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Big Ten Bradley-Terry Projections: Post-Week 5

[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

TeamBT WPctAverage wins8-07-16-25-34-43-52-61-70-8
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-championsCount
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

TeamBT WPctAverage wins8-07-16-25-34-43-52-61-70-8
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-championsCount
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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