It’s A Livin Thing – 2022 College Football Rankings

Written by Sriram

Well, in this space we’ve messed around a lot with the Bradley-Terry rating system to try to rank the FBS college football teams. I liked it – it made me happy. However, while I defend the mathematical integrity of the system, with so few games played, the error within seasons was consistently extremely high. To be able to get more samples, you need more games. In college football that means you need to look at previous seasons. The seasons are new – but not really. The teams do enter the season with some parts of the year before.

Based on this, I am trying out a version of the ELO Rating system, which is used for chess and is going to be implemented in the future for the UEFA Champions League. A good nuts and bolts discussion of the method can be found here – but here are some of the highlights:

  • It is an incremental rating system. So teams are adjusted each week. If a team grows during the season (or proves more) it will show in the ratings.
  • The weekly rankings are used to determine win likelihood. Winners gain points, losers lose points – but favorites get less credit for winning and lose more for losing. Put another way, defeating teams above you move you up faster.
  • Typically these models have win values as low as 3 (for chess or baseball). College Football with its short season requires a more volatile model. So we go with 75 points with a multiplier based on the natural log of the margin of victory. Testing this across 22 seasons of results, this fits with how we perceive the teams pretty well.
  • We can do preseason ranks! The beginning ranking of each team is the previous year’s ending ranking regressed to the mean (1500) by 1/3. Basically we are saying about 1/3 of a team’s success-failure is turned over each year. It is a decent compromise I think – an acknowledgement that these teams are NOT starting as equal in the eyes of the world. Any new FBS team starts with the 25th percentile team rating.
  • 1500 is the average rating. I looked at all the results from 2000 through 2021, starting with “all teams being the same” in 2000 and proceeding through now.

Here is the preseason Top 25 (with last year’s W/L)

  1. Georgia (14-1)
  2. Alabama (13-2)
  3. Baylor (12-2)
  4. Cincinnati (13-1)
  5. Louisiana (13-1) <- look at last 3 years record and this is not so weird
  6. Ohio State (11-2)
  7. Oklahoma State(12-2)
  8. Michigan (12-2)
  9. Clemson (10-3)
  10. Oklahoma (11-2)
  11. Michigan State (11-2)
  12. Utah (10-4)
  13. Notre Dame (11-2)
  14. Ole Miss (10-3)
  15. Houston (12-2)
  16. Pitt (11-3)
  17. Wisconsin (9-4)
  18. Arkansas (9-4)
  19. Western Kentucky (9-5)
  20. San Diego State (12-2)
  21. Minnesota (9-4)
  22. Kentucky (10-3)
  23. Coastal Carolina (11-2)
  24. Central Michigan (9-4)
  25. Boise State (7-5)
  26. NC State (9-3)
  27. Utah State (11-3)
  28. Purdue (9-4)
  29. Air Force (10-3)
  30. BYU (10-3)

#5 is awfully high for Louisiana-Lafayette, but this is the model giving a team credit for only losing 5 games over the last 3 seasons. But there is just not a lot of upside in their schedule – but who knows what will happen?

I do have rankings for each week, and this week’s rankings will get burped out in another post.