Brady Hoke's self-avowed goal is to win Big Ten championships. Since we're facing the make-or-break section of Michigan's season after this bye week, it seems worth looking at what needs to happen for Michigan to win the Legends division and make it to the Big Ten championship game.
I decided to do this after reading on Football Study Hall that Michigan's chances of getting to Indianapolis by winning the division outright were 0.1% in a computer simulation. Why so low, I wondered? The author of that piece opined that
What truly surprised me is the almost zero chance that Michigan has to win the Legends Division outright. In 999 of 1000 cases model runs it needed help from someone else, or relied on tiebreakers to secure their place in the conference championship game. It looks like this is a direct result of the vagaries of their schedule...of the Legends Division contenders, they alone must face Ohio State. Also, if Michigan is to win the division outright it has to defeat both Nebraska and MSU. But in doing that it greatly aids the case of each to tie. It's a bit of a Catch-22 that Michigan finds itself in this year. Together, the odds of beating Nebraska, MSU, and Ohio State while Nebraska and MSU implode is pretty remote, hence the improbability of an outright Michigan division title.
To review, then: a team is selected to play in the Big Ten championship game by its overall conference record. Then there are a series of tiebreakers. If the records are the same, the head-to-head result is the tiebreaker. If three teams are tied for the same record, their records are compared to each other.
Scenario One: Michigan wins out
If Michigan wins out, then it ends the regular season at 11-1 overall, 7-1 in the conference. With wins over Nebraska and Michigan State, Michigan wins the tiebreakers even if Nebraska and Michigan State win the rest of their games (both Nebraska and Michigan State are undefeated in B1G play thus far).
Result: Big Ten championship game, almost certainly against Ohio State or Wisconsin.
Scenario Two: Michigan loses only one game, to a team not in the running for the Legends division
In this scenario Michigan ends the regular season at 10-2 overall, 7-2 in the conference, with wins over Nebraska and Michigan State. Michigan in this scenario drops one game against a team that is not a factor: Ohio State (not a factor because they're in the other division) or Northwestern (not a factor because they already have 3 B1G losses). We could probably put Iowa in this category: they have 2 B1G losses and are unlikely to run the table against Northwestern, Wisconsin, @Purdue and @Nebraska.
With wins over Nebraska and Michigan State, Michigan wins the tiebreakers. However, in this scenario Michigan needs Michigan State and Nebraska to lose one additional game in B1G play.
Nebraska still has to play @ Minny, Northwestern, Michigan State, @Penn State, Iowa.
Michigan State still has to play @Illinois, @Nebraska, @Northwestern, Minny.
So as long as Nebraska or State each lose a game, which seems very possible, then there would be three teams with two B1G losses, but Michigan would have wins against both of them, so Michigan goes to Indianapolis.
Scenario Three: Michigan loses to Michigan State or Nebraska
Note: this section has been edited thanks to a note by Key Play (see comments below).
Here is where it gets hairy. If Michigan loses to one of these teams, then it needs the following to advance to Indianapolis:
Win the rest of its games, to end the regular season with two losses.
The team that has defeated Michigan must lose three games in conference play (since it will have the tie-breaker over Michigan) OR it must defeat the other team and lose one other game in conference play.
The other of the two teams, assuming that Michigan defeats it, must lose one additional game in conference play (since Michigan will have the tie-breaker).
Thus, if we lose to Michigan State and defeat Nebraska, we need Nebraska to lose one additional game (say, at Penn State) and we would need Michigan State to lose three of its four remaining games not against Michigan (say, at Illinois, at Nebraska, and at Northwestern) OR we would need Nebraska to defeat Michigan State and for Michigan State to lose one additional game. In the latter case, we would have a three-way tie, with no head-to-head tie-breaker because each of the three teams would have beaten one and lost to the other. Then the next tie-breaker is overall record, and both State and Nebraska have out-of-conference losses (to Notre Dame and UCLA respectively).
Discussion and conclusions
I won't go into further permutations, because it gets too complicated and would require running simulations, something that I'm not prepared to do at the moment. But this basic analysis points out several things:
Michigan still has the ability to control its own destiny and win the Big Ten, by defeating every remaining team on its schedule and then winning the Big Ten Championship Game.
BUT: The loss to Penn State is a really serious problem, because Nebraska and Michigan State have not lost yet in B1G play. That loss means that if we lose to Ohio State, beating both Nebraska and Michigan State may not be enough.
It is more important at this point that Michigan beat Michigan State and Nebraska than it is to beat Ohio State. A loss to Ohio State means that we need Nebraska and Michigan State each to drop a game, something that is certainly possible. But a loss to Michigan State or to Nebraska is much more problematic.
Our rooting interest is for Nebraska and Michigan State to lose games. It would be great if Wisconsin beat Iowa, just to put them out of the running.