Sunday, October 28, 2012

Rankings through October 27th

Last week's RWFL rankings had 10 undefeated teams in our top-16 plot. Now six undefeateds remain. Notre Dame moves into the #1 slot across all values of our bias parameter p. Kansas State is #2 at most values, swapping places with Alabama at high values.

Full disclosure details: The figure below only goes to a value of p slightly below the value 1. Going undefeated becomes more and more important as one approaches the value p=1 on the right edge of the plot. But we don't actually calculate exactly at p=1 because this is what a mathematician calls a singular limit, with multiple solutions at p=1. On the right edge of the plot, we are only interested in values of p strictly less than 1 but very close to 1. If we looked much closer there than we actually plot below, we would see FCS undefeated Lehigh would shoot up to 7th place on the extreme right edge of the figure.

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Sunday, October 21, 2012

Rankings through October 20th

There are a ton of undefeated teams out there still, and many ways to organize them at the top of the rankings (see Kenneth Massey's College Football Ranking Comparison). For now, we wait and see how many of them drop a game.


Sunday, October 14, 2012

Rankings through October 13th

With the first BCS Standings of the season soon to be released, it seemed appropriate to get some rankings posted (even though we have nothing to do with the official BCS Standings).

We are once again enormously grateful to both Peter Wolfe and Kenneth Massey for making this task easier on all of us. Both are part of the official Bowl Championship Series standings. Wolfe provides the data in an easy-to-process form. Massey publishes the College Football Ranking Comparison; The RWFL rankings at p=0.75 run on the full network of connected teams should appear there for this season starting this week (where the rankings are broken out separately for the FBS and FCS). The rankings on the restricted network including only the FBS teams are equivalent to Eugene Potemkin's "E-Rating" that sometimes appears there too.

For those new to the way that we present these rankings, you might want to wade through some of the previous posts and---if you are so mathematically inclined---the papers. The quick explanation is that the plot below represents a whole family of rankings obtained by varying the "bias parameter" p along the horizontal axis (p sets the probability that a random walker moves to the winner of a considered game, represented as an edge in the network of teams). For p near 0.5, strength of schedule dominates. As p moves closer to 1, the outcome of individual games gains greater importance. The middle value of p=0.75 is included in Massey's ranking comparisons.