tag:blogger.com,1999:blog-5204092591876211047.post95361982587908755..comments2023-03-23T07:34:12.473-04:00Comments on Advanced NFL Stats Community: Towards a Better Pythagorean: Should Football Outsiders "hold the update"?Unknownnoreply@blogger.comBlogger6125tag:blogger.com,1999:blog-5204092591876211047.post-20263083807458575112011-12-30T08:25:46.478-05:002011-12-30T08:25:46.478-05:00Michael Beouy is absolutely correct. Take it as a...Michael Beouy is absolutely correct. Take it as a homework exercise, Jim, to show that as the exponent goes to infinity, the correlation goes to 1. The <a href="http://en.wikipedia.org/wiki/Lp_space" rel="nofollow">Wikipedia article on p-norms</a> may be useful, particularly the bit on L-infinity.Andrew Folandhttp://nuclearmangos.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-34669927740559317482011-12-27T19:35:22.976-05:002011-12-27T19:35:22.976-05:00Nice work Jim.
"So one can easily produce ...Nice work Jim. <br /><br />"So one can easily produce a ranking of all teams by strength using Unit Pythagorean and a strength-of-schedule adjustment."<br /><br />Just curious, have you done this for 2011 and could you post the results?Behan01https://www.blogger.com/profile/10473218515663716599noreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-2230044514763170932011-12-26T16:42:39.334-05:002011-12-26T16:42:39.334-05:00Boston Chris, thanks.
Tom, Pythagorean has always...Boston Chris, thanks.<br /><br />Tom, Pythagorean has always been expressed in terms of win probabilty, I stuck with that for the sake of conformity (however mindless). I don't doubt there are better ways to do these things but they are for others. This was just an exercise in curiosity for me. I'd never have brought up the subject here but for the FOers commentary.<br /><br />Michael, the 2.67 exponent is to maximize the fit of regular Pythagorean. It's effect compared to the traditional 2.37 is so tiny I probably shouldn't have mentioned it at all, it's on the same order as that of the FOers exponent formula. The increase to 95% correlation is virtually entirely the result of applying Pythagorean game by game -- the same result comes from doing the same thing using 2.37.<br /><br />I did however make a mistake in writing this piece up a 2am, I realized when considering the 500 exponent you mentioned. The standard deviation numbers quoted aren't for the difference between expected and actual wins, they are for the Pythagorean numbers themselves. That is, regular Pythagorean win expectation for all teams over the ten years had a 91% correlation with actual winning percentage and a .180 standard deviation, unit Pythagorean a 95% correlation and .130 standard deviation (one-SD winning percentages from .370 to .630), a tighter distribution around the mean. I don't know why my brain spun out the other line except for maybe I was sleep deprived. My bad on that one.Jim Glassnoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-69043336208172132732011-12-25T23:09:25.590-05:002011-12-25T23:09:25.590-05:00I like the concept, but I wonder if the improved c...I like the concept, but I wonder if the improved correlation isn't just a case of over fitting. <br /><br />For example, using your unit approach, if you ratcheted up the exponent from 2.67 to 500, I would expect that the correlation with win percentage would be rise to nearly 1.0.Michael Beuoyhttps://www.blogger.com/profile/03960600491528993233noreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-76367751331238898722011-12-25T19:04:19.342-05:002011-12-25T19:04:19.342-05:00Very interesting, nice work. One suggestion regard...Very interesting, nice work. One suggestion regarding the averaging... May I suggest you average the odds and not the probabilities? There's sound mathematical reasons to do this.Tomnoreply@blogger.comtag:blogger.com,1999:blog-5204092591876211047.post-82434610637998108572011-12-24T01:28:18.384-05:002011-12-24T01:28:18.384-05:00Nice work, Jim. I really like it.Nice work, Jim. I really like it.Boston Chrisnoreply@blogger.com