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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