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What was wrong with the old BCS formula?

2004 rankings

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2006 rankings

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2006 Random Walker Rankings

With the BCS as its one-piece sequin jump suit, college football
is essentially figure skating combined with Microsoft Excel, a
subjective taste test on what emotional voters and soulless
computers perceive as the two teams most worthy to play in the
national championship game. Sunday night we will find out what
matchup the humans and the computers give us.
                                    -- John Buccigross, ESPN SportsCenter

Yes, ladies and gentlemen, it's that time of year again. The leaves have fallen, the smell of fireplace-burning wood hangs in the crisp winter air, and the arguments about who should play in the Division I-A football title game ring in our ears... Yeah, I liked Buccigross's quote better too...

So, what happens next? We'll find out when the bowl matchups are announced. The random walkers definitely prefer Florida to Michigan. At our preferred p=0.75 value, this simplistic measure even says to go ahead and lineup Florida against USC, because the system doesn't know anything about margins of victory (neither do any of the official BCS computer rankings, by decree), nor about dates of games. Some of the official systems take date of game into account, some do not; the ones that do not consider dates treat Michigan's loss to Ohio State and USC's loss to UCLA as if they had happened at any time, not in the last games of their respective regular seasons. At p just about 0.75, Ohio State moves up into the top two. Please don't complain about how an undefeated team isn't always ranked in the top two, else we have to talk about Boise State... But of course in the revised BCS system, the voters have 2/3 of the power and will possibly make the decision on their own without the official computer rankings (which we again emphasize we are not part of) affecting the outcome. Who will play Ohio State in the Championship game? Will Notre Dame make a BCS bowl? Who will get tasked with playing Boise State?

We remain grateful to both Kenneth Massey for maintaining his comparisons page and to Peter R. Wolfe for making game results available online.

Below we list the Top 25 according to the Random Walker (RW) system of first-place votes and the Random Walker First-Last (RWFL) system at our selected p=0.75. We also make available rankings of all 119 Div-IA teams at p=0.75. The breakdown of the top teams across different p values for both RW and RWFL can be seen in the figures below. Additionally, we plot the fraction of ranking violations---that is, the fraction of game outcomes that have been contrary to the rankings---for each system across the p values. Ranking violations like these are also included on Kenneth Massey's site, and can be used as one measure of the efficacy of a rank ordering; indeed, one could instead choose p to minimize such errors, but we are more comfortable at the selected fixed values for ease of explanation.

2006-2007 Post-Bowl Random Walker Rankings

While our primary interest here at Random Walker Rankings is in what the rankings say prior to the bowl games, we were particularly interested this year to see how the teams were rated after all the bowl games were played. There isn't any drama about who is ranked #1 and #2 by these methods, since both Florida and USC won their bowl games against the RW/RWFL #3 and #4 teams, Ohio State and Michigan, respectively. But our love of the purported underdog made us particularly want to see whether and how far Boise State would rise from their #8 pre-bowl ranking. Alas, as tabulated below and in the rankings of all 119 Div-IA teams, the Broncos only picked up one spot by passing Michigan, which isn't surprising since previously-unbeaten Ohio State was the only other team in the top 8 besides Michigan who lost their bowl game.