## Wednesday, April 23, 2008

### While I'm on a Roll...

I have written about this before, and asked nicely. Now I’m going to be a little snarky, since I’ve seen more of it lately. “It” is the use of OBA-BA, which goes by all sorts of different names, to measure patience or walking ability or however you would phrase it. If you take just a second to look at the underlying math, you will see what a stupid, stupid stat this is.

Let’s make everything a lot more simple by eliminating sacrifices from existence, and if you want to consider hit batters, you can count them as walks.

Now, what is OBA-BA? It is:

(H + W)/(AB + W) - H/AB

Anyone who thinks about this should immediately notice that the different denominators are going to make things difficult. The difficulty is illustrated when I ask you, “What is the unit of OBA-BA?” I challenge anyone to explain what this denominator represents, in coherent baseball terms, in ten words or less.

If you write it with a common denominator, you end up with something equal to this (you can obviously re-write it in some other ways):

W*(AB - H)/(AB*(AB + W))

You are multiplying walks by outs. And then dividing by at bats times plate appearances. Great stat you have there.

Tying this back into BA, you can also write that as:

W/PA * (1 - BA)

Walks/PA is what you are after…the player’s walk rate. But OBA-BA multiplies walk rate by one minus BA. So if you have two guys who each draw 50 walks in 550 PA, but one gets 150 hits (.340) and one gets 135 hits (.270), the one with the lower BA has a higher OBA-BA, .066 to .060.

It is remarkably lazy to leave it in the form OBA-BA. You can very easily get walk rate from (OBA - BA)/(1 - BA). If you’d like, you can also use (OBA - BA)/(1 - OBA) = W/AB. Walks per AB is not in as useful a form as Walks per PA, but given the assumptions of this post, it will produce a ranking in the same order. All W/AB is is (I like doing that, even though my English teachers would strangle me) a ratio of walks to non-walks, which if divided by one plus it self will give W/PA.

Of course, a lot of this confusion can be traced to the somewhat silly nature of Batting Average and At Bats themselves. Joe Posnanski’s rift on that subject encapsulates my thoughts fairly well (and of course is a billion times funnier than the way I’d write it).

1. I appreciate your giving us the formula (O-B)/(1-B). It serves as a good companion to a similar formula I have for non-BB production. But are people really using O-B for any serious analysis? I use it, but only in my head as a quick indictor of how often a player walks. Used as such, it's nice to have...

2. I don't disagree that it's good for a quick computation; obviously no one can divide by (1-BA) on the fly, and the distortion is fairly small.

However, I have seen it used on a few blogs in an analytical way. I think I've seen it in some THT articles too. I can't remember which ones specifically, though, so I may have been subconsciously magnifying the extent of its usage.

BTW, can you please send me an email at walksaber@gmail.com? I want to ask you something about your Base Wins method.

3. Oops, and I forgot to ask, what is your formula for non-BB production? It's interesting to see the different permutations that can come from BA, OBA, and SLG.

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