## Sunday, April 11, 2004

### Runs Versus Wins in Major League Baseball

One of Bill James[*] basic contributions to sabermetrics was to note that you can pretty much predict a team's winning percentage by comparing how many runs it scores compared to how many runs it gives up. He called his version the "Pythagorean Rule" because it went:

Winning percentage = (Runs Scored)2/ [(Runs Scored)2 + (Runs Allowed)2]
On the SABR-L mailing list (a place where people talk baseball, including equations like this) Ralph Caola mentioned that a linear version of this formula,
Winning Percentage = 1/2 + (Runs Scored - Runs Allowed)/ (Runs Scored + Runs Allowed)
works nearly as well.

Playing with this notion a bit made me realize that Ralph's approximation is pretty good even if the Pythagorean Rule isn't. That is, whatever the "best" rule is for relating runs scored to winning percentage, for Major League teams, which aren't that far apart in ability, Ralph's formula is going to be pretty good, with one modification.

I wrote this up for SABR-L and put it up on the web as Linearization of Win Formulas.

Does this apply to basketball? Football? Soccer? It's something that should be looked into. For what it's worth, I'd guess that it works better for basketball than football or soccer, because football seasons (either kind) are short, so there can be big fluctuations that aren't covered by statistical formulas like the one above.

[*]Who went to KU the same time as I did, though we never met.

January 19, 2006: Thanks to Ralph Caola for correcting the linearized win formula, which I had mistyped.