THE BOOK--Playing The Percentages In Baseball

Friday, August 05, 2011

Indirect v direct standardization

By Tangotiger, 07:57 AM

Great piece by Max.

So, let me reiterate the issue. When using indirect standardization (i.e., when using whatever existing fielding metric), you are entitled to say that both Player A (+20 plays) and Player B (+22) performed better than the average shortstop, but there is no way you can infer Player B performed two plays better than Player A.
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I believe fielding metrics should shift to the direct standardization method when data become more objective, detailed and unbiased. Until then the indirect standardization is an improvement over no standardization at all when players face different set of opportunities (but that’s when improper ranking might come out).

Indeed, back in the original UZR, MGL used direct and then switched to indirect after comments at the old Baseball Boards.

• Sabermetrics • Fielding • Statistical_Theory

#1 (see all posts) 2011/08/05 (Fri) @ 13:19

Wow,
did not remember about that on the original UZR.

#2 Tangotiger (see all posts) 2011/08/05 (Fri) @ 13:24

We’re talking about going back a decade!

#3 MGL (see all posts) 2011/08/05 (Fri) @ 23:10

I only read the first half of the article, but I think (I am not sure) that a player’s raw UZR uses the indirect method and UZR/150 uses a direct/indirect hybrid method. No? The “150” in a player’s UZR per 150 is not 150 of “his” games, but 150 games for an average fielder at that position given the same number of opps. I also think that if we want to know how good a fielder “would be” if he played for an average or an unknown team, we would want to take this even further and figure out what his UZR would be if had an average distribution of chances (not just an average number of chances). I don’t do this but I could. I don’t think it would make much difference, but it might make a small difference.

BTW, I don’t remember ever using the direct method, but I might have…

#4 Tangotiger (see all posts) 2011/08/08 (Mon) @ 10:09

I posted this there:

Max, if you have a small number of bins, then it’s true you won’t get the effect I’m saying. But, if you have larger number of bins, then you could get the effect I’m saying. Suppose a SS faces 300 balls in play, at this frequency, with the pro-rated league average in parens:

Bin OurSS (league prorated) --- ----- ---------------- A 50 (20) B 80 (30) C 100 (100) D 40 (70) E 30 (80)

If he happens to be great in Bin A, say he’s at 100% out rate, he’s only going to get n=20 for that, dropping his 50-50 down to 20-20.

If he happens to be terrible in Bin E, say he’s at 50% out rate, his 15-30 will get bumped up to 40-80.

The problem is that all these things are observations. And you cannot simply increase his observed rate up to the number of trials you need.

The indirect method is simply answering a specific question: how many more plays did OurSS make than an average SS would have made? It’s a specific question with a specific answer.

The direct method is saying: IF OurSS had a league average frequency distribution of plays, how many outs WOULD he have made, had he continued to play as he did? But, this presupposes that his observed rate is actually some sort of true rate, that it comes with no random variation.

So, I reject the direct method out of hand. Not unless you use Bayes. And if you are going to use Bayes, then you have to include an uncertainty level in your estimate of the “extra” plays that you are giving him to fill up the bins where he is short.

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THE BOOK--Playing The Percentages In Baseball

Friday, August 05, 2011

Indirect v direct standardization

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