Most people are familiar with the so-called Pythagorean theorum for baseball - that winning percentage will be roughly equal to runs squared divided by the sum of runs squared and runs allowed squared. The game even automatically tracks of Pythagorean records and includes them in the standings report. (Incidentally, River Cities' Pythagorean record this year of 110-52 is the highest in SDMB OOTP history. One more reason I'm destined to experience heartbreak again.)
Anyway, using my handy dandy Excel spreadsheet, I found that using 2 as the exponent in the formula is not as accurate as it could be. For our game, the most accurate exponent to use is 1.62. In other words, the most accurate formula is runs to the power of 1.62 divided by the sum of runs to the power of 1.62 and runs allowed to the power of 1.62. This reduces the cumulative "error" between Pythagorean records and actual records by about 17%.
As the title indicates, this is purely a random fact. But, using the traditional Pythagorean formula has, on the whole, overestimated the quality of good teams and underestimated the quality of bad teams.
By the way, the team that most underperformed compared to this standard is 2005 Austin/Covington, who lost 11.5 games more than they should have, and the team that most overperformed is the 2005 Seattle team, who won 10 more games than they should have.
I think the bludgeoning I gave you in the Cup that year exposed the 10-games you mentioned.
ReplyDeleteAlthough your team had a slightly better revised Pythagorean percentage, the difference is so small as to be statistically irrelevant. Your revised P% was .631 while mine was .629. I'm afraid that the small sample size considerations swamp any meaningful difference between the teams.
ReplyDeleteThat said, championship banners fly forever and all that jazz.
ARen't you Johnny-on-the-spot.
ReplyDeleteThe Baseball Prospectus guys did a thing a few years ago in which they determined the true figure to be 1.7 for MLB.
I may not be familiar with these modern mathematical concepts like exponents and addition and whatnot, but I do know that Saskatoon's actual record is something like 20 games below their projected Pythagorean record over the years 2003-07. Yay, me.
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