Monday, April 07, 2008

Monday Pythagorean 4/7/2008

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.



Well, the Red Sox opening week is finally over, 12 days, 7 games and 6500 miles after it started. The first series went pretty well, the second was a disaster.

  • By the numbers, the team hasn't hit well, as they're currently 11th out of 14 AL teams in runs scored.


  • By the numbers, the team hasn't pitched well, as they're 13th out of 14 in runs allowed.


  • The bullpen was the big problem in Toronto. The games were close when the starters left, but none of them finished that way. Wakefield left a tie game on Friday night, they lost by three. Buccholz left down 4-2, they lost 10-2. Beckett left the game down 2-1, they lost 7-4. All told, the starting pitchers allowed 4.6 runs/9IP while they were on the mound in Toronto, the bullpen allowed 14.0 runs/9IP.


  • But it's one week, they finished it at 3-4, and anyone who's fretting really needs to relax. If I were a Tigers fan, I'd be a little concerned, because 0-6 can get you into a bad spot pretty quickly, but the Orioles aren't going to win the East, the Royals aren't going to win over 100 games, and there's no reason to be worried about the Red Sox yet.


  • If you absolutely must fret about something, try this - there was no week in the 2007 season in which the Red Sox had a pythagorean winning percentage as low as the .328 that they had this week. I'm not going to worry about it, but, as I say, if you absolutely have to have something to fret about, well, there it is.


  • They have got a very tough April. When the month ends, they will have played the Angels, Tigers, Indians and Yankees, in addition to the presumably improved Blue Jays, Rangers and Rays. If they get to May 1 at 15-14 or better, they'll be in good shape. Obviously, we'd like to see a better record than that, but, all things considered, if they're over .500 and healthy, they will have had an acceptable month.






AL Pythagorean Projection Report - 4/7/2008
ProjectedActual

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

Toronto5.33(4)2.83(2)0.761(1)5142-1

Tampa Bay6.2(2)4(5)0.69(2)32320

Kansas City3.83(8)2.67(1)0.66(3)42420

Chicago6.33(1)4.67(11)0.636(4)42420

Baltimore5.4(3)4.4(10)0.593(5)32411

Texas5(5)4.17(7)0.583(6)33330

Oakland3.43(10)2.86(3)0.583(7)4334-1

Los Angeles4.14(6)4.29(9)0.484(8)34431

Cleveland4(7)4.17(7)0.481(9)33330

Seattle3.83(8)4(5)0.481(10)3324-1

Minnesota2.71(13)3.86(4)0.345(11)25341

Boston3.29(11)4.86(13)0.328(12)25341

New York2.83(12)4.67(11)0.286(13)24331

Detroit2.5(14)6.5(14)0.148(14)1506-1




Top 5 projections (using current winning %)
Baltimore13032

Toronto10854

Kansas City10854

Chicago10854

Tampa Bay9765




Top 5 projections (starting with today's record, using Pythagorean winning %)
Toronto12339

Tampa Bay11151

Kansas City10755

Chicago10359

Baltimore9765

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