Random Walker Rankings for NCAA Football
How well did the Monkeys do in 2003?
Of course, the rankings of the teams can depend on which value of the coin weighting "p" one uses; just another one of the difficulties caused by having so few games relative to the number of teams. We have investigated behaviors for different p values and determined a few things about which values are preferable, as described in our manuscripts.
Prior to the Bowl Games:
Yes, Oklahoma is still #1 below (p=0.75), despite losing the Big 12 Championship game, because the simplest monkey rules used here don't factor the date the game is played (neither do some of the official BCS systems). As seen in the above plots, the monkeys rank Oklahoma #1 at most coin weightings; but rank LSU #1 at high p values.
Who are the "top two" teams as ranked by the monkeys? Depends on what value of the coin weighting you choose. For p below 0.7, the monkeys pick Oklahoma and USC, the specific strength of schedule rewarded by the monkeys at small coin weightings favoring these teams. For p above 0.7, the monkeys pick Oklahoma and LSU, strongly influenced by each of their losses coming against top 20 teams (Kansas State and Florida, respectively). In contrast, USC lost to California in overtime. However, neither the monkeys nor any of the official BCS systems consider margin of victory, at the direction of the BCS---don't blame the computers there. Many computer rankings do include margin of victory (see Kenneth Massey's comparisons page); it is interesting to compare how both USC and Oklahoma do in those systems.
Those final-week Syracuse over Notre Dame and Boise State over Hawaii victories did affect these rankings---swap those two results and the monkeys would rank USC #2 over a wider range, including the p=0.75 value considered below.
The main problem (in our humble opinion) with the BCS is not the computer rankings, the problem is how those computer rankings and other factors were used to obtain the BCS Standings.
Rankings of all 117 Div-IA teams also available, though it would perhaps seem odd for a large collection of "first-place votes" to accurately rank anything beyond the top few teams. This ranking appears along with many others on David Wilson's ranking page and on Kenneth Massey's comparisons page. We are exceptionally grateful to both of them and to Peter R. Wolfe for making game results and other data available online. Of course, one may also want to compare with the official Bowl Championship Series (BCS) standings.
After the Bowl Games, who is National Champion?
Okay, fine, we didn't all get the bowl games we wanted, but can we
say anything about the bowl games that we did get? In particular, who
do the monkeys vote for as 2003 "National Champion" of
college football? It depends on which coin weighting (p value) they
use, and even then it's a close race. For p<0.65, USC garners the most
votes. For p>0.65, LSU takes the #1 spot. Surprise, co-champions!
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