The win probabilities for U-M's remaining games did not change over the bye week (week 8), so there was no need to bother with an update. But now on the heels of a tight road win over a Minny team that turned out to be more as they were expected to have been at the beginning of the season, as well as some other surprises around the conference, an update is in order. That said, it still remains that Bill Connelly’s S&P+ is quite smitten with our beloved Wolverines, just not quite as much as in previous cycles.  The change is not due so much to U-M’s performance on the field this past week, but more that of the remaining opponents (see another Diary for details).

This time around, I'm including the Total Wins Probabilities for Sparty and OSU, as looking at their profiles provides some valuable insight into how the remainder of the season might play out. In order to show the results all in one chart, I've diddled the formatting a bit, but otherwise the data is still the same S&P+based win probabilities shown in the table below for each team's remaining games. Here's your embiggable chart:

Mr. Obvious: “WTF! It looks like U-M’s gonna lose a game, even though they’re favored in all of ‘em?!”

“There are three kinds of lies: lies, damned lies, and statistics.”
                                                                                - Mark Twain, or not

Factoring a cascade of probabilities into an aggregate number is intuitive to the extent that you're able to multiply numbers in your head. Determining total win probabilities however is good bit less intuitive, largely due to lots of sequences to be evaluated, and also because the continuous nature of probabilities does not mesh so neatly with the discrete nature of wins and losses. It's more analogous to our dear friend Schrödinger's cat ... or just imagine a football transporting through Stribling's or Thomas' hands and magically appearing in a receiver's, and you get the picture.  But I digress. As always, there are some interesting elements to be gleaned from the chart:

• U-M is the most likely team to win out (35.1%), followed by OSU (20.1%) and then Sparty (7.4%).
• U-M’s two most expected totals are 9 and 10 wins; for Sparty and OSU, 10 and 11 wins – with Sparty leaning toward 10, and OSU toward 11.
• The most expected result for both U-M and OSU is one more loss.
• For Sparty, the most expected result is two more losses.

At this point in the season, to be making a legitimate run at 9 or 10 wins is beyond all expections in retrospect. Before the first game, many people, myself among them, were thinking 7 wins was a reasonable expectation, and 8 would be optimistic. To see this team where it's at now is impressive, and it hasn't been by virtue of a lot of lucky breaks either. To the contrary, turnover luck has worked against this team thus far, which bodes well for the future, both near term and into next season.

So - given all of this win probability data, it's also possible to investigate how things might play out for the remainder of the season, or rather, how likely it is that a particular sequence of events would actually transpire. Of course, the primary question revolves around what are U-M's chances of making it to Indy for the B1G Championship Game?  Is there any hope beyond a 3-way tie and putting it in the hands of the CFPSC?  Is the cat dead, or is it alive?

To address these questions, it makes sense to characterize the obvious factors that would block U-M from going to Indy, such as MSU or OSU simply winning out, which are noted above. Still other scenarios exist that will do U-M in, and those are described in the table below, with the attendant likelihood, and who the B1GE representative would be. The second table accumulates the scenarios that enable U-M to go to Indy.

So, for all of the buzz surrounding the impending 3-way tie atop the B1G East, it’s really only the fifth most-likely scenario of the twelve (12) listed above. Moreover, it’s only the second most-likely scenario by which U-M would advance to Indy! Quite coincidentally, there is a two-way tie for the most-likely scenario.  They are either: OSU wins out and advances; or UM wins out (beating OSU along the way) and Sparty loses two or more of its remaining games (this is actually the most likely scenario for U-M to advance). For the sake of completeness, I looked at prospects for U-M advancing even if it should drop one more game, and though the prospects aren’t great, they do exist, and includes another tie-break scenario. Summing up the scenario probabilities, OSU has the lion’s share of about a 48.7% likelihood to advance directly, while U-M has about a 20.9% chance, and MSU about 20.6% (this might be a good time for full belly-laugh of “Sparty NO!”). If you’ve read this far, that, dear reader, is your reward!

Oh, and the remaining 10% is taken up by the tie-break scenarios.

So just to get a complete picture of how all of these probabilities impact conference standings and prospects for U-M to win a B1G Championship, here you go:

Note: these standings incorporate the win probabilities for each individual game, and not the most-likely scenarios, and so in this case, it results in the 3-way 1-loss tie-breaker scenario. That's why this scenario gets so much discussion, but from a statistical standpoint, it's a 1 in 12 shot.  The main reason for the difference is because Sparty isn't favored in one game, but as mentioned above, in the aggregate Sparty can be expected to drop two. So, the cat’s dead, and at the same time it’s not. You don’t know until you open the box.

Yours in football – Go Blue!