Monday, April 11, 2005

AL Pythagorean Report - 4/11/05

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 - 4/11/2005
TeamR/G(rank)RA/G(rank)Pyth(rank)projw act wluck

Detroit6.667-14-20.718-143-1

Toronto6.167-24.5-60.64-2440

Oakland4-133.333-10.583-3330

Tampa Bay4.667-84.333-50.534-4330

Baltimore4.833-64.833-80.5-5330

Chicago4.167-114.167-30.5-5341

Minnesota4-134.167-30.481-7330

Seattle5.167-35.5-100.471-832-1

Texas5.167-35.5-100.471-8330

Anaheim4.167-114.667-70.448-10330

Kansas City4.833-65.5-100.441-11330

Cleveland4.333-95-90.435-12330

New York5.167-36-130.432-13330

Boston4.333-96.167-140.344-14220





Top 5 projections (using current winning %)
Toronto10854

Chicago10854

Detroit8181

Oakland8181

Tampa Bay8181




Top 5 projections (starting with today's record, using Pythagorean winning %)
Detroit11547

Toronto10458

Oakland9468

Tampa Bay8676

Chicago8280


This was a fairly ugly week for Red Sox nation. They didn't hit much and the starting pitching wasn't great. And the less said about the bullpen, the better.

But 6 games is a miniscule sample size. They'll have another week or two this bad before the season's over. It just gets magnified when the small sample is the only sample that you've got...

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