Tuesday, November 13, 2012

Better Than Expected

More fun with math.

So, it started with a simple note that the @umichfootball Twitter account put out yesterday morning that Michigan is 40-13-4 all-time against Iowa.  I was stunned that Iowa and Michigan had only played 57 times all-time despite being conference mates for over 100 seasons, but more stunned to realize that Iowa has only beaten Michigan thirteen total times.  Ever.  But then I wondered if that was in line with what you would expect, so I started on the project with this question in mind:

Taking into account only B1G conference games, which team has most outperformed its overall conference winning percentage against a single opponent?  Which team has most underperformed its overall conference winning percentage?

Using the always awesome Stassen database, I culled all of the records of B1G games between 1896-2011.  I included Nebraska's eight games in the conference winning percentage calculations, but due to the ridiculously small sample size, they have been excluded from this conversation.  I did, however, include the University of Chicago in both calculations, because it's interesting.  I did not include Michigan's 1907-1916 conference interregnum, no Ohio State games prior to 1912, no Michigan State games prior to 1953, and no Penn State games prior to 1993. I then calculated the team's all-time winning percentage, calculating ties as half a win and half a loss.

So, with all of that done, I then calculated each school's winning percentage against each opponent.  I compared that to their overall winning percentage and got the following result:

The B1G team that has most outperformed its overall conference winning percentage against a single opponent is...complicated because of variable sample sizes.
The top five results are as follows:
  • Penn State vs. Indiana-36.18 percentage points better (Penn State has never lost to Indiana in B1G play.)
  • Chicago vs. Indiana-28.15 percentage points better (Indiana was glad to see the Maroons depart.)
  • Michigan State vs. Indiana-21.98 percentage points better (Oh, and yes, that's Michigan State's protected cross-division game.)
  • Minnesota vs. Chicago-21.95 percentage points better (back when Minnesota and Chicago were good at football!)
  • Northwestern vs. Indiana-21.07 percentage points better (remember, these two teams are #1 and #2 in all-time losses among FBS schools.)

So, over the longest term, it's Northwestern over Indiana.  But really, it's everybody over Indiana!  (Also, for all of Iowa's collective grousing about their issues against Northwestern, they are in the top ten of this list.)

The B1G team has most underperformed its overall conference winning percentage against a single opponent is Minnesota vs. Ohio State, 33.49 percentage points worse than their overall conference winning percentage.

Now, since this is a Michigan blog, what about the Wolverines?  Well, let's have a look, shall we?

Michigan's all-time B1G winning percentage is 71.33%, which is just a shade behind Ohio State's 71.66% for first place all-time in the conference (this does not take into account Ohio's vacated games in 2010, if you want to feel better about yourself, since Michigan moves back into first place when it does..)

When we look at the chart, what we see is that Michigan doesn't really have a high positive variance against anyone team, which is to say that they have handled their business against pretty much everyone historically:

So much opposing red.
What we also can see is that while Michigan has "struggled" against Penn State, Ohio State, and Michigan State, relative to its overall conference success, every B1G team has done worse against Michigan than their overall conference winning percentage.  In a fit of ironic pique, Northwestern actually has the lowest variance because they are so bad overall in conference that even performing poorly against Michigan doesn't hurt them that much because they don't  have as far to fall.  Sparty's relatively strong performance against Michigan puts them in second, and when Ohio State is the greatest variance game for Michigan, Ohio's variance is more negative than Michigan's when compared side by side.  Also, Indiana football is still terrible.

The ten most positive and most negative variance comparisons, by the way:
Penn State's still relatively small sample size helps them (and hurts them a little too.)
If you'd like to see all of the data (to play with it), please drop me a line, and I will pass it along.

No comments: