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 two separate pieces:

  • a rating that considers scores and can predict margins of victory; and
  • a rating that considers only wins and losses and strength of schedule.

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.

What's new in 2025?

Welcome back! For my own formula, this year I am trialling a formula that predicts only D-1 scores (none of the "lower" divisions). Offseason testing makes me think that those divisions are dragging the success rate down a little. So this season, we try something slightly different.

I might do an alternate something-or-other for D2-D3-NAIA. Still thinking about what that might look like.

Is your rating system influenced by...

  • Where the game is played? Yes, home advantage matters.
  • When the game is played? Yes, more recent games always count a little bit more. In the first few weeks, last season's games have a strong influence which diminishes as time goes on.
  • Margin of victory? Yes, but a "diminishing returns" principle applies for very high-scoring teams so that, beyond a point, it doesn't matter as much.
  • Yards, turnovers, free throws, penalties, earned runs, or other statistics? No.

How does your system compare to the dozens of others already out there?

These ratings are one of many included on Dr. Kenneth Massey's comparison page for college football. Please check them all out.

I don't keep statistics as thoroughly as I should, but from 2021 to November 2024, I can report that:

  • My ratings predicted about 70% of Division I FBS winners corect;
  • Jeff Sagarin's system predicted about 71% of winners;
  • The ESPN FPI predicted about 71% of winners; and
  • The mid-week Vegas line predicted about 72% of winners.

A one percent difference, over a typical 750-800 games in a Division I FBS football season, corresponds to about 7-8 more games correct/incorrect. So a score-based system as crude as mine, to have almost the same amount of success as a multi-billion dollar broadcaster or the betting industry? Yeah, I'll take that.

Math details: the components

The overall rating is a blend of two distinct 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.

More 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. It's a little bit faster than the built-in LSQR routine in Matlab. 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.

Starting in 2023, early-season ratings are weighted more toward the points-based system. This should help reduce the noisy/jumpy nature of the ratings early on, which has always annoyed me. Gory details: at the beginning of the season the ratings are 100% points-based, and once an average of five games has been played for all teams, the ratings are a 50-50 combo of both systems.

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.