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Monday, September 08, 2008
Win% estimators
UPDATE: This post has been corrected due to a bug on my part.
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Great job by Zach, but I’ll quibble on the conclusion:
What’s funny is that Clay Davenport, inventor of Pythagenport, denounced his method in favor of Pythagenpat, yet it is in reality the best method when compared to actual record.
When the RMSE of one is 3.990 and from another is 3.992, that is essentially a tie. What I did is repeated Zach’s study, with a wrinkle of my own. Through 2007, he has 1792 team-seasons in his study. I figured out the Clay and Pat win%, which I then multiplied by W+L, and then rounded to the closest whole number to get a win estimate.
The results. Out of those 1792 team-seasons, there was a tie 1713 times! In the other 79 times, Clay did better 39 times and Patriot was 40. If we give each of them half-wins for their ties, Clay’s head-to-head win% over Patriot is .4997. What works in Patriot’s favor is that it is a simpler construction that doesn’t break down at the extremes.
It’s fair enough to say that they are both equals for the sample at hand (where most teams play in a 9-10 runs per game environment), while Patriot won’t break down at the extreme levels.
I’m not surprised at all that Pythport/pat have essentially equal accuracy for actual teams. The way I “found” the exponent was to try to find a function that matched Davenport’s results in the normal RPG range but also would give an exponent of 1 @ 1 RPG. So there was never any claim or expectation on my part that there would be any accuracy gain for normal teams.