Race to the Playoff

October 25, 2016

It is also fun to listen to the pundits talk about the possibilities of a more-than-one loss team making the plyoffs, or more than one team from the same conference making the playoffs. I always root against those who argue that it shouldn't happen because they have a "philosophical objection" to those ideas. If those were to prevail we would usually not wind up with the "four best" in the playoff.

I report a playoff Watch List that includes every team that might still be considered in contention for one of the four playoff spots. Criteria for inclusion from stongest to weakest are:

Pseudo Smith Set

In elections that use ranked ballots, the Smith Set is the smallest subset of all alternatives for which all members of the set "beat" all alternatives that are not in the set. For our purposes, this is the list of teams that are

1. Undefeated
   or
2. Have only lost to undefeated teams
3. Have only lost to teams in categories 1 and 2
4. have only lost to teams in categories 1-3
5. Have only lost to...

If we were to consider the whole season as a playoff, these would be the only teams that have not been eliminated. Through week eight we would have

{ Alabama Clemson Texas A&M Tennessee Auburn Michigan Western Michigan Boise State West Virginia Louisville Nebraska Washington Arkansas Troy Florida Baylor }

in no particular order. Every one of these teams has an I beat you or somebody who beat (somebody who beat) you chain to every team not in this list.

Computer Ratings

If any of the computer ratings that Ken Massey records at College Football Ranking Composite ranks a team in the top four, the team is included in the watch list. As of this writing, Ohio State, LSU and Virginia Tech would be added to the list even though they have losses to teams that are not in the pseudo-Smith Set.

Any remaining 1-loss teams

These are included only to satisfy the pundits. They will be talking about their chances with straight faces despite the fact there will be more than four teams selected by the first two criteria. Including them does provide an opportunity to analyze their seasons using what I call the Bad Loss Index. From the report legend:

"∗" indicates that the team is in the Pseudo Smith Set. Otherwise this is the number of teams outside of the Pseudo Smith Set that have a stronger A→B→... chain to the team than the team has to them.

One-loss teams not in the Pseudo Smith Set and not receiving a top-four vote in any computer ranking are Utah, Toledo, Navy and San Diego State.

The list is ordered by the Bucklin Majority ranking of the computers followed by Dr. Massey. I like the Watch List a lot, mainly because the BLI provides an objective discriminant among teams with the same number of losses. Follow the links to the teams' resumes and then the link to the resume of the team they lost to. Instead of "Utah lost to #49 California by 5 and San Diego State lost to #96 South Alabama by 18" we can say "Utah's loss to California caused 27 other teams to have a stronger position in the directed games graph than Utah and San Diego State's loss to USA caused 50 other teams to have a stronger position in the DGG than SDSU."

I do believe it might be too fine a filter. After week eight with 101 computers reporting, #13 Wisconsin is not on the list. The Badgers would still be in the pseudo Smith Set were it not for Ohio State's loss at Penn State, and their BLI is 8 – lower than that of the non-pseudo Smith Set team that beat them. LSU is on the list with a loss outside of the p-Smith Set (to Wisconsin!) because it has a #4 vote from one computer, while Wisconsin's best rank is #5.

Tempted as I am to fiddle with the criteria, I have faith in the computer composite ranking. If Wisconsin has no bad losses the rest of the way they'll get at least one top four vote, lots more if they knock Nebraska out of the p-Smith Set this weekend (a loss to Nebraska would not hurt their BLI and a win would pretty much cinch a position in the watchlist.)

I have a lot more faith in the computers than I do "the committee' whose rankings will come out next week.