Chances of a Rivalry Upset

Maizenbrew has an interesting discussion between Drew Hallett and Anthony Broom on the chances of our Wolverines beating either the Spartans or the Buckeyes this year:

http://www.maizenbrew.com/2015/8/27/9213819/michigan-football-biggest-storylines-in-2015-rivalry-redemption-ohio-state-michigan-state

Their conclusion is that Michigan will not do it.  They look at recent history, talent/matchups, home field advantage, general Harbaughness, etc.  I would like to respectfully disagree with their conclusion.  I think the general randomness of college football means that we can reasonably expect to savor an upset over a hated rival this year.  I won’t go full Mathlete on you, but my reasoning is based on probability.

We’ve all become conditioned to expect the worst kind of luck persistently.  When was the last time Michigan had a favorable turnover ratio?  When was the last time turnovers broke even or better against a top 20 opponent?  (The first B1G Michigan-Nebraska game?  Yeah, it has been that long.)  Even during the glory years, we all knew that in any given season Michigan was likely to have one “say what?!” loss against a clearly weaker team.  When was the last time a top 20 team had an “off day” against us?  Yeah, it’s been that long.  My point being that luck changes season to season, game to game, or even play to play.  (2011)  To use the language of probability, football plays are independent variables.  We don’t know what normal luck feels like anymore against MSU or OSU, but that can change in a moment.

To add some numbers to it, let me use one of the NOT fun facts from the article.  Drew pointed out that Michigan is 2-12 in the last seven seasons’ worth of games with MSU & OSU.  (Combine that with Michigan’s recent history in Bowl games, and the whole fan base heads for the rest room, but I digress…)  Let’s apply a little probability analysis.  Suppose that all seven years both the Spartans and the Buckeyes were clearly superior, such that they had an 80% chance of winning any given game.  I don’t think it was near that bad, certainly not in some seasons, but let’s go with the pessimistic case to illustrate the point.  If you apply math to these numbers, Michigan still should have won 3 games or more (55% of the time).  Even assuming we stunk, we still should have gotten lucky more often than two times.

Turning to this season, we may not know exactly when or how the ball bounces in our favor, but the odds are reasonably good it will decisively bounce in our favor in one of those two games.  (To use another illustration, Ohio State is the overwhelming favorite to repeat as National Champions.  They will be favored in each and every one of their games, possibly excepting a playoff match-up.  What is the chance someone other than OSU actually wins the Championship?  Yes, a lot more than 50%.)  Again, assume that this season the Spartans and the Buckeyes are clearly superior.  Even if that is as much as a 70% chance, Michigan still has a 50% chance of winning one of those games (0.7 squared).

So I’m saying there’s a chance; a mathematically significant chance.