Race for the Roses 2012: Week 7

Last week, both division races had tightened up a bit due to Michigan and Wisconsin losing and Indiana winning. This week, the stratification between the top and bottom appears to have reasserted itself in the West, while out in the East, the division that was expected to be a foregone conclusion at this point is not.

As always, ratings are here. Division title scenarios are now calculated from individual game probabilities, with tiebreakers taken into consideration. Tiebreakers (source):

• Head-to-head
• Division record
• Record against the remaining teams in the division, in order from top to bottom (I'm assuming ties are not broken and those games are lumped together, as this is the case for basketball when they use this tiebreaker; however, I didn't see any cases where this mattered)
  
• Record against common conference opponents (since division record was tied, this is the same as record against common cross-division opponents)
• BCS, with the exception that if the top two teams are one spot apart in the standings, head-to-head among those two is used instead. Not clear what happens if none are in the BCS - do they extend the standings down all the way to every team that got a single vote? Do they look at the computer ratings all the way down if nobody even managed to reach that threshold?
  
• Overall record (I'm unsure what the note about "exempted games" not counting means; could be 1-AA games).
• Random draw

Last Week's Results

Nebraska 28, Michigan State 24

Finagle's Law strikes again.

Michigan 35, Minnesota 13

No Denard Robinson? No problem. Devin Gardner threw for 234 yards and two touchdowns as Michigan kept pace with Nebraska - but they still need some help even if they manage to win in Columbus in two weeks.

Ohio State 52, Illinois 22

For one quarter, it looked like Illinois could make a game of it (trailing just 7-6 at the end of the first). They didn't score again until they were down 32. With Illinois having lost to both Wisconsin and Indiana already, this officially eliminates them from both bowl contention and the race for Indianapolis.

Penn State 34, Purdue 9

The Boilers scored a FG two minutes into the game and a touchdown on the final play. The time between didn't go so well. Purdue is still mathematically alive for Indy, believe it or not, but the odds are pretty seriously against them (obviously).

Indiana 24, Iowa 21

Indiana remains in control of their own destiny after coming back from a very early 14-0 deficit. Meanwhile, the loss seriously damages Iowa's bowl hopes; now they have to beat either Michigan or Nebraska along with Illinois.

West Division Scenarios

Individual game projections are listed as (basic method win percentage / margin-aware win percentage / margin-aware projected margin).

Tiebreakers at 5-3

Two-way ties are straightforward.

Nebraska, Michigan, and Northwestern: Nebraska wins on head-to-head sweep.
Nebraska, Michigan, and Iowa: Iowa wins on head-to-head sweep.
Nebraska, Northwestern, and Iowa: Head-to-head split goes to the division record. Iowa would be 4-1. Nebraska's second loss must be to Penn State, not Minnesota, in order to stay in; Northwestern's loss must be to Illinois instead of Michigan or MSU. If all three stay in, their common cross-division opponent (Penn State) beat them all, so it goes to the BCS. If Northwestern drops out, Iowa wins; if Nebraska drops out, Northwestern wins.
Michigan, Northwestern, and Iowa: If Northwestern beats Michigan, they have the head-to-head sweep and win. If Michigan beats Northwestern, the head-to-head split takes it to division record, which Iowa wins.

A four-way tie is surprisingly simple: if Michigan beats Northwestern, both of them are eliminated on head-to-head (they'll be 1-2, with Nebraska and Iowa at 2-1), then Iowa wins due to head-to-head over Nebraska. If Northwestern beats Michigan, Michigan falls out at 0-3 in the head-to-head games with the others 2-1. Then, as with the direct three-team tie, division record determines it.

Tiebreakers at 4-4

Yes, this can happen. If Nebraska and Michigan both lose out, Iowa loses to Purdue, and Northwestern loses to MSU and Illinois, there will be at least a four-way tie at 4-4. (The winner of Minnesota-MSU can potentially join that tie.)

If neither MSU nor Minnesota joins the tie, Michigan will drop out for being swept by the other three. Then it goes to division record, and only Iowa would be 4-1. If MSU is the fifth team involved, Nebraska and Iowa would survive the first pass of head-to-head at 3-1 and Iowa would again advance. If Minnesota joins instead, the 3-1 teams would be Iowa and Northwestern, and Northwestern would advance.

Nebraska

Remaining games: PSU (74% / 69% / +5.5), Minn (85% / 94% / +18), @Iowa (76% / 71% / +6)
Division record: 3-0 (wins over Mich, MSU, NW)
Cross-division games: beat Wisc, lost to OSU

If they win out: They are division champions, holding the head-to-head tiebreaker over Michigan if necessary.
If they lose once: Michigan has to lose once, but that's all they need, holding the tiebreaker over both Michigan and Northwestern.
If they lose twice: They need two losses by Michigan and one by Northwestern, at a minimum. If Nebraska's win is against Iowa, that's enough. If the win is over Penn State, Iowa has to lose a game, as the only multi-way tie Nebraska can win is with Michigan and Northwestern. If the win is over Minnesota, another option opens up - Iowa wins out, Michigan loses to Northwestern and Iowa (the Ohio State game doesn't matter), Northwestern beats MSU but loses to Illinois, and it goes to the BCS among Iowa, Nebraska, and Northwestern.
If they lose all three: They can still, theoretically, tie for the division title, but they can't win the tiebreakers.

Chances of reaching Indianapolis: 87.45% no-margin / 86.76% margin-aware, plus about a 1 in 6,000 or 1 in 27,000 shot at a BCS tiebreaker with Iowa and Northwestern.

Michigan

Remaining games: NW (59% / 68% / +5), Iowa (80% / 88% / +13), @OSU (17% / 14% / -12.5)
Division record: 2-1 (wins over MSU, Minn; loss to Neb)
Cross-division games: beat Ill and Pur

If they win out: A Nebraska loss gives them the title.
If they lose once: Nebraska has to lose twice. If the loss is to Northwestern, the Wildcats also have to drop one.
If they lose twice: Nebraska has to lose all three, whichever game Michigan wins. If the win is against Iowa, Northwestern has to lose the two non-Michigan games, allowing Michigan to claim the title outright. If it is against Northwestern, Iowa has to lose to Purdue. If it is against Ohio State, both of those two have to happen.
If they lose all three: As with Nebraska, a tie for the division title is still possible but they cannot reach Indianapolis.

Chances of reaching Indianapolis: 9.34% / 10.85%

Northwestern

Remaining games: @Mich (41% / 32% / -5), @MSU (53% / 42% / -2), Ill (89% / 97% / +22.5)
Division record: 2-1 (wins over Iowa, Minn; loss to Neb)
Cross-division games: beat Ind, lost to PSU

If they win out: Nebraska has to lose twice, as they win the tiebreaker whether Michigan is involved or not.
If they lose once: The loss cannot be to Michigan. If they lose to MSU, Nebraska has to lose all three and Michigan has to lose another game besides the one to Northwestern. If the loss is to Illinois, another possibility exists: Nebraska can lose only two as long as Iowa wins out. (That includes a win over Michigan, which takes care of that portion of the equation.) If Nebraska's win is over Penn State, Northwestern wins after Nebraska drops out on the division record tiebreaker; if it's over Minnesota, it goes to the BCS between Nebraska, Northwestern, and Iowa.
If they lose twice: The win must be over Michigan. Nebraska and Michigan have to lose out, Iowa has to lose to Purdue, and Minnesota has to win out. Then they win a five-way tiebreaker.

Chances of reaching Indianapolis: 2.39% / 1.62%, plus the BCS tiebreaker possibility mentioned under Nebraska.

Iowa

Remaining games: Pur (69% / 79% / +9), @Mich (20% / 12% / -13), Neb (24% / 29% / -6)
Division record: 2-1 (wins over MSU, Minn; loss to NW)
Cross-division games: lost to Ind and PSU

If they win out: Nebraska and Michigan each have to lose another game as well, as does Northwestern. If Northwestern's loss is to Michigan or if they lose both of the other games, that's enough (and Michigan and Nebraska can lose all three without affecting the tiebreakers). If Northwestern loses to MSU or Illinois but not both, Nebraska must be part of the tie (splitting their non-Iowa games) to avoid a Northwestern head-to-head sweep (Michigan's presence is irrelevant). If Northwestern's loss is to MSU, they will drop out of the tie on division record and Iowa wins. If Northwestern's loss is to Illinois, Nebraska's must be to Penn State (not Minnesota) and then it goes to the BCS.
If they lose once: The loss has to be to Purdue. Michigan and Nebraska both have to lose out, Northwestern has to lose to MSU and Illinois, and Minnesota has to lose either to Illinois or to MSU (or both).

Chances of reaching Indianapolis: 0.79% / 0.77%, plus the BCS scenario listed under Nebraska.

Michigan State

Remaining games: BYE, NW (47% / 58% / +2), @Minn (52% / 65% / +4)
Division record: 0-3 (lost to Mich, Neb, Iowa)
Cross-division games: beat Wisc and Ind, lost to OSU

If they win out: It's possible to reach a five-way tie at 4-4, but a 1-3 record in the head-to-head would eliminate MSU.

Minnesota

Remaining games: @Ill (61% / 58% / +2), @Neb (15% / 6% / -18), MSU (48% / 35% / -4)
Division record: 0-3 (lost to Iowa, Mich, NW)
Cross-division games: beat Pur, lost to Wisc

If they win out: As with MSU, a five-way tie is possible but head-to-head will eliminate them.

East Division Scenarios (All Teams)

Ohio State

Remaining games: BYE, @Wisc (77% / 62% / +3.5), Mich (83% / 86% / +12.5)
Division record: 4-0 (wins over PSU, Pur, Ill, Ind)
Cross-division games: beat Neb and MSU

If they win out: They are the champions.
If they lose once: Still the champions, owing to the tiebreaker against Penn State.
If they lose both: Penn State and Wisconsin each have to lose a game.

Chance of division title: 98.65% no-margin / 98.12% margin-aware.

Penn State

Remaining games: @Neb (26% / 31% / -5.5), Ind (78% / 88% / +13), Wisc (62% / 72% / +6)
Division record: 2-1 (wins over Ill, Pur; loss to OSU)
Cross-division games: beat Iowa and NW

If they win out: Ohio State has to lose both.
If they lose once: No good. They're guaranteed to lose the tiebreaker to Ohio State (or Wisconsin, if it's a three-way tie).

Chance of division title: 0.48% / 1.02%

Wisconsin

Remaining games: @Ind (60% / 58% / +2.5), OSU (23% / 38% / -3.5), @PSU (38% / 28% / -6)
Division record: 2-0 (wins over Ill, Pur)
Cross-division games: beat Minn, lost to Neb and MSU

If they win out: Ohio State has to lose to Michigan.

Chance of division title: 0.87% / 0.86%

East Division Scenarios (Eligible Teams)

Wisconsin

If they beat Indiana: They clinch the division (among eligible teams), at worst holding the tiebreaker at 4-4.
If they lose to Indiana but win the other two: Indiana has to lose one.
If they win one game and it isn't against Indiana: Indiana has to lose the other two.
If they lose all three: This could still get as far as the BCS - if Indiana loses the other two and Purdue wins out, a three-way tie at 3-5 gets a head-to-head split, with all three beating Illinois and losing to OSU and PSU and no common cross-division games.

Chances of reaching Indianapolis: 69.59% / 69.90%, plus a 1.13% / 0.79% chance of the BCS tiebreaker.

Indiana

Remaining games: Wisc (40% / 42% / -2.5), @PSU (22% / 12% / -13), @Pur (49.99% / 55% / +1.5)
Division record: 1-1 (win over Ill, loss to OSU)
Cross-division games: beat Iowa, lost to MSU and NW

If they win out: They're going to Indianapolis.
If they lose once: It can't be the Wisconsin game, and Wisconsin has to lose one of the other two.
If they beat Wisconsin and lose the other two: Wisconsin has to lose out. If Purdue wins out, it goes to the BCS; if not, Indiana wins.

Chances of reaching Indianapolis: 29.27% / 29.31%, plus the BCS tiebreaker possibility listed under Wisconsin.

Purdue

Remaining games: @Iowa (31% / 21% / -9), @Ill (48% / 53% / +0.5), Ind (50.01% / 45% / -1.5)
Division record: 0-3 (losses to OSU, PSU, Wisc)
Cross-division games: lost to Mich and Minn

If they win out: They can get to a BCS tiebreaker if Wisconsin loses every game and Indiana loses to Penn State.

Chances of reaching Indianapolis: Only via the 1.13% / 0.79% chance of a BCS tiebreaker.

Illinois

Remaining games: Minn (39% / 42% / -2), Pur (52% / 47% / -0.5), @NW (11% / 3% / -22.5)
Division record: 0-4 (losses to Wisc, Ind, OSU, PSU)
Cross-division games: lost to Mich

If they win out: A tie at 3-5 with Wisconsin and Indiana is possible, but they lost to both teams and therefore would lose the tiebreaker.

Tables

A * indicates that the possibility of a BCS tiebreaker has been included (with 1/3 of those chances added to each team in the tiebreaker).

West, Basic Method

Team	Avg wins	0-8	1-7	2-6	3-5	4-4	5-3	6-2	7-1	8-0	Bowl	Indy
Nebraska (#12)	6.36	N/A	N/A	N/A	N/A	0.89%	10.67%	40.11%	48.33%	N/A	Yes	87.45%*
Michigan (#26)	5.56	N/A	N/A	N/A	N/A	6.71%	38.20%	46.98%	8.10%	N/A	Yes	9.34%
Northwestern (#28)	4.83	N/A	N/A	N/A	3.06%	30.20%	47.43%	19.31%	N/A	N/A	Yes	2.39%*
Iowa (#74)	3.12	N/A	N/A	19.15%	52.61%	24.99%	3.26%	N/A	N/A	N/A	28.25%	0.79%*
Michigan State (#52)	2.98	N/A	N/A	25.71%	50.12%	24.17%	N/A	N/A	N/A	N/A	74.29%	0
Minnesota (#70)	2.24	N/A	17.17%	46.01%	32.54%	4.29%	N/A	N/A	N/A	N/A	82.83%	0

East, Basic Method

Team	Avg wins	0-8	1-7	2-6	3-5	4-4	5-3	6-2	7-1	8-0	Bowl	Division	Indy
Ohio State (#4)	7.60	N/A	N/A	N/A	N/A	N/A	N/A	3.85%	31.93%	64.22%	N/A	98.65%	N/A
Penn State (#36)	5.65	N/A	N/A	N/A	N/A	6.33%	34.41%	46.87%	12.38%	N/A	N/A	0.48%	N/A
Wisconsin (#42)	4.20	N/A	N/A	N/A	19.32%	46.16%	29.39%	5.12%	N/A	N/A	Yes	0.87%	69.97%*
Indiana (#76)	3.13	N/A	N/A	23.17%	45.48%	26.83%	4.52%	N/A	N/A	N/A	31.35%	0	29.65%*
Purdue (#90)	1.30	17.74%	42.42%	32.26%	7.58%	N/A	N/A	N/A	N/A	N/A	7.58%	0	0.38%*
Illinois (#100)	1.02	26.30%	48.08%	23.40%	2.22%	N/A	N/A	N/A	N/A	N/A	0	0	0

West, Margin-Aware

Team	Avg wins	0-8	1-7	2-6	3-5	4-4	5-3	6-2	7-1	8-0	Bowl	Indy
Nebraska (#23)	6.33	N/A	N/A	N/A	N/A	0.57%	11.15%	42.55%	45.73%	N/A	Yes	86.76%*
Michigan (#35)	5.69	N/A	N/A	N/A	N/A	3.44%	32.17%	56.22%	8.17%	N/A	Yes	10.85%
Northwestern (#39)	4.71	N/A	N/A	N/A	1.32%	39.77%	45.91%	13.00%	N/A	N/A	Yes	1.62%*
Michigan State (#43)	3.23	N/A	N/A	14.53%	47.47%	38.01%	N/A	N/A	N/A	N/A	85.47%	0
Iowa (#72)	3.21	N/A	N/A	12.80%	56.54%	27.83%	2.83%	N/A	N/A	N/A	30.66%	0.77%*
Minnesota (#81)	2.00	N/A	25.32%	50.95%	22.44%	1.29%	N/A	N/A	N/A	N/A	74.68%	0

East, Margin-Aware

Team	Avg wins	0-8	1-7	2-6	3-5	4-4	5-3	6-2	7-1	8-0	Bowl	Division	Indy
Ohio State (#10)	7.49	N/A	N/A	N/A	N/A	N/A	N/A	5.19%	41.08%	53.73%	N/A	98.12%	N/A
Penn State (#27)	5.91	N/A	N/A	N/A	N/A	2.41%	24.24%	53.66%	19.69%	N/A	N/A	1.02%	N/A
Wisconsin (#37)	4.24	N/A	N/A	N/A	18.55%	44.66%	30.54%	6.24%	N/A	N/A	Yes	0.86%	70.16%*
Indiana (#68)	3.09	N/A	N/A	23.03%	47.80%	26.33%	2.84%	N/A	N/A	N/A	29.17%	0	29.57%*
Purdue (#87)	1.18	20.73%	45.30%	29.12%	4.86%	N/A	N/A	N/A	N/A	N/A	4.86%	0	0.26%*
Illinois (#105)	0.92	29.73%	48.93%	20.68%	0.66%	N/A	N/A	N/A	N/A	N/A	0	0	0