As every college football message board debater knows, winning football games is transitive. In other words, if Team A beats Team B and Team B beats Team C, the fans of Team A are perfectly within their rights to talk trash to fans of Team C. Obviously, Team A could have completely wiped the floor with Team C, they just didn't happen to play each other. If Team D happens to lose to Team C, they are also deserving of as much scorn as possible. Thus one way of ranking teams just counts how many teams' fans are permissible trash talk targets (minus those in the reverse situation).

We've reached the unfortunate time of the year where we must deal with cycles (for example, the mess described below with Penn State and Michigan).  My solution is to give the transitive win to the team with the shorter path (in this case Michigan).

1 Michigan State 107-0 (#1 in FBS)

MSU remains in the top spot by remaining unbeaten (just barely).  Had Northwestern managed to finish that game, MSU would still have been the highest rated Big Ten team, but they would have been 16th nationally.  If the Spartans can get by #22 Iowa, their remaining opponents are all #60 or lower.  

Next Week: At Iowa.  MSU beat Wisconsin who beat Iowa

2 Wisconsin 106-1 (#3)

Wisconsin keeps above the fray with only their second win at Iowa since 2000.  After playing 3 of their last 4 against top 25 teams, Wisconsin has no such games remaining.  

Next Week: Bye

3 Ohio State 105-2 (#8)

OSU is tied for 4th in transitive wins, but their losses to Wisconsin and transitively to MSU push them down to #8.  

Next Week: At Minnesota.  Ohio State beat Purdue who beat Minnesota.  

4 Illinois 103-4 (#16)

Illinois doesn't have anything resembling a great win, but their losses are to the teams ranked #1t, #1t and #8t.  Transitively speaking, they aren't going to be punished much for that.   

Next Week: Purdue.  Illinois beat Penn State who beat Temple who beat Connecticut who beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Wyoming who beat Toledo who beat Purdue.  

5 Nebraska 100-19 (#18)

Nebraska is the highest ranked team in the country with a "bad" loss.  Their three reasonably high quality wins (Oklahoma State, Kansas State and Washington) gives the Huskers a lot of wins on the "shorter path" tie breaker.  Their only transitive losses are to the 17 "above the fray" teams, Texas who beat them directly, and Iowa.  (Nebraska beat Washington who beat Oregon State who beat Arizona who beat Iowa, but Iowa beat Iowa State who beat Texas who beat Nebraska.  Iowa's path is 1 team shorter, so they win on the tiebreaker).  

Next week: Missouri (who is tied with MSU for #1 overall).  Missouri beat Oklahoma who beat Texas who beat Nebraska.  

6 Iowa 94-25 (#22)

Iowa has a similar situation as Nebraska.  Their loss to Arizona isn't that bad, but it does open them up to chains from almost every FBS team.  However, their quality wins over Michigan and Iowa State (who looks a lot better after beating Texas) allows Iowa to have shorter paths back to almost all those teams.  

Next Week: Michigan State.  .  

7 Michigan 80-39 (#36)

Michigan's wins over Notre Dame and Connecticut haven't held up quite as well, so their loss to Iowa hurts them a little bit more.  

Next Week: Penn State.  Michigan beat Connecticut who beat Vanderbilt who beat Mississippi who beat Kentucky who beat South Carolina who beat Alabama who beat Penn State.  (Note: since the path for Penn State to beat Michigan is longer that the path for Michigan to beat Penn State, Michigan gets the transitive win.)

8 Northwestern 64-55 (#59)

Losing to MSU doesn't hurt, but winning sure would have helped.  As it stands, Northwestern gets 1 transitive loss from Michigan State and 54 from Purdue.  

Next Week: At Indiana.  Northwestern beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Washington who beat Oregon State who beat Arizona who beat Iowa who beat Michigan who beat Indiana.   

9 Purdue 61-58 (#60)

On the flip side, beating Northwestern accounts for 54 of Purdue's transitive wins.  Unfortunately, their losses look either about as bad as expected (Toledo lost to the 1-6 in FBS Wyoming Cowboys, who apparently play a lot like the Dallas Cowboys) or much worse (ND just lost to an iffy Navy team).

Next Week: At Illinois

10 Penn State 55-64 (#68)

Losses to Iowa and Alabama shouldn't hurt so much, but Penn State would need better (or at least more) wins to overcome the admittedly long paths through each of those teams.  

Next Week: At Michigan.  Penn State beat Temple who beat Connecticut who beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Washington who beat Oregon State who beat Arizona who beat Iowa who beat Michigan.  (Note: since the path for Penn State to beat Michigan is longer that the path for Michigan to beat Penn State, Michigan gets the transitive win.)

11 Indiana 46-73 (#74)

Indiana has a similar problem as Penn State.  The Hoosier's worst loss is to Michigan which isn't so bad.  However, their wins are against teams ranked 90th, 95th, and 116th in the 120 team FBS.  

Next Week: Northwestern.  Indiana beat Arkansas State who beat FAU who beat UAB who beat UTEP who beat Rice who beat Houston who beat Tulane who beat Rutgers who beat Connecticut who beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Wyoming who beat Toledo who beat Purdue who beat Northwestern.

12 Minnesota 40-79 (#82)

BCS programs ranked lower than Minnesota: Connecticut, Boston College, Virginia, Wake Forest, Washington State, and Duke.  Academically, it's a decent group.  Football-wise, not so much.  

Next Week: Ohio State

For what it's worth, these rankings have the same order as Sagarin's BCS input rankings, except for flipping Northwestern and Penn State.  

Of course, that method isn't perfect. One flaw is that a transitive win over a good team (e.g. Wisconsin) should be worth more than one over a bad team (e.g. Western Michigan). A reasonable idea, so it deserves its own set of rankings.  In these rankings, MSU receives 100 win shares for their win over Wisconsin since they are the only team with a transitive win over the Badgers.  However, 107 teams have a transitive win over Western Michigan, so thats only worth 100/107~=1 win share for MSU (and the other 106 teams).  

These rankings have converged to the point where they have the identical order to the first, with just a few spots difference in the national ranking.

Another perspective might be "Sure Team A and Team C haven't played and don't have a transitive chain, but Team A beat Team B by 14 points. Team C only beat Team B by 2. Therefore, Team A is better than Team C". While I might not agree with this idea, it is a reasonable line of thought. The final set of rankings considers the margin of victory along the shortest path of games from one team to another.  The "marginal win" goes to the team with the net better score along the path, with a home field advantage of 3 points and a maximum victory of 21 points.  This method also allows predictions which I've included below.

This method takes a much dimmer view of nearly every team in the Big Ten, especially MSU and Illinois.  The notable exception is Iowa, who gets hit much less hard for two 1 point losses.  

MSU -1.5 at Iowa

OSU -5.5 at Minnesota

Purdue +6.5 at Illinois

Missouri -2.5 at Nebraska

Penn State +5.5 at Michigan

Northwestern -1.5 at Indiana