### OPS is kind of like Linear Weights

Here, Dan Fox does a bunch of algebra on the OPS formula and discovers that it’s similar in form and results to a Linear Weights function. So now we have a better idea why OPS works – because it’s a lot like Linear Weights.

Cool.

A few years ago (pdf, see page 25-26), I pointed out (although Clay Davenport did first) that Paul Johnson’s “Estimated Runs Produced,” introduced in Bill James’ 1985 Abstract, also simplified to something close to Linear Weights.

Maybe the same can be done for Runs Created?

## 6 Comments:

http://gosu02.tripod.com/id104.html

Go to the bottom.

The calculus in question was described in the BaseRuns (Total Rewrite) article, also on the same site.

Didn't I post this same result at least 5 years ago on SABR-L? And, if the recent discussion Dan's alluding to is the same one I'm thinking of, I posted exactly this result in that discussion.

This is why we really need to get that wiki that was discussed in Seattle operational, so people can stop rediscovering the wheel, finally. Anyone know the status of that?

Hi, Arb,

Do you have a link to your post in the SABR-L archives? Or a list of keywords I can search on?

My search came up empty.

Phil

Ugh, the SABR-L archives search is obnoxious. :)

But, I found something: 30 June 2003, in a thread "Does OPS double-count BA?" The key phrase is:

"Oh, what *are* the weights? Normalized so the weight on a single is 1, they work out to typically be *close* to 2/3 for BB, 2 for 2B, 3 for 3B, and 4 for HR. Not *exactly* -- but not bad either, and the weights you get from methods (1) and (2) aren't statistically different from these ratios."

Looking around, I don't think I ever posted the full calculations, largely because I didn't think they were of general interest to the majority of SABR-L readers.

Here here arb. A site with links to past studies that is searchable by category is greatly needed.

Most recently I saw the beginnings of this on SABR-L around Dec 05/Jan 06 as I referenced in the article but I haven't looked in the archives.

I don’t know if the same can be done, but some interesting things happen under Runs Created. For example, the difference is the same between a walk (or HBP) and single, a single and a double, a double and a triple, and a triple and a home run. That difference is the OBA after the hit. A walk is worth the new OBA minus the old OBA times bases.

In other words, for each hit or walk you get, you get a flat rate for increasing your OBA. On top of that, you get a proportional increase for how many bases, which is equal to your new OBA.

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