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. 



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