Yeah, yeah, yeah – all season long I’ve been tracking things through an ELO model and it’s all fine I guess. But one of the nice things is now having some side by side comparison with the Bradley Terry model I’ve been using since 2008 to see what I like better. Overall, after much deliberation – it is pretty clear that the Bradley-Terry method works a lot better. The attractiveness of the ELO method is its week to week “matchups determined by weekly rankings” thing – but that is more than offset by the idea that preseason expectations (especially carried over from a previous season) played too big a role. It makes sense to treat each season freshly.
Fortunately, we still have the Bradley-Terry method. The pure form of the method works like this:
- All games are worth 1 point
- Each team’s ability is assumed to have a base ability.
- If team X has twice the ability of team Y, team X will win twice as many games as team Y in a head to head.
- The games played by all Z FBS teams (and an extra team for all non-FBS teams) results in a ZxZ matrix of head to head win percentages
- Using iteration, solve for the ability for each team. (here is a mathy explanation)
- As a result, this method implicitly solves for home field advantage as well as strength of schedule.
I’ve been doing rankings like THAT since 2008 – save for 2020 where the pandemic eliminated most of the non-conference games that allow a Bradley Terry model to converge. Now, I don’t use a pure model – I do incorporate margin of victory. After tinkering with methods I settled on the winning team getting 0.75. The team can get up to the full 1 based on a multiplicative factor (from 1 to 1.3333) based on a logarithmic factor of up to 28 points. This means that the marginal value of the 28th point of victory margin is worth less bonus than the 2nd point of victory margin.
With the first College Football Playoff ranking looming, it seemed like a good time to reveal the first Bradley-Terry ranking.
| Rank | Team | W | L | Rating | RR% |
|---|---|---|---|---|---|
| 1 | Georgia | 8 | 0 | 2441.34 | 96.7 |
| 2 | Ohio State | 8 | 0 | 2363.77 | 96.63 |
| 3 | Tennessee | 8 | 0 | 1772.99 | 95.92 |
| 4 | Clemson | 8 | 0 | 851.42 | 93.51 |
| 5 | Michigan | 8 | 0 | 725 | 92.85 |
| 6 | TCU | 8 | 0 | 689.2 | 92.62 |
| 7 | Alabama | 7 | 1 | 589.14 | 91.9 |
| 8 | Oregon | 7 | 1 | 353.31 | 89.11 |
| 9 | LSU | 6 | 2 | 232.87 | 86.28 |
| 10 | Kansas State | 6 | 2 | 183.61 | 84.42 |
| 11 | Penn State | 6 | 2 | 178.05 | 84.16 |
| 12 | Oklahoma State | 6 | 2 | 173.76 | 83.96 |
| 13 | USC | 7 | 1 | 171.94 | 83.87 |
| 14 | UCLA | 7 | 1 | 160.59 | 83.28 |
| 15 | Ole Miss | 8 | 1 | 152.5 | 82.82 |
| 16 | Tulane | 7 | 1 | 120.1 | 80.6 |
| 17 | Utah | 6 | 2 | 113.58 | 80.05 |
| 18 | Wake Forest | 6 | 2 | 105.32 | 79.29 |
| 19 | Florida State | 5 | 3 | 100 | 78.75 |
| 20 | Texas | 5 | 3 | 90.92 | 77.75 |
| 21 | Mississippi State | 5 | 3 | 85.19 | 77.04 |
| 22 | NC State | 6 | 2 | 80.7 | 76.44 |
| 23 | Syracuse | 6 | 2 | 79.36 | 76.26 |
| 24 | Kentucky | 5 | 3 | 71.31 | 75.04 |
| 25 | Oklahoma | 5 | 3 | 62.11 | 73.41 |
Ten more: Arkansas (5-3), Kansas (5-3), Florida (4-4), Oregon State (6-2), Notre Dame (5-3), Liberty (7-1), Louisville (5-3), North Carolina (7-1), Baylor (5-3), South Carolina (5-3)
Now, with years of experience with this model – I can say that using this to pick the Top 4 teams is somewhat flawed though a Georgia-Ohio State-Tennessee-Clemson Final 4 looks right to me for now. We know the committee would value an 8-1 Ole Miss over a 6-2 Oklahoma State. And if you look at the standard error of the ability scores (this is a small sample after all), the ranking error bars are high. But what if we used it like an NET rating, like with the NCAA Basketball Tournament? Let’s go to the 12 team model that is going to be implemented in the coming years.
Automatic Bids
- SEC: Georgia (1)
- Big Ten: Ohio State (2)
- ACC: Clemson (4)
- Big 12: TCU (6)
- Pac 12: Oregon (8)
- American: Tulane (16)
At Large Bids – Clear
- Tennessee (3) – 95.92%
- Michigan (5) – 92.85%
- Alabama (7) – 91.90%
The Bubble
- LSU (9) – 86.28%
- Kansas State (10) – 84.42%
- Penn State (11) – 84.16%
- Oklahoma State (12) – 83.96%
- USC (13) – 83.87%
- UCLA (14) – 83.28%
- Ole Miss (15) – 82.82%
There is a distinct drop to the next at-large team, Utah at 80.05%, so this seven team list seems like a solid tier. USC, UCLA and Ole Miss are 1-loss teams. LSU has the win over Ole Miss but got trampled by Tennessee in Baton Rouge. USC and UCLA have only lost to good teams on the road. Oklahoma State’s losses are justifiable but Kansas State was pretty rough. Kansas State has that win over Oklahoma State but lost at home to Tulane. Now, Tulane is good, and early in the season – but that does count.
The committee of one would vote for the 1-loss teams … USC, UCLA and Ole Miss. But you can argue for any of the 2-loss teams and I’d be cool.
A 12-team bracket
Byes: Georgia, Ohio State, Clemson, TCU
First Round
- (16) Tulane at (3) Tennessee
- (15) Ole Miss at (5) Michigan
- (14) UCLA at (7) Alabama
- (13) USC at (8) Oregon
Meadow Muffins of the Mind 