04 August 2008

Hate the stat, love the statter

I spent part of the last week of July reading the various, mostly extremely short, obits of Jerome Holtzman, sportswriter extraordinaire (and the Chicago cubs follower who did not incite the city of Sandy Eggo to riot by calling the selling of Sushi and the installation of baby-changing stations in Men's rooms at S.D.'s ballpark "the beginning of the decline of America." q.v., one M. Royko). Throughout all the obits, the discussion centered on Holtzman's invention of the "save" as baseball statistic.
(N.Y. Times obit.)

What puzzled me the most is, with the notable exception of The Hardball Times, how often commentators were blasting Holtzman for what a bad statistic the save is. To be sure, it is a bad statistic: it rewards (in the end, financially) players for participating in one facet of the game that has never been shown to be more significant than several others. It gives the same benefit to pitchers who bail their team out of the toughest of all situations as to closers who record a few outs with a pretty sizable lead. But consider again what the save replaced: a world where relief pitching had no worth on paper (and in a world where the "Win", another terrible stat, was even more important). Also consider what it meant in the early 60s to introduce a new stat into the world. Computing saves retroactively for every baseball player was not as simple as a few lines of Perl and a download from retrosheet. And, the tinkering that Holtzman and others applied to the save suggests that he did not believe he had discovered the perfect, never to be supplanted statistic. Admire what he did for the time in which he lived.

No, marshal your scorn for those who with the hindsight of time and better access to information still defend the save. Those who cling to a bad idea are far worse than those who throw the idea out to the marketplace in the first place.

P.S. I wish there were a stat with more sophistication than Ari Kaplan's "Fan Save Value", but with fewer lookup charts than his more accurate "Save Value." The former is not much of an improvement over the Save (and couldn't easily translate to a generalized "relief value") while the latter has too many "hidden" constants relating to expected runs (that aren't really constant, but actually change from year to year that I can't see it actually being adopted.

Here's a simple(r) formula for calculating expected runs, that you can carry around with you:

ER = (5 + total_runners + 3 * (total bases occupied))
* outs_left / 30

total bases occupied simply means to sum up the base numbers with runners. So runners on second and third is 2+3 = 5. Outs left is 3 - outs. So no outs = 3.

Here's how this version of expected runs compares to the standard expected runs chart:

Outs 1B 2B 3B My ERs Table Difference
0 0 0 0 0.50 0.54 -0.04
0 0 0 1 1.50 1.46 0.04
0 0 1 0 1.20 1.17 0.03
0 0 1 1 2.20 2.14 0.06
0 1 0 0 0.90 0.93 -0.03
0 1 0 1 1.90 1.86 0.04
0 1 1 0 1.60 1.49 0.11
0 1 1 1 2.60 2.27 0.33
1 0 0 0 0.33 0.29 0.04
1 0 0 1 1.00 0.98 0.02
1 0 1 0 0.80 0.71 0.09
1 0 1 1 1.47 1.47 0.00
1 1 0 0 0.60 0.55 0.05
1 1 0 1 1.27 1.24 0.03
1 1 1 0 1.07 0.97 0.10
1 1 1 1 1.73 1.60 0.13
2 0 0 0 0.17 0.11 0.06
2 0 0 1 0.50 0.38 0.12
2 0 1 0 0.40 0.34 0.06
2 0 1 1 0.73 0.63 0.10
2 1 0 0 0.30 0.25 0.05
2 1 0 1 0.63 0.54 0.09
2 1 1 0 0.53 0.46 0.07
2 1 1 1 0.87 0.82 0.05

As you can see, the formula slightly over-predicts expected runs (though with the important exception of the most-common occurrence, no outs, no one on, which almost balances out the rest of the error). The only case where it's over 13 hundreths of a run off is the rare case of no outs, bases loaded, which it over-estimates by 1/3 of a run. If a formula is to overestimate any situation, I'm happy with it being this rare situation: an "oh shit!" moment for any incoming reliever. In any case, it's an easier formula to remember than 24 "random" numbers.

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