Talisman Red's College Football Computer Ratings
Talisman Red's College Football Computer Ratings |
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Introduction This is my contribution to the college football computer rating universe. My rating is a combination of: How to use it: to estimate the point spread between two teams, just use the Points column. Don't forget to add in home field advantage, which is usually around 2.5 to 3 points. It fluctuates some, but I don't bother publishing the actual number: in 2011, at the end of week 6 it was 2.7. Last season's games have a strong but diminishing influence for the first few weeks. More recent games are always weighted heavier. This is always a work in progress, and I reserve the right to change the algorithm at any time, without telling you (errors, tweaks, whatever). The ratings are one of many included on Dr. Kenneth Massey's comparison page for college football. Enjoy! Email me if you have a question. The components The rating is a blend of two different and unique formulas. Rating 1: An almost "pure points" system. Only margins of victory are included in this system, which appears in the Points column. The tweak I make is to apply "diminishing returns" when scores are above 40 points. Over 40, the excess is halved, i.e., 42 becomes 41, 50 is 45, 70 is 55, etc. This is done without regard to margin of victory. I know I could (and should) be a bit more elegant, but it works. You can use this data plus the known home field advantage to predict the outcome of any game if it were to be played today. Rating 2: A system that considers only winning and losing, with games weighted based on how recently they were played. Essentially, you earn a point if you win, and give up a point if you lose, and the result is weighted by the number of days since the game was played. The weighting factor is that number of days, divided by 400. So a game played four months ago is weighted only 0.7 compared to "today's" games (weight 1.00); for games eight months ago the weight is about 0.4, and obviously for games one year ago the weight becomes even smaller, less than 0.1. This rating correlates highly to the other BCS-style ratings, since like those it does not consider any information about margin of victory. I then combine the two ratings (see the math details below) for one overall result. That's what you see in the Rating column, and is what is used to rank the teams. Some math details Finding each set of ratings requires solving an overdetermined matrix problem (thousands of games, for only hundreds of teams), which is popularly done either via SVD or with an iterative technique. SVD for college basketball requires a few gigabytes of RAM, which I didn't have at home when I started this project, so I went with iterative methods. They are much slower, but will produce the same result. Right now I use a Matlab routine called LSMR, written by David Fong and Michael Saunders of Stanford University. Prior to using their algorithm, I used ugly, clunky, slow programs that I wrote myself; they resembled the predictor-corrector methods from your numerical analysis courses. For both ratings, I then normalize the entire list (so that the mean is zero and the standard deviation is one), and simply add the two normalized ratings together to get the final value, shown in the "Rating" column. In other words, Rating = normalized_rating1 + normalized_rating2. That's it. I normalize both results because there is essentially no other way to compare or combine two ratings that are so different. Neither rating is given more preference than the other. There's probably a better way to get the end result than just adding the two normalized ratings together, but again, it seems to work. That's why the ratings are bounded in roughly a range of +5 to -5...it will be rare to have a team with either rating more than about 2.5 SD's beyond the mean, let alone both of them. About the author I have a Ph.D. in Atmospheric Science from the University of Alabama in Huntsville, and am currently a faculty member at Indiana University in Bloomington. In addition to lots of teaching, I have research interests in the broad areas of thunderstorms and numerical weather prediction (forecasting using computers). Contact me using this email form if you have questions or non-hateful comments. |