Football Rankings

I'm not a huge football fan, but I enjoy following BYU football. It seems like one of the recurring debates in college football (and probably most sports) is about the best way to rank teams.

If A beats B by 10 points, and the next week B turns around and beats A by 10 points, who is better?

If A beats B, and B beats C, and C beats A, who is better?

Anyway, it's only two weeks into the football season, but we can already start to compare teams with each other. BYU has only played two teams (Oklahoma and Tulane), but those teams have each played one other team, and those teams have each played one other, etc. Our network begins to come together.

If we take all the connections we can make and look strictly at the scores, we can come up with an initial ranking. It doesn't tell us much, because if BYU beats Oklahoma by 1 point and Utah beats Utah State by 18, Utah might look better strictly based on the score, but it really depends on how Oklahoma compares to Utah State.

As the network starts to fill out (e.g. as Oklahoma is eventually connected to Utah State) I think the numbers will make more sense, but just for kicks here's my own top 25 rankings after two weeks:

Florida: 40.8 (same)
California: 39 (same)
Nebraska: 37.5 (same)
Texas: 35 (same)
Brigham Young: 33.2 (same)
Iowa: 32
Cincinnati: 32 (same)
Oklahoma: 32 (same)
Texas Tech: 31
UCLA: 30.3
Boise State: 29.4 (same)
Alabama: 29.3 (same)
USC: 27.4 (same)
Boston College: 27
Auburn: 26.3
Tennessee: 25.3
Ohio State: 24 (same)
Duke: 23.7
Houston: 23.5 (same)
LSU: 22.8 (same)
Kentucky: 22.6
Pittsburgh: 22
Penn State: 22 (same)
Michigan: 21.8 (same)
Georgia Tech: 21

The numbers are the average points they beat other teams by (directly, or indirectly through intermediate teams). If it says "(same)" afterwards, then it was also on the AP top 25 rankings (although not necessarily at the same rank).

Surprisingly, the AP poll and I had 15 of the 25 teams in common, although all this really tells me is that my method isn't totally flawed. I'd still trust the AP poll over my technique because they're taking (most likely) better things into account than I am, but I'll be interested to see how we compare once more games are played.

AP ranking:

1 Florida
2 Texas
3 USC
4 Alabama
5 Mississippi
5 Penn State
7 Brigham Young
8 California
9 LSU
10 Boise State
11 Ohio State
12 Oklahoma
13 Virginia Tech
14 Georgia Tech
15 TCU
16 Oklahoma State
17 Cincinnati
18 Utah
19 Nebraska
20 Miami (FL)
21 Houston
22 Kansas
23 Georgia
24 North Carolina
25 Michigan