It wouldn't have just been easier for teams to schedule if the rules required 12 1A opponents: it would make it much easier for all of us to compare teams with no common opponents.
Defining "resume" would be easy if schedules were relatively symmetric since there can't be a round-robin. What if we form a "committee" of as many different objective rankings (i.e. computer algorithms) as we can find and let them decide?
As I'm writing there are 99 computer rankings available, and the process to determine "the best 4" could go something like this.
Clemson and Georgia are ranked by a majority (50 or more) of the ratings ranking them in the top four, so they are in.
# Team 92 Clemson 84 Georgia 48 Oklahoma 43 Ohio State 40 Alabama 33 Wisconsin 29 UCF 18 Penn State 3 Auburn Washington 2 Southern California 1 Miami-Florida Memphis Notre Dame
Since there are two spots left and four teams ranked 5th or better by a majority of the committee we can eliminate all of the teams ranked worst than 5th, leaving Ohio State, Oklahoma, Wisconsin, and Alabama as four choices for the last two spots.
Maj Team 5 Ohio State 5 Oklahoma 5 Wisconsin 5 Alabama 7 Penn State 8 UCF 9 Auburn 10 Notre Dame 11 Washington 12 Southern California 12 Miami-Florida 20 Memphis
Our computer committee might have chosen Alabama and Wisconsin for the last two spots.
Rank Team W L Conf BLI T4votes SOWP WW LL TT 5 Alabama 11 1 SEC 6 40 0.9496 121 5 3 5 Wisconsin 12 1 B10 9 33 0.9264 118 8 3 5 Oklahoma 12 1 B12 15 48 0.8798 112 14 3 5 Ohio State 11 2 B10 24 43 0.8372 103 16 10
It is interesting that all the human discussion notwithstanding, the last spot was between Oklahoma and Wisconsin, not Alabama and Ohio State. And the loss that hurt Ohio State the most was probably not at Iowa but the home loss to Oklahoma.
From the SOWP data for all teams we can find the pseudo Smith Set – the set of teams that have a stronger path to every team outside of the set. This year that is undefeated UCF and Memphis, whose only losses were to UCF. My "Bad Loss Index" (BLI) is the number of second-order losses or ties to teams outside of the Smith Set. (There isn't a "good loss" but there's no shame in losing to a team that nobody beat.)
The BLI is lower for Wisconsin than Ohio State because Wisconsin's wins over common opponents "cut off" some of the potential ?→Ohio State→Wisconsin chains. The same structure prevents LSU's bad loss to Troy from affecting Alabama, since Troy→LSU→Auburn→Alabama is trumped by Alabama→LSU. Ohio State can make up for the conference loss by beating teams that beat Iowa, but it couldn't beat any teams that beat Oklahoma.
But consider that if instead of comparing the four contenders for the last two spots based upon how their resumes with respect to the whole field, we only consider their relative position in the directed games graph against only the remaining teams. Taking the six pairs in turn we assign a 1 for a second order win, 0 for a loss, and ½ for a tie. Here's what we get if we use
Pairwise Alabama Oklahoma Ohio State Wisconsin 2½ Alabama * 1 1 ½ 2 Oklahoma 0 * 1 1 1 Ohio State 0 0 * 1 ½ Wisconsin ½ 0 0 *
Seed Clemson Georgia Alabama Oklahoma 3 1 Clemson * 1 1 1 2 2 Georgia 0 * 1 1 1 3 Alabama 0 0 * 1 0 4 Oklahoma 0 0 0 *
© Copyright 2017, Paul Kislanko