Monday, December 19, 2005

Win Shares Walkthrough, pt. 3

Runs Created Formulas Used in Win Shares
James’ own RC formula is the basis for dividing team Win Shares to individual hitters. The versions used in the book are the 24 “Historical Data Group” formulas published in the STATS All-Time Major League Handbook. For the modern era, this is only one formula.

Since publishing Win Shares, James has again revised his RC formula. Also, the RC formula used includes situational offensive data which I do not have for the Braves. Because of this, I will use the Tech-1 RC formula as the starting point in my analysis here. This formula is less accurate, but it will save a lot of hassle. In the spreadsheet, I have allowed entry of other coefficients so that you can use whichever RC variation you want.

Tech-1 RC is:
A = H + W + HB - CS - DP
B = TB + .26(W + HB - IW) + .52(SB + SH +SF)
C = AB + W + HB + SH + SF
We will use Jeff Blauser as our example player. He had an A factor of 264, a B factor of 300.82, and a C factor of 710. The “classic” RC construct A*B/C gives him 111.9. However, we use Theoretical Team RC here. For more on this, see the “Runs Created” article on my site. Basically, we add the player to a reference team of 8 players who hit at fairly average rates of A/C and B/C(.3 and .375 respectively). Then we calculate the team’s RC with our player and the team’s RC without our player. The difference is the number of runs our player has created. If you let a be the chosen value of A/C(.3) and b be the chosen value of B/C(.375), we have:
TT RC = (A + 8*a*C)*(B + 8*b*C)/(9*C) - (8*a*b*C)
With a =.3 and b = .375(which is what Bill uses):
TT RC = (A + 2.4C)*(B + 3C)/(9C) - .9C
For Blauser:
TT RC = (264 + 2.4*710)*(300.82 + 3*710)/(9*710) - .9*710 = 109.65

This is only the initial RC estimate; we make two adjustments to it. First, an adjustment for hitting in certain situations. What this does is add one run for each “extra” homer with a man on base and one run for each “extra” hit with runners in scoring position. If AB(OB) is AB with runners on base, H(SP) is hits with men in scoring position, etc. then this adjustment is:
SIT = H(SP) - BA*AB(SP) + HR(OB) - (HR/AB)*AB(OB)
Since I do not have the situational data for the 1993 Braves, we’ll set this at zero for everybody.

The second adjustment is to reconcile the individual values to equal the team total of runs. We just sum up the individual runs created and divide that into the team runs scored. The Braves scored 767 runs, but the players are credited with 757 RC. 767/757 = 1.013 = RF(reconciliation factor). Then each individual’s final RC estimate is:
For Blauser, this is (109.65 + 0)*1.013 = 111

My Take: RC is a flawed method, although using the TT version helps correct for this. The issue of RC’s weaknesses can be read about in my aforementioned article on it. For here, I will focus on the other stuff. The situational adjustments are perfectly appropriate in a value method, my only question is imprecision. Why one run for each extra hit and home run? The effect Bill found may well be close to one run, but I’m sure it’s not exactly one run. The reconciliation is completely appropriate so that the players are credited with the same number of runs that their collective efforts actually led to.

The use of constant A/C and B/C of .3 and .375 is another case of imprecision. If you want to estimate how many runs Jeff Blauser created in 1993, value-wise, the best thing to do would be to use the actual context of the Braves team. In the end, doing this will not change your estimate very much, because the differences between real teams are small enough that most hitters will not vary by much. And then you reconcile all of the individual estimates to the actual team runs scored, so you will not gain much. If we use the Braves actual A/C of .299 and B/C of .404, Blauser’s RC estimate becomes 112.46 instead of our original 111.12. His OWS actually decrease, though from 22.58 to 22.34, because of the changes in the other hitter’s performances. You will see how we calculate OWS in the next section.

Distributing Offensive Win Shares to Individuals
We now distribute the team Offensive Win Shares to individuals on the basis of their personal Marginal Runs. Each player’s Marginal Runs is found by:
MR = RC - LgR/Out*Out*PF(R)*.52
Where Out = AB - H + CS + SH + SF + DP
The NL average is .1662 R/O. Blauser created 111 runs, made 446 outs, and the PF(R) is 1.015. So Blauser had:
MR = 111 - .1662*446*.998*.52 = 72.53
We now total these for all players on the team, zeroing out any negative numbers. The Braves totaled 418 MR, so Blauser will get 72.53/418 of the 130 available win shares = 22.6 offensive win shares, the highest total of any Brave hitter.

My take: It only makes sense that if we apportion win shares to the offense based on their percentage of marginal runs that we do the same for players. The biggest problem in this step is zeroing out negative performers. Of course, negative performers are rare, because .52 of the Lg R/O is equivalent to about a .215 OW%, which nobody does and keeps a job. So the margin is set low enough that among players with significant playing time, only pitchers compile negative numbers, which will cause problems later. But this step as a whole is tough to argue with given the assumptions previously made.

The part about this process that I find most concerning is that the distribution of performance by a player’s teammates can impact his own rating. For example, the 1981 Blue Jays are one of the teams with the lowest percentage of win shares assigned to offense. James tells us that they earned 28.083 OWS. The most productive hitter on their team was John Mayberry, who created about approximately 44.67 runs, which is 23.25 runs above the margin. The Blue Jays hitters totaled 74.74 total MR, so Mayberry gets 31.1% of the OWS, for 8.74. So he (and the other TOR hitters), got 1 WS for every 2.66 MR.

Looking at the team, though, two players with very significant playing time are zeroed out. Alfredo Griffin, in 408 PA, was 3.5668 runs below the margin, and Danny Ainge, in 269 PA, was 5.5554 runs below the margin. Suppose that we take those sub-marginal runs and subtract them from two players, Llloyd Moseby(+8.42 MR) and Otto Velez(+15.65 MR). By doing this, we have done nothing to change the run scoring of the team--their RC is still the same, and the team-based MR are still the same. But now the individual MR totals add up to only 65.62, for 2.367 MR/WS, pushing Mayberry up to 9.95 WS. So John Mayberry gains 1.21 Win Shares by moving around about 9.12 RC by his teammates.

The distribution of the other player’s performance should not impact John Mayberry’s value. The performance of his team in a value method can certainly do this(and of course it does in Win Shares), but there is no reason why the distribution of his teammates’ RC should impact our assessment of his value.

WS advocates will probably point out that it is unusual to have significant playing time go to hitters as bad as Griffin and Ainge, and that this was a strike-shortened season so perhaps that is why they ended up so bad, and that therefore this is a nitpick. That is a reasonable viewpoint, but I don’t think there’s anything wrong with nitpicking, because it can point out things that perhaps could be improved upon. Is Win Shares fatally flawed and worthless because of this issue? No. But is it something that should be fixed (if possible)? Yes.

There are actually much worse cases then the Mayberry example I just demonstrated. James discusses an actual case in his book. He has an article comparing the offensive seasons of Chuck Klein in 1930 and Carl Yastrzemski in 1968. Klein had 27% of his team’s MR, and thereby 27% of his team’s 91.72 OWS, for 25.04. Except there were some submarginal performances in there, which are zeroed out. This INCREASES the team’s total of marginal runs, since the individual MR must add up to the team MR, but when we remove negative individual MR, the individual MR are greater. So Klein loses WS, and winds up with 24.09. In the Mayberry example, I eliminated sub-marginal performances by reducing super-marginal performances, and thereby decreased the individual total of marginal runs, causing Mayberry to gain WS. In practice, though, any variation between the team MR and the summed individual MR will drive WS down.

Yaz comes out even worse, dropping from 41.45 to 38.18. This is going to be a problem in any league in which the DH is not used, because a fair percentage of pitchers are sub-marginal. It will be less of an issue in the modern AL then the NL, so now we have introduced a bias towards AL players. Going back to Klein and Yaz, Klein loses 3.8% of his OWS, and Yaz loses 7.9%.

And for what? The distribution of performance by his teammates, which as I have already made the case should not impact our estimate of a player’s value. The fundamental problem here (which I will discuss again later when we get to fielders) is that Bill uses marginal runs to distribute absolute wins. But isn’t it intuitive that absolute wins must be distributed on the basis of absolute runs? We know that when dealing with team dynamics, it is necessary to accept negative figures. If you figure Linear Weight run estimations for hitters (like ERP, XR, etc.), the very bad players will get negative runs. This is unfortunate, but unavoidable, at least as far as we know. James’ system purports to give absolute win estimates, but cannot do so because he does it on the basis of MR. Bill’s methods have the exact same problems as linear absolute run estimators, but he just chooses to ignore them. This is nice, but by ignoring the negatives, we are forced to skew all of the positives.

The individual player’s OWS would add up to the team OWS by using the % of team MR--if you accept negative numbers. This is why individual player’s ERP will add up to the team total. Negative absolute wins aren’t easy to grasp intuitively. They bother us. But what is worse? Rating some shlub at -2, or artificially reducing Yaz’s value because he plays with shlubs? Who do we really care about ranking, shlubs or Hall of Famers? And of course, the shlubs deserve the negative numbers, it’s not like we’re forcing them to inflate Yaz’s value. It’s the other way around. We’re forcing the shlub’s up to zero, and since the slices of the pie must add up to the whole pie, we have to take some pie away from Carl, and Jeff Blauser, and Chuck Klein, and anybody else who has teammates with sub-marginal performances.

And the kicker is that many of the sub-marginal offensive players would get negative OWS but still wind up with positive overall Win Shares, particularly pitchers. Since overall WS are the payoff of the system anyway, what is wrong with accepting negative component values but a positive overall value? Instead you distort everything, instead of accepting some confusing but correct negative numbers for atrocious hitters.

1 comment:

  1. I'm glad to here that (actually, I'm sure I read that before, but forgot it).

    Do you guys[Hardball Times] or yourself have a comprehensive list of the changes that you incorporate in your own WS calculations?

    Your point on negative RC is interesting and something that did not occur to me. Ultimately though, the negative RC doesn't really matter in and of itself, but of course negative RC will always give negative MR.


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