Pythagorean Theorem of Baseball
From BR Bullpen
The Pythagorean Theorem of Baseball is a creation of Bill James which relates the number of runs a team has scored and surrendered to its actual winning percentage, based on the idea that runs scored/runs allowed is a better indicator of a team's (future) performance than a team's actual winning percentage. This results in a formula which is referred to as Pythagorean Winning Percentage.
[edit] The Formula
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]
Expected W-L can then be obtained by multiplying W% by the team's total number of games played, then rounding off. Expected W-L for each team is published by ESPN on their website.
[edit] Justification
The rationale behind Pythagorean Winning Percentage is that, while winning as many games as possible is still the ultimate goal of a baseball team, a team's run differential (once a sufficient number of games have been played) provides a better idea of how well a team is actually playing. Therefore, barring personnel issues (injuries, trades), a team's actual W-L record will approach the Pythagorean Expected W-L record over time, not the other way around. Expected W-L is almost always within 3 games of actual W-L at the end of a season (although a recent exception is the 2005 and 2007 Arizona Diamondbacks, who both beat their expected W-L by 11 games). Deviations from expected W-L are often attributed to the quality of a team's bullpen, or more dubiously, "clutch play"; many sabermetrics advocates believe the deviations are the result of luck and random chance.
Because of this, expected W-L makes for a good predictor of performance in mid-season. If a team has a 40-25 record, but a Pythagorean winning percentage at or below .500, it should not be surprising when this team's record drops as they start losing close games. In fact, expected W-L correctly predicted the fate of the 2005 Washington Nationals. On July 5 of that season, Washington was 19 games over .500 and 4.5 games ahead of second place, but had a Pythagorean W% of exactly .500. They went 30-49 the rest of the season to finish at .500 (four games ahead of their final expected W-L).
[edit] Other Sports
Pythagorean Winning Percentage has also been used in basketball. The exponent used varies between 13 and 16.5.
