Transitive Rankings Post Week 6- I for one welcome our new corn fed overlords

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).

Of course, this method isn't perfect. One flaw is that a transitive win over a good team (e.g. Michigan) should be worth more than one over a bad team (e.g. WMU). A reasonable idea, so it deserves its own set of rankings.

Another complaint 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. This idea also gets its own set of rankings. 

First, straight transitive wins.


1 Nebraska 75-0  (#6 in the country)

Nebraska's win over Kansas State gives them the #1 position.

Next week: Texas.  Nebraska beat Kansas State who beat UCLA who beat Texas.  


2 Iowa 66-4 (#16)

Iowa's loss to Arizona got slightly worse with Arizona's loss to Oregon State, but not enough to knock them down much.  Their wins over Iowa State and Penn State are less impressive overall, however.  

Next Week: Michigan, worth 7 wins or 2 losses


3 Michigan State 61-0 (#17)

MSU's win over Michigan gives them 35 of their transitive wins.  

Next Week: Illinois, worth 4 wins or 3 losses.


4 Ohio State 58-0 (#20)

Ohio State's best win so far is Illinois, as Miami continues to not contribute.  The 'Canes only FBS wins are over 1-3 Pittsburgh and 1-3 Clemson.  

Next Week: Wisconsin, worth 3 wins or 2 losses


5 Michigan 57-1 (#23)

Like Ohio State, Michigan is lacking a top-notch win.  Their most impressive performance was Connecticut, accounting for 34 of their wins.  

Next Week: Iowa, worth 16 wins or 5 losses


6t Illinois 53-2 (#32)

Illinois' wins are unexpectedly evenly split between NIU and Penn State.  Those two both beat Temple and not anyone else of significance.  

Next Week: MSU, worth 12 wins or 1 loss.


6t Wisconsin 52-1 (#32)

Wisconsin's narrow win over ASU became substantially more impressive this week after ASU beat Washington (who beat USC).  

Next Week: Ohio State, worth 9 wins or 1 loss


8 Penn State 51-11 (#43)

Beating Temple only carries a team so far.  

Next Week: Bye


9 Purdue 52-19 (#48)

Transitive rankings guarantee that a team is never ranked below a defeated foe, so Purdue gets a big bump to be ranked over Northwestern.  50 of Purdue's 52 transitive wins come from their last game.  

Next Week: Minnesota.  Purdue beat Northwestern who beat Minnesota.


10 Northwestern 51-20 (#50)

Even if Northwestern won, 5th or 6th in the conference was probably the ceiling this week.  Since they lost to Purdue, 5th or 6th is probably the ceiling for the rest of the season.  

Next Week: Bye


11 Indiana 2-3 (#60)

Indiana still doesn't have much information available.  They have lost to 5-1 Michigan and 6-0 Ohio State (which doesn't condemn them much), but their wins are over teams who are a combined 0-11.  Their next game will allow the Hoosiers to claim superiority over some MAC and Sun Belt teams if they win, or establish them as one of the worst FBS teams if they lose.    

Next Week: Arkansas State, worth 12 wins or 90 losses


12 Minnesota 12-69 (#87)

Right now, the USC loss is still what really hurts.  USC lost to Washington, who lost to BYU, who lost to a bunch of (not very good) teams.  

Next Week: Purdue.  Purdue beat Northwestern who beat Minnesota.  


The next set of rankings devalues common transitive wins.  For example, Michigan State is the only team with a transitive win over Michigan, so that's worth 100.0 win shares to MSU.  However, 74 different teams have transitive wins over WMU, so that only gives (100/74)~=1.4 win shares to MSU (and each of the 73 other teams to transitively beat WMU). 


National Rank Team Win-Loss Shares
4 Michigan State 394-0
9 Nebraska 322-0
13 Ohio State 222-0
21 Michigan 163-1
23 Iowa 155-4
31 Wisconsin 100-1
36 Illinois 92-3
46 Penn State 75-16
53 Purdue 77-28
55 Northwestern 72-29
62 Indiana 2-5
88 Minnesota 13-125



The final set of rankings (aka "The Not Quite as Evil As Last Week Ones") 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 with some explanations.


National Rank Team Marginal Win-Loss
16 Nebraska 95-24
16 Iowa 95-24
16 Ohio State 95-24
21 Michigan State 92-27
25 Wisconsin 84-35
31 Michigan 78-41
35 Illinois 76-43
61 Northwestern 55-64
64 Indiana 54-65
64 Penn State 54-65
91 Purdue 41-78
96 Minnesota 33-86



Texas +19 @ Nebraska (UCLA beat Texas by 22, which counts as the maximum 21.  Kansas State at home beat UCLA by 9, which counts as 6 since it was at KSU.  Nebraska beat KSU by 35, which counts as the maximum 21.  (21+6+21)/3=16.  Since Nebraska is home, they get 3 extra points.)

Minnesota +8 @ Purdue (Purdue beat Northwestern by 3 at Northwestern, which counts for 6.  Northwestern beat Minnesota at the Bank by 1, which counts as 4.  (4+6)/2=5, and then add 3 points for being at Purdue).

Arkansas State +6.5 @ Indiana

Ohio State +.5 @ Wisconsin

Iowa +2 @ Michigan

Illinois +6.5 @ Michigan State

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