem to be a pretty big one in that area to me--not that I am a "Win Shares purist" or anything. If it causes the system to work better, I'm all for it, whatever it is. But IMHO it would be a sgnificant departure from the WS approach.

    BTW, thanks for reading/commenting/linking/etc.


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