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Big Ten Bradley-Terry Projections: Post-Week 9 (plus Rose Bowl tiebreaker analysis)


Previous projections: pre-conference, post-Week 5, post-Week 6, post-Week 7, post-Week 8

Full national rankings: here


The MSU-Iowa game had the potential to either clarify the Big Ten title race (with an MSU win) or turn it into a mad scramble (with an Iowa win). Unfortunately from my perspective (although probably fortunately for the purpose of keeping these posts interesting), it's the latter. With four weeks to go yet, it's still too early to do title scenarios by pure calculation (there are just over 1,000,000 possible combinations of outcomes in the remaining 20 Big Ten games; many of these are redundant in the sense of who wins it all, but even so the task remains nontrivial); I expect to switch from simulation to pure calculation after Week 11 (when there will only be 1024 combinations and it will be much more clear which games are mathematically irrelevant).

Indiana joins the "mathematically eliminated" brigade since Minnesota's fifth loss makes an 11-way tie at 4-4 mathematically impossible. Michigan still has a theoretical chance if they can get to 5-3 and all hell breaks loose, but this is spectacularly improbable. The two-loss teams can be considered alive in the race, although they will need three upsets of the top four (one of Iowa and Ohio State will knock off the other).

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
MSU 0.9281 6.79 N/A 79.89% 19.17% 0.93% 1 in 15,900 N/A N/A N/A N/A
Wisconsin 0.9246 6.67 N/A 70.74% 25.82% 3.27% 0.17% 1 in 33,200 N/A N/A N/A
Iowa 0.8924 6.3 N/A 40.68% 48.88% 9.91% 0.52% 1 in 19,800 N/A N/A N/A
Ohio St 0.8886 6.08 N/A 30.90% 48.19% 18.76% 2.15% N/A N/A N/A N/A
Illinois 0.7846 5.36 N/A N/A 46.78% 42.82% 10.15% 0.25% N/A N/A N/A
Penn St 0.6944 3.81 N/A N/A 1.69% 16.90% 46.73% 30.03% 4.65% N/A N/A
Purdue 0.4190 2.97 N/A N/A 0.05% 1.81% 19.97% 50.97% 27.20% N/A N/A
Northwestern 0.5761 2.89 N/A N/A 0.14% 2.78% 17.91% 43.92% 35.25% N/A N/A
Michigan 0.6518 2.38 N/A N/A N/A 0.62% 8.11% 33.23% 45.14% 12.91% N/A
Indiana 0.3442 0.71 N/A N/A N/A N/A 0.02% 0.87% 11.56% 45.15% 42.40%
Minnesota 0.0936 0.05 N/A N/A N/A N/A N/A 1 in 372k 0.06% 4.65% 95.28%

 

MSU and Wisconsin have the edge partly due to easier finishing schedules (both are done playing teams in the top five, while Iowa and OSU play each other) and partly due to better ratings (Iowa's second loss, and Ohio State's soft schedule to date - their third-best game is against #41 Miami! - drag them down). Illinois has clearly emerged as the probable #5 and the team far most likely to benefit if chaos breaks loose among the top four. Penn State has a brutal finishing kick (MSU and OSU await, along with a scrappy NW team), which plays a significant role in the separation in the standings. Michigan, likewise, has a tough finishing schedule (Wisconsin, Illinois, and OSU all ahead).

Dueling 0-8s watch: 40.4% chance that Indiana and Minnesota both go winless in the Big Ten.

This week's games: (as always, there is no home field adjustment)
Illinois @ Michigan: Illinois 66% to win
Northwestern @ Penn State: Penn State 63% to win
Iowa @ Indiana: Iowa 94% to win
Wisconsin @ Purdue: Wisconsin 94% to win
Minnesota @ Michigan State: Michigan State 99.2% to win

Bowl chances:
Already eligible: MSU, OSU, Wisconsin, Iowa, Northwestern
Already invited to the Queso Bowl: Minnesota
Illinois: 1 in 1900 chance of failing to reach a bowl
Michigan: 27 in 31 chance of reaching a bowl
Purdue: 12 in 55 chance of reaching a bowl
Penn State: 41 in 43 chance of reaching a bowl
Indiana: 1 in 8 chance of reaching a bowl

Conference title simulations:

Champions or co-champions Count
Iowa-MSU-Wisc 2348
MSU-OSU-Wisc 1729
MSU-Wisc 1622
Iowa-MSU 948
MSU-OSU 700
MSU outright 615
Iowa-Wisc 585
OSU-Wisc 432
Wisc outright 429
Iowa outright 252
OSU outright 190
Iowa-MSU-OSU-Wisc 42
Ill-Iowa-MSU-OSU-Wisc 40
Ill-Iowa-MSU-Wisc 10
Ill-MSU-OSU-Wisc 9
Ill-Iowa-MSU-OSU-PSU-Wisc 8
Ill-Iowa-MSU-OSU
Iowa-MSU-OSU-PSU-Wisc
6
Iowa-MSU-OSU
Iowa-MSU-PSU-Wisc
5
Ill-MSU-OSU
Ill-Iowa-OSU-Wisc
Ill-Iowa-MSU-PSU-Wisc
Iowa-MSU-NW-OSU-Wisc
2
MSU-PSU-Wisc
Iowa-OSU-Wisc
Ill-OSU-Wisc
Iowa-MSU-NW-Wisc
MSU-NW-OSU-Wisc
Ill-Iowa-MSU-PSU
MSU-OSU-PSU-Wisc
MSU-OSU-Pur-Wisc
Iowa-MSU-OSU-PSU
Iowa-MSU-OSU-Pur-Wisc
Ill-Iowa-MSU-OSU-PSU
1
MSU outright or shared 8108
Wisc outright or shared 7279
Iowa outright or shared 4267
OSU outright or shared 3181
Ill shared 82
PSU shared 26
NW shared 4
Pur shared 2
MSU Rose Bowl 4605
Wisc Rose Bowl 1450
Iowa Rose Bowl 1200
OSU Rose Bowl 190
Indeterminate Rose Bowl 2555

 

Bold indicates ties where the Rose Bowl team is known. The majority of the "indeterminate" scenarios probably favor Ohio State or Wisconsin (Iowa, Illinois, Purdue, and Penn State all have a non-conference loss and so have to win outright on head-to-head; MSU and NW are almost certainly worse off in the BCS standings, though in two-loss chaos scenarios who knows how the BCS will react). For tiebreaker purposes, remember that head-to-head ONLY matters if teams can be separated into two groups such that everyone in the first group beat everyone in the second; as the official tiebreakers are worded it appears that a four-team tie with two at 2-1 and two at 1-2 would not be broken by head-to-head. (That is the assumption used in the scenarios below.) Tiebreaker scenarios are as follows (listed mostly in order of simulated likelihood):

  • Iowa-MSU-Wisc: Head-to-head fails to break the tie (everybody's 1-1). Iowa drops out due to a non-conference loss, at which point MSU's head-to-head win over Wisconsin gives them the nod.
  • MSU-OSU-Wisc: Head-to-head fails (OSU and MSU do not play each other, and Wisconsin split those two games; had they won both they would win the tiebreaker, and had they lost both they would be eliminated). None of the teams have a non-conference loss, so it goes to the BCS standings.
  • MSU-Wisc, Iowa-MSU, Iowa-Wisc, OSU-Wisc: All broken by simple head-to-head.
  • MSU-OSU: No head-to-head game, no non-conference losses, so it goes to the BCS standings.

Now we get to the crazy scenarios, at two losses all around:

  • Iowa-MSU-OSU-Wisc: Head-to-head fails to break the tie (this will always be true if Iowa-MSU-Wisc is included, unless a tie at three losses occurs and somebody loses to all three). Iowa drops out due to a non-conference loss, so this reduces to MSU-OSU-Wisc.
  • Ill-Iowa-MSU-OSU-Wisc: Head-to-head fails again, and Iowa and Illinois drop out, so it's MSU-OSU-Wisc again.
  • Ill-Iowa-MSU-Wisc: Head-to-head fails, Iowa and Illinois drop out, MSU head-to-head over Wisc.
  • Ill-MSU-OSU-Wisc: Head-to-head fails (Illinois lost to MSU and OSU but won't play Wisconsin). Illinois drops out, and yet again we have MSU-OSU-Wisc.
  • Ill-Iowa-MSU-OSU-PSU-Wisc: Head-to-head fails, Iowa, Illinois, and PSU drop out, MSU-OSU-Wisc goes to the BCS standings.
  • Ill-Iowa-MSU-OSU: Head-to-head fails, Illinois and Iowa drop out, MSU-OSU decided by the BCS.
  • Iowa-MSU-OSU-PSU-Wisc: Head-to-head fails, Iowa and PSU drop out, MSU-OSU-Wisc decided by the BCS.
  • Iowa-MSU-OSU: This depends on how it's achieved. If Iowa beats OSU then loses another game, they will have the tiebreaker on head-to-head. If they lose to OSU and OSU drops another game (more likely, given the remaining schedules), head-to-head fails and Iowa drops out on non-conference record, leaving MSU-OSU decided by the BCS.
  • Iowa-MSU-PSU-Wisc: Head-to-head fails, Iowa and PSU drop out, MSU beat Wisconsin.
  • Ill-MSU-OSU: Illinois drops out on head-to-head (losing to both), MSU-OSU decided by the BCS.
  • Ill-Iowa-OSU-Wisc: This won't be broken by head-to-head since Illinois plays neither Iowa nor Wisconsin. Illinois and Iowa drop out on non-conference record, Wisconsin beat OSU.
  • Ill-Iowa-MSU-PSU-Wisc: Head-to-head fails, Illinois, Iowa, and PSU drop out, MSU beat Wisconsin.
  • Iowa-MSU-NW-OSU-Wisc: Head-to-head fails, Iowa drops out, and it's a four-way tie decided by the BCS standings among the four teams that didn't lose a non-conference game.
  • MSU-PSU-Wisc: If MSU beats PSU but loses elsewhere, they win this on head-to-head. If they lose, because PSU does not play Wisconsin, head-to-head will fail and PSU will drop out on non-conference record, at which point MSU beats Wisconsin head-to-head.
  • Iowa-OSU-Wisc: Straight head-to-head.
  • Ill-OSU-Wisc: Head-to-head fails due to OSU splitting these games and the other two not playing, but Illinois drops on non-conference and Wisconsin beats OSU head-to-head.
  • Iowa-MSU-NW-Wisc: Head-to-head fails, Iowa drops out, MSU beat NW and Wisconsin head-to-head.
  • MSU-NW-OSU-Wisc: Head-to-head is useless, nobody lost a non-conference game, BCS standings decide it.
  • Ill-Iowa-MSU-PSU: Head-to-head fails, so it goes to non-conference record and MSU is the only one with a perfect record there.
  • MSU-OSU-PSU-Wisc: Head-to-head fails, PSU drops, MSU-OSU-Wisc decided by the BCS standings.
  • MSU-OSU-Pur-Wisc: Head-to-head fails (assuming Purdue beats Wisconsin and MSU, which is about the only way this can happen), but Purdue drops on non-conference record and MSU-OSU-Wisc goes to the BCS standings.
  • Iowa-MSU-OSU-PSU: If Iowa beats Ohio State, they'll have a head-to-head sweep and win this tiebreaker; if not, head-to-head will fail and they and PSU will be eliminated, leaving MSU-OSU decided by the BCS standings.
  • Iowa-MSU-OSU-Pur-Wisc: Head-to-head fails, Iowa and Purdue drop, MSU-OSU-Wisc goes to the BCS standings.
  • Ill-Iowa-MSU-OSU-PSU: Head-to-head fails, Illinois, Iowa, and PSU drop, MSU-OSU goes to the BCS standings.

In "triangle" situations like MSU-Wisconsin-Iowa, having the loss to the first team to be eliminated by later tiebreakers gives MSU the edge. But when the BCS standings are invoked, MSU's blowout loss is likely to hurt them severely.

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
MSU 0.9425 6.86 N/A 86.25% 13.46% 0.28% 1 in 86,600 N/A N/A N/A N/A
Wisconsin 0.9185 6.77 N/A 78.41% 19.96% 1.59% 0.05% 1 in 186k N/A N/A N/A
Iowa 0.9729 6.52 N/A 53.30% 45.37% 1.32% 0.01% 1 in 5.26M N/A N/A N/A
Ohio St 0.9672 6.33 N/A 39.88% 53.61% 6.31% 0.19% N/A N/A N/A N/A
Illinois 0.8557 5.68 N/A N/A 70.54% 27.10% 2.33% 0.03% N/A N/A N/A
Penn St 0.6837 3.82 N/A N/A 0.53% 11.47% 59.87% 25.47% 2.66% N/A N/A
Purdue 0.2358 2.66 N/A N/A 1 in 27,300 0.35% 9.20% 46.85% 43.59% N/A N/A
Northwestern 0.3803 2.38 N/A N/A 1 in 55,600 0.16% 3.82% 30.20% 65.81% N/A N/A
Michigan 0.6118 2.22 N/A N/A N/A 0.11% 3.26% 25.89% 59.97% 10.77% N/A
Indiana 0.2703 0.73 N/A N/A N/A N/A 1 in 38,600 0.35% 9.86% 52.61% 37.18%
Minnesota 0.0812 0.02 N/A N/A N/A N/A N/A 1 in 5.17M 0.01% 2.22% 97.76%

 

The big differences here: Iowa and Ohio State are actually considered the best teams in the Big Ten but still have to play each other; MSU and Wisconsin still come out ahead because they've finished the difficult portion of their schedules. Also, Purdue and Northwestern are both rated substantially lower than they are in the basic method, to the point that Indiana is actually favored in the Bucket game. The order of the final standings is the same, however.

Dueling 0-8s watch: 36.3% chance.

This week's games: (as always, there is no home field adjustment)
Illinois @ Michigan: Illinois -8, 79% to win
Northwestern @ Penn State: Penn State -8, 78% to win
Iowa @ Indiana: Iowa -28.5, 99.0% to win
Wisconsin @ Purdue: Wisconsin -22.5, 97% to win
Minnesota @ Michigan State: Michigan State -32.5, 99.5% to win

Bowl chances:
Already eligible: MSU, OSU, Wisconsin, Iowa, Northwestern
Already invited to the Queso Bowl: Minnesota
Illinois: 1 in 25,000 chance of failing to reach a bowl
Michigan: 58 in 65 chance of reaching a bowl
Purdue: 2 in 21 chance of reaching a bowl
Penn State: 73 in 75 chance of reaching a bowl
Indiana: 5 in 49 chance of reaching a bowl

Conference title simulations:

Champions or co-champions Count
Iowa-MSU-Wisc 3653
MSU-OSU-Wisc 2674
Iowa-MSU 1040
MSU-OSU 678
Iowa-Wisc 571
MSU-Wisc 462
OSU-Wisc 394
Iowa outright 164
MSU outright 131
OSU outright 127
Wisc outright 83
Ill-Iowa-MSU-OSU-Wisc 10
Iowa-MSU-OSU-Wisc
Ill-Iowa-MSU-OSU-PSU-Wisc
4
Ill-Iowa-MSU-OSU 2
Iowa-MSU-OSU
Iowa-MSU-OSU-PSU-Wisc
Ill-Iowa-MSU-PSU-Wisc
1
MSU outright or shared 8661
Wisc outright or shared 7857
Iowa outright or shared 5451
OSU outright or shared 3895
Ill shared 17
PSU shared 6
MSU Rose Bowl 4247
Iowa Rose Bowl 1204
Wisc Rose Bowl 1048
OSU Rose Bowl 127
Indeterminate Rose Bowl 3374

 

All scenarios here are described above in the basic-method section. Here Iowa slightly overtakes Wisconsin for Rose Bowl chances in known scenarios, though they're still likely fourth overall because none of the indeterminate scenarios here favor them.

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