Random Walker Rankings for NCAA Football
2004 Random Walker Rankings
We still don't make any claims about what value of the bias parameter p is "best" in any sense. Our main point remains that we have created a reasonably-performing family of ranking algorithms with a single, transparently-defined parameter in terms of simple behaviors of random walking voters. Nevertheless, at the end of the day, one would like to see how these rankings perform at a specified value of p, so we continue to tabulate values for p=0.75 below and on Kenneth Massey's comparisons page. The two plots show the rankings across all p values, the plot on the left indicating the percentage of monkeys voting for each team across different p values, while the right shows the resulting rankings. We also post rankings of all 117 Div-IA teams at a few different p values. We remain exceptionally grateful to Peter R. Wolfe for making game results available online.
One could certainly write a wordy commentary here about how Auburn is going to be left out of the National Championship game, both as officially tabulated by the BCS and in agreement with the algorithmic rankings here. Trust us, we live in the South, we've heard all the arguments about the truly impressive season that Auburn has put together. Unfortunately for the War Eagles, both USC and Oklahoma have had impressive seasons too. In the absence of a wordy commentary, we instead call attention to the consistency in the top two slots of the random walker rankings across different p values. Qualitatively speaking, p values near 0.5 effectively emphasize the overall schedule strength, p values near 1.0 specifically reward single wins over highly ranked teams, and the p values in between continuously vary these contributions. At both extremes, and at all p values in between, USC and Oklahoma each outrank Auburn; on the one extreme, their overall schedule strength is calculated to be stronger than Auburn's, while at the other extreme their respective wins over Cal and Texas presumably help their ranking here (and in other systems) more than Auburn's 4 wins over Georgia, LSU & Tennessee. Auburn has had an amazing season, and it is certainly a shame that they can't play for a national title; but the BCS system clearly can't fit 3 undefeated teams (or 5, remembering Utah and Boise State) onto a single football field.
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