THE BOOK--Playing The Percentages In Baseball

Beautiful, very nice explanation.

Some people have suggested that I would have been better off scaling it to batting average.

There are good reasons I did not do so.

For starters, scaling to OBP(*) guarantees the “1.000” average is met perfectly.  If I used batting average, then I won’t get to 1.000.  Indeed, the line it would match is lgBA/lgOBP, which basically means it would be right around 0.800.

(*) By OBP I mean, my version of OBP, that includes in the numerator and denominator whatever I use in wOBA, but unweighted.

Secondly, the denominator is all wrong.  The denominator in BA is at bats, while wOBA is plate appearances.

Granted, people may be more used to the batting average scale than the OBP scale.  As for what was needed in The Book, that was irrelevant.  OBP and something akin to that was needed to get to statistical significance discussion.  I had to be able to easily go between OBP (a true binomial with the proper denominator) and something else.  Hence wOBA.

I didn’t envision wOBA then being used on a grander scale beyond The Book.  And in any case, it doesn’t matter, because I can’t stand batting average as some central measure of a player’s abilities.  It’s a peripheral metric that should stay there.

That really is a beatiful explanation.  Where does the p * (1.1 - p) come from?  Multinomial distribution math suggests to me that the variance for wOBA should be smaller than for an equivalent binomial.

The calculation for the 1.1 is in the appendix of The Book.  It’s basically the weight of each component squared, multiplied by the frequency of each component.

Tango, this is a very neat visualization.  thanks.

As we’ve discussed before, I see people often misinterpreting wOBA weights to say things like “a home run is worth about twice as much as a single” and things like that.

I wish there were some way to squash that.  Oh well.

Right.  The correct thing to say is:

wOBA says that you can trade 1 HR (and 1.2 outs) for 2.2 singles. 

The denominators have to match.  In either case, you end up with around +1.05 runs.

Thanks, Tango.  When I actually calculated it, instead of speculating, I got the 1.1.

When I put together the current LWTS-based TAv, I did similar testing to what’s in the appendix of The Book, and you can do p * (1 - p) for TAv if you want to figure random variance for it. (It’s not EXACTLY that, but I’m betting 1 is as close for TAv as 1.1 is for wOBA - if you really need the extra precision for either there are better methods, as Tango mentions.)

Colin: when I did some quick testing for TAv, I had to do p * (.87-p).  In order to do p * (1-p), I had to set the league mean of p to .300.

That was just quick testing though…