relates the number of runs a team has scored and surrendered to its actual winning percentage....There are two ways of calculating Pythagorean Winning Percentage (W%). The more commonly used, and simpler version uses an exponent of 2 in the formula.
W%=[(Runs Scored)^2]/[(Runs Scored)^2 + (Runs Allowed)^2]
More accurate versions of the formula use 1.81 or 1.83 as the exponent.
W%=[(Runs Scored)^1.81]/[(Runs Scored)^1.81 + (Runs Allowed)^1.81]
An analysis of statistics available at Baseball-Reference.com, which include expected W%, yields the following straightforward version of the Pythagorean expectation:
W% = 1.8195*RS% - 0.4098, whereThe Pythagorean formula used by Baseball-Reference.com bears a strong resemblance to the long-term (1901-2009) relationship between W% and RS%, which is:
W% = games won/(games won + games lost),
RS% = runs scored/(runs scored + runs allowed), and
* indicates multiplication.
W% = 1.8372*RS% - 0.4191
This equation is no longer accurate, however. Nor is any equation that neglects the evolution of the game through its six "modern" eras: Deadball (1901-1919), Lively Ball I (1920-1941), Wartime Lull (1942-1946), Lively Ball II (1947-1961), High Plateau (1962-1993), and Juiced Player (1994-2xxx). Here are the formulae for each of the six eras:
Deadball
W% = 1.7679 * RS% - 0.3843
Lively Ball I
W% = 1.8965 * RS% - 0.4482
Wartime Lull
W% = 1.7389 * RS% - 0.3686
Lively Ball II
W% = 1.8704*RS% - 0.4377
High Plateau
W% = 1.7521*RS% - 0.3760
Juiced Player
W% = 1.9882*RS% - 0.4940
This final equation seems like the one to use, until there is a marked change in the style of play. Results will vary from year to year, of course. Here, for example, is the equation for 2009:
W% = 1.9419*RS% - 0.4707
Related post: Explaining a Team's W-L Record
