Sunday, November 13, 2011

Rankings through November 12th

And then there were... three? No, sorry Houston, there's no way you're going to be part of the BCS discussion; but they nevertheless deserve congratulations for being one of the few undefeated FBS teams remaining at this point.

As long as LSU and Oklahoma State keep winning, they will play for the championship. But their winning out is far from certain. Obviously, they can't look past anyone, and they have particularly tough tests before the end of the season, with LSU playing Arkansas and a tough SEC Championship opponent, and Oklahoma State still has Oklahoma on their schedule.

While we wait for those tests, we call attention to the sharp changes on the right edge of the plot below of this week's RWFL rankings. This gives us an opportunity to recall some of the features of this family of rankings as we consider different values of p. As p approaches 1 on the right edge of the plot (the last point plotted is p=0.9999), going undefeated trumps everything else. Houston climbs quickly to #3 near the edge and undefeated FCS Sam Houston State (not shown, but you can see the gap that none of the plotted teams is ranked #5 at p=0.9999 [click the plot to see a larger version]) rises quickly on the right edge from even deeper in the rankings, eventually passing all of the 1-loss teams at p even closer to 1. But at the middle ranges of p we consider (typically p=0.75), the game outcomes are naturally balanced with a notion of strength of schedule, with Houston at #17 for p=0.75 and falling as low as #21 in the left half of the plot (as p gets closer to 0.5).

Our rankings (at p=0.75) for the full FBS and FCS are available on Kenneth Massey's College Football Ranking Comparison.

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At November 13, 2011 at 10:54 AM , Blogger Mason said...

I still say you should consider taking the various discussions over the seasons and write a popular book with them. It would really be an exceptionally good way to suck high school students into mathematics.

At November 14, 2011 at 7:51 AM , Blogger Peter J. Mucha said...

Thanks for the encouragement, Mason. But I don't plan to take on writing a book at this time. When I have fewer administrative duties in the future, that might be a great time for me to take on such a project.

At November 20, 2011 at 1:51 PM , Blogger Mason said...

You could always try to convince someone like VIGRE-poster-boy Callaghan to help you.


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