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Wins Above Expectation (with a side of run differential) September 1, 2008

Posted by tomflesher in Baseball.
Tags: , , , , ,

In continuing my thoughts about the Pythagorean Expectation from about a week ago, I took a look at the MLB standings for the period ending August 31, 2008. I played with the stats a little bit, since I haven’t really thought through the basis for most of them.

Today’s project: find Pythagorean expectations for each team, then find the difference between the actual and expected win percentages (“pythagorean difference”). Apply the pythagorean difference to the total number of games played to determine a team’s Wins Above Expectation by multiplying the total number of games by the pythagorean difference.

Practical application: none.

Discussion and numbers behind the cut.

I’m using OpenOffice.org Calc and numbers that I copypasted from ESPN.com, cited above. The formatting is a little wonky because this was just a play session for me, but here are my data in handy dandy PDF format (original spreadsheet format available upon request).

Wins Above Expectation is a measure of the economy of a particular baseball team – the ability to win more games than the number of runs scored would predict. I would therefore hypothesize it to be useful as a measure of defensive ability, though of limited use from a predictive standpoint because anything it would predict could be more elegantly but less surely predicted using other measures.

Speaking of elegance, I can’t help but notice that the pythagorean expected rank and the rank by run differential are the same in all cases. The elegance of run differential as a method of ranking teams’ performance hadn’t occurred to me before, but I’ll probably continue to use it. The use of pythagorean expectation is to predict a number of wins given a particular number of games. (The correlation between expected rank and rank by run differential is obvious after thinking it through, since pythagorean expectation is basically just a special case of differential.)

The Rays’ exceedingly economical performance isn’t surprising, since they’ve been squeaking out wins regularly all season. As a team, they rank second in MLB in the teams’ number of saves (a stand-in variable for close wins), behind only the LA Angels (who beat them in terms of WAE as well). There’s also no surprise that one of this season’s biggest punching bags, Toronto, is last in the league in negative WAE (that is, wins below expectation).  This is what happens when you lose tight games and get your wins by enormous margins. Lesson to be learned: consistent performance creates measuring statistics that closely match performance.

Edit to Add: I added an additional page of stats using the 1.81 exponent cited in the Wikipedia article. The numbers changed; the ranks didn’t.



1. How Useful is the Pythagorean Expectation? | Heureusement, ici, c'est le Blog! - May 18, 2010

[…] When I played with the Pythagorean expectation a while back, I used it to generate a stat called Wins Above Expectation (which appears to have been invented independently by several other people as well) with the […]

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