[Ed. - Bumped, because this is a fascinating read. If only we could actually watch these teams play 10,000 times...]
This year I've started maintaining a couple of ranking systems for college football and basketball: the Bradley-Terry method (familiar to college hockey fans as KRACH) and a modified version of it that also considers the score ("victory points" are awarded based on a logistic function of the margin of victory, then those victory points are used in place of the team's actual record; a 7-point win is worth approximately 0.75 "wins", a 14-point win worth 0.9, a 28-point win worth about 0.988, and a 70-point win worth 0.9996). Full national rankings are here. Last week I posted a pre-conference season projection over at The Only Colors; since it's a topic of interest for the entire conference I figured it would be worth posting here. This time I ran 10,000 season simulations with each set of rankings instead of 1,000 and broke out shared titles into which teams are involved in each tie.
Two big caveats: Home field is not included in the projections at all, and five games is not a huge sample size. In particular, the W-L method puts a big emphasis on being unbeaten (if two teams have equal strength of schedule and one has no losses, the other has one, the unbeaten is a 3:1 favorite). The margin-aware method seems to give reasonable results even this early, for the most part.
Basic (W-L only) Method| Team | BT WPct | Average wins | 8-0 | 7-1 | 6-2 | 5-3 | 4-4 | 3-5 | 2-6 | 1-7 | 0-8 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ohio St | 0.9033 | 6.54 | 16.42% | 38.09% | 31.37% | 11.76% | 2.16% | 0.19% | 1 in 15,100 | 1 in 1.6M | N/A |
| MSU | 0.8974 | 6.32 | 12.04% | 33.31% | 34.08% | 16.34% | 3.80% | 0.40% | 0.02% | 1 in 585k | N/A |
| Michigan | 0.9054 | 6.1 | 9.02% | 28.43% | 34.55% | 20.55% | 6.36% | 1.02% | 0.08% | 1 in 50,000 | N/A |
| Northwestern | 0.8188 | 5.57 | 3.62% | 17.70% | 32.36% | 28.77% | 13.63% | 3.47% | 0.44% | 0.02% | N/A |
| Iowa | 0.8502 | 5.22 | 1.80% | 11.29% | 27.64% | 33.06% | 19.92% | 5.66% | 0.63% | 0.01% | N/A |
| Wisconsin | 0.6794 | 3.33 | N/A | 0.14% | 2.03% | 11.26% | 29.27% | 35.84% | 18.09% | 3.22% | 0.14% |
| Penn St | 0.7070 | 3.21 | N/A | 0.12% | 1.79% | 9.98% | 26.80% | 35.24% | 20.96% | 4.89% | 0.22% |
| Illinois | 0.5796 | 3.03 | N/A | 0.05% | 1.00% | 7.25% | 23.76% | 36.42% | 24.74% | 6.35% | 0.42% |
| Indiana | 0.5559 | 2.42 | N/A | 0.02% | 0.41% | 3.32% | 13.32% | 28.64% | 32.75% | 18.04% | 3.50% |
| Purdue | 0.3327 | 1.78 | 1 in 6.58M | 1 in 88,500 | 0.03% | 0.50% | 3.97% | 16.99% | 36.90% | 34.57% | 7.03% |
| Minnesota | 0.1202 | 0.47 | N/A | 1 in 3.05B | 1 in 13.8M | 1 in 162k | 0.03% | 0.56% | 6.24% | 33.00% | 60.17% |
Not much separates the four remaining unbeatens here; with only wins and losses as data strength of schedule is all that can distinguish them.
This week's games (remember, home field is completely ignored for ratings purposes and for these projections):
Illinois @ PSU: PSU 64% to win
Minnesota @ Wisconsin: Wisc 94% to win
Indiana @ OSU: OSU 88% to win
MSU @ Michigan: Michigan 52% to win
Purdue @ Northwestern: NW 90% to win
Conference titles:
| Champions or co-champions | Count |
|---|---|
| OSU outright | 1941 |
| MSU outright | 1471 |
| Mich outright | 1390 |
| MSU-OSU | 827 |
| NW outright | 482 |
| Mich-OSU | 467 |
| Iowa outright | 439 |
| Mich-MSU | 335 |
| NW-OSU | 312 |
| Mich-MSU-OSU | 279 |
| Mich-NW | 201 |
| Iowa-OSU | 193 |
| Mich-NW-OSU | 142 |
| MSU-NW | 135 |
| Iowa-MSU | 132 |
| MSU-NW-OSU | 126 |
| Iowa-Mich | 114 |
| Iowa-MSU-OSU | 93 |
| Mich-MSU-NW | 88 |
| Mich-MSU-NW-OSU | 85 |
| Iowa-Mich-MSU | 64 |
| Iowa-NW | 52 |
| Iowa-Mich-OSU | 50 |
| Wisc outright | 47 |
| Iowa-NW-OSU | 43 |
| Iowa-Mich-MSU-NW-OSU | 34 |
| Iowa-Mich-MSU-OSU | 32 |
| Iowa-Mich-NW, MSU-OSU-Wisc | 27 |
| Mich-Wisc | 24 |
| Iowa-MSU-NW-OSU | 23 |
| MSU-Wisc, OSU-Wisc | 22 |
| Iowa-Mich-NW-OSU, Iowa-MSU-NW | 16 |
| Mich-MSU-OSU-Wisc | 14 |
| Iowa-Mich-MSU-NW | 13 |
| PSU outright, Mich-MSU-Wisc | 12 |
| Iowa-MSU-OSU-Wisc | 11 |
| Mich-MSU-NW-OSU-Wisc, Mich-OSU-Wisc | 10 |
| MSU-NW-OSU-Wisc | 9 |
| Iowa-Mich-MSU-OSU-Wisc, Iowa-MSU-Wisc, NW-Wisc | 8 |
| Iowa-MSU-NW-OSU-Wisc, MSU-NW-Wisc | 6 |
| Iowa-Mich-NW-Wisc, NW-OSU-Wisc | 5 |
| Mich-PSU, 4 different three-way or larger ties | 4 |
| OSU-PSU, 10 different three-way or larger ties | 3 |
| Ill-OSU, 11 different three-way or larger ties | 2 |
| Ill outright, Ind-OSU, PSU-Wisc, 32 different three-way or larger ties | 1 |
| OSU outright or shared | 4856 |
| MSU outright or shared | 3936 |
| Mich outright or shared | 3483 |
| NW outright or shared | 1893 |
| Iowa outright or shared | 1435 |
| Wisc outright or shared | 302 |
| PSU outright or shared | 54 |
| Ill outright or shared | 25 |
| Ind shared | 7 |
| Pur shared | 1 |
| Minn shared | 0 |
The basic method sees this as a five-team race, with OSU, MSU, and Michigan the main contenders and NW and Iowa as outside shots. There's a little more than a 13% chance of a tie at the top between two teams that do not play each other (MSU-OSU, NW-OSU, or NW-Mich).
Margin-Aware Method
| Team | BT WPct | Average wins | 8-0 | 7-1 | 6-2 | 5-3 | 4-4 | 3-5 | 2-6 | 1-7 | 0-8 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ohio St | 0.9800 | 7.38 | 48.88% | 40.81% | 9.43% | 0.85% | 0.03% | 1 in 156k | 1 in 23.3M |
1 in 12B | N/A |
| Iowa | 0.9627 | 6.66 | 15.98% | 44.18% | 30.43% | 8.36% | 1.00% | 0.05% | 1 in 81,900 | 1 in 17.3M | N/A |
| MSU | 0.8996 | 6.21 | 7.18% | 32.20% | 38.94% | 17.75% | 3.59% | 0.33% | 0.01% | 1 in 855k | N/A |
| Michigan | 0.8909 | 5.21 | 0.79% | 8.76% | 29.75% | 37.06% | 18.88% | 4.33% | 0.42% | 0.01% | N/A |
| Northwestern | 0.5791 | 3.62 | 0.01% | 0.47% | 4.35% | 16.75% | 31.77% | 30.74% | 13.87% | 2.03% | N/A |
| Illinois | 0.6194 | 3.45 | N/A | 0.19% | 2.70% | 13.84% | 31.03% | 32.94% | 16.08% | 3.04% | 0.17% |
| Penn St | 0.7293 | 3.37 | N/A | 0.07% | 1.87% | 12.14% | 31.15% | 34.12% | 17.02% | 3.48% | 0.15% |
| Wisconsin | 0.6645 | 3.20 | N/A | 0.01% | 0.58% | 7.39% | 29.89% | 39.10% | 19.54% | 3.33% | 0.16% |
| Indiana | 0.6337 | 2.85 | N/A | 1 in 10,800 | 0.44% | 5.85% | 21.52% | 34.59% | 26.94% | 9.55% | 1.10% |
| Purdue | 0.2671 | 1.50 | 1 in 113M | 1 in 566k | 1 in 10,900 | 0.20% | 2.12% | 11.58% | 32.53% | 40.84% | 12.72% |
| Minnesota | 0.1402 | 0.56 | N/A | 1 in 22B | 1 in 39.6M | 1 in 233k | 0.03% | 0.68% | 7.85% | 38.23% | 53.22% |
The top half looks quite plausible here; Illinois ahead of PSU and Wisconsin is mostly because Illinois already got the OSU game on the books and doesn't play Iowa. The big gap between MSU and Michigan in projected wins is based on schedule: MSU skips Ohio State and Indiana, while Michigan skips Minnesota and NW.
This week's games (again, ignoring home field advantage):
Illinois @ PSU: PSU -3, 62% to win
Minnesota @ Wisconsin: Wisc -15.5, 92% to win
Indiana @ OSU: OSU -20.5, 97% to win
MSU @ Michigan: MSU -0.5, 52% to win
Purdue @ Northwestern: NW -8, 79% to win
Conference titles:
| Champions or co-champions | Count |
|---|---|
| OSU outright | 4866 |
| Iowa outright | 1792 |
| Iowa-OSU | 875 |
| MSU-OSU | 700 |
| Iowa-MSU-OSU | 535 |
| MSU outright | 431 |
| Iowa-Mich-OSU | 157 |
| Mich-OSU | 156 |
| Iowa-MSU | 126 |
| Mich outright | 95 |
| Mich-MSU-OSU | 77 |
| Iowa-Mich | 55 |
| Iowa-Mich-MSU | 25 |
| OSU-Wisc | 12 |
| Mich-MSU | 11 |
| Iowa-Mich-MSU-OSU | 9 |
| NW-OSU, Iowa-OSU-Wisc | 7 |
| Wisc outright, Iowa-Wisc | 6 |
| MSU-OSU-Wisc | 4 |
| OSU-PSU, NW outright, 3 different three-way or larger ties |
3 |
| MSU-Wisc, Iowa-NW, 6 different three-way or larger ties |
2 |
| Mich-Wisc, Iowa-PSU, Ill-Iowa, 14 different three-way or larger ties |
1 |
| OSU outright or shared | 7439 |
| Iowa outright or shared | 3620 |
| MSU outright or shared | 1946 |
| Mich outright or shared | 602 |
| Wisc outright or shared | 47 |
| NW outright or shared | 24 |
| PSU shared | 11 |
| Ill shared | 8 |
| Ind shared | 4 |
| Pur shared | 0 |
| Minn shared | 0 |
Throw in margin, and the race shakes out much more clearly: the OSU-Iowa game is likely for all the marbles, with MSU as a dark-horse contender and Michigan a somewhat longer shot.
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