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Big Ten Football Ratings Week 6: Vectors For Teams that Matter to Minnesota


Thanks to some positive feedback from last week, I decided to refresh the S&P Vectors visualization with the latest data from Football Outsiders.  I'm truly standing on the shoulders of giants here, and I should say up front that nothing I've done here is particularly ground-breaking.  However, if you're looking for an easy way to look at lots of complex data, I think I can help.

Link to Full Size Chart

For instance, looking at the Minnesota vs. Nebraska match-up on Saturday, it's easy to say "Minnesota's defense is better than Nebraska's, but Nebraska's offense is better than Minnesota's."  It's not easy to know what that means in terms of the overall strength of each team.  Using this visualization, you can tell that it pretty much evens-out, with a slight advantage in Nebraska's favor.

It's also easy to see that Michigan is much stronger than than everyone else on the chart, primarily due to their FBS-leading defense.

Same as last week, we'll start with a few words on method.  First, the theoretical best possible team is a combination of the highest rated offense (Texas A&M) and the highest rated defense (Michigan - please someone send help) in FBS.  This theoretical team is the red square in the top left corner of the chart.

All Teams are placed on the chart based on their offensive and defensive S&P+ ratings.  The defensive rating runs along the x-axis and the offensive rating is on the y-axis.  Better offenses get higher ratings.  Better defenses get lower ratings.

The vectors are a measure of distance on the chart from the best theoretical team.  The shorter the vector is, the better the team in question.  Vectors are calculated by leveraging the Pythagorean Theorem, which allows for the calculation of the hypotenuse of a right triangle based on the length of the other two sides (A^2 + B^2 = C^2).

These week I've also included a curve that represents the average length of the teams' vectors and two other curves which represent one standard deviation on either side of the mean (Thanks for the suggestion GophNYC).  With that, let's talk about some descriptive statistics re: the vectors:

Mean 27.19
Standard Error 1.37
Standard Deviation 4.10
Range 15.29
Minimum 20.50
Maximum 35.79

The mean vector is 27.19.  The teams that are closest to the average are Illinois and Wisconsin, but Northwestern, Minnesota, and Nebraska are all less than half of a standard deviation from the mean as well.  Iowa and Ohio State are better than the average, but within one standard deviation of the mean.

For you maths nerds out there, if you consider my average curve a regression line, and then you create a residual plot, the data are randomly distributed and the residual mean is zero.  Enough maths.

The big standouts are (unsurprisingly) Michigan and Purdue.

Michigan's defense is so good that you would need to trade the current (above-average) offense with a much lesser one to make them an average team in our visualization.  The comparable offense that would fit that bill: Washington.

On the other hand, Purdue's defense is so bad that you would have to pair them with a very good offense to make them average.  Based on the current ratings, you would need to swap-in Bowling Green's offense or Arkansas' offense to make it work.

Positive Takeaways

The blowout loss to Northwestern continues to look fluky in the data.  Having watched the game, that statement strains credulity somewhat, but time will tell if that was just a very bad day for the Gophers and a very good day for Northwestern.  At least by this metric, that game looks fluky.

The blowout win over Purdue is what should have been expected.  Minnesota is an average team.  Purdue is a very bad team.  I think S&P+ predicted the Gophers had a 76% chance of winning that game, which is a pretty strong.

Negative Takeaways

I think we all already knew there are no easy games left on the schedule.  There are three toss-ups and three bearcats in the future.  We get the best team (and defense) in the conference at home against Michigan, a team vying for promotion to the NFL (Ohio State) at home, and we have to play an OSU comparable (performance so far) Iowa team on the road.

So there you have it, sports fans. I'll update the visualization each week and we'll see if anyone pulls away from the middle of the pack.

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