There's a good article by Phil Birnbaum giving a common-sense explanation why an additional ten runs in a team's record changes one loss to a win. You can access it from tangotiger's insidethebook.com website if you're interested.
I've been fooling around with the Pythagorean formula and some other predictors, and I got a surprising result with simple run differential as a predictor: Runs - Runs Against.
I pulled out all 154-game seasons (actually 152-156) and regressed WL% against the differential (D) and got
WL% = .500 + .000653D
with an R-square of 91.1% and a standard error for the slope of .02912.
In other words, with a differential of 0, R = RA, you start off at .500, of course, and then an increase of one run in the differential is worth an increase of .000653 in WL%. If you multiply .000653 times 154, you get .100562. So if you have an increase of 10 runs, you get 1.00562 more wins.
That R-square isn't great, but it's about the same as the 1.81 exponent version of the pythagorean predictor, 91.8%
Regressing on wins themselves spells it out:
W = 76.6 + .100D
With the same number of runs as runs against, you'd expect to win half your games, about 77, and each additional run adds a tenth of a game.
For 162-game seasons (160-164), the R-squares are a little smaller, 87.8%, but the equations make just as much sense:
WL% = .500 + .000644D (.000644*162 = .104329)
W = 80.9 + .105D
The unexpected support for the 10-run-1-win rule is just icing. What surprised me was how well an utterly simple-minded linear expression explained data that we are pretty sure is not linear, over a wide range of eras, conditions, team quality, and run averages. If a rough back-of-the-envelope approximation can do this well, it sets the bar pretty high for formulas that actually claim to explain something.