Monday, April 10, 2006

AL Pythagorean Report - 4/10/2006

One of the things that I like to do during the baseball season is compile a weekly report of the AL standings, looking at runs scored and allowed, to see who's better than their records and who's worse.

For those unfamiliar, the Pythagorean report is based on a Bill James discovery regarding the relationship between runs scored, runs allowed and winning percentage. It intuitively makes sense that a teams record will be related to how many runs they score and how many they allow. What James discovered was that, for almost all teams, the winning percentage is very close to a ratio of the square of the runs scored to the sum of the squares of the runs scored and runs allowed. Which was dubbed the "Pythagorean" theorum of baseball.

The report consists of, for each team, their runs/game, runs allowed/game and Pythagorean project winning percentage, along with their rank among the teams in the league for each of those categories. The Pythagorean winning percentage is calculated as (r ^ 1.83) / ( (r ^ 1.83) + (ra ^ 1.83) ). (1.83 has been determined to be a slightly more accurate exponent with the current offensive levels than 2.) Using the Pythagorean winning percentage, the expected wins total is calculated and compared to the actual win total. Finally, any difference is expressed as "luck", with negative numbers representing underperforming teams.

Finally, there's a linear projection of final records, based on current winning percentage, and based on Pythagorean winning percentage.





AL Pythagorean Projection Report - 4/10/2006
ProjectedActual

R/G(rank)RA/G(rank)Pythagorean(rank)WLWLLuck

Detroit7(1)2.83(1)0.84(1)51510

New York5.83(2)3.83(2)0.683(2)4224-2

Cleveland5.5(5)3.83(2)0.659(3)42511

Boston5.5(5)4(4)0.642(4)42511

Baltimore5.83(2)5.67(11)0.513(5)3324-1

Oakland4.43(10)4.57(5)0.485(6)34522

Toronto5.67(4)6.17(13)0.461(7)33330

Seattle4.29(11)4.71(6)0.457(8)34340

Chicago4.67(8)5.33(7)0.439(9)3324-1

Minnesota4.5(9)5.5(9)0.409(10)2415-1

Los Angeles4.17(12)5.5(9)0.376(11)24331

Tampa Bay5.33(7)7.17(14)0.368(12)24331

Texas3.86(14)5.43(8)0.349(13)25250

Kansas City4(13)6(12)0.323(14)23230




Top 5 projections (using current winning %)
Detroit13527

Cleveland13527

Boston13527

Oakland11646

Toronto8181




Top 5 projections (starting with today's record, using Pythagorean winning %)
Detroit13626

New York10953

Cleveland10854

Boston10557

Baltimore8280

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