Post Week 5 Transitive Rankings, Hawkeye Uprising- Now With 3 Times the Rankings

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. Miami) should be worth more than one over a bad team (e.g. EMU). 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 Iowa 48-1 (#3 overall in the country)

The win over Penn State (worth a whopping 30 wins) is the primary reason Iowa is leading the conference, but the win over Iowa State became even better after the Cyclones beat Texas Tech.  Even Ball State contributed by beating CMU.

Next Week: Bye


2 Michigan 43-0 (#5)

Beating Indiana didn't do much, but the Connecticut win became much more valuable with the Husky victory over Vanderbilt.  While beating Vanderbilt doesn't sound like much, the Commodores have a chain that contains Washington, USC, and 30 other teams.

Next Week: MSU, worth 8 wins or 1 loss.


3t Penn State 40-3 (#10t)

All but 2 of Penn State's wins come from Temple.  Similar to Michigan, Temple's win over Connecticut gives the Lions all of the Vanderbilt wins.  

Next Week: Illinois, worth 2 wins or 3 losses


3t Northwestern 37-0 (#10t)

Like the three previous teams, Northwestern benefits greatly from the Vanderbilt win.  

Next Week: Purdue, worth 2 wins or 15 losses


5 Nebraska 28-0 (#20t)

Nebraska's win over Washington looks much better since they beat USC, but their other wins over Idaho and Western Kentucky are worth 5 combined transitive wins.  

Next Week: Kansas State, worth 22 wins or 1 loss


6 Michigan State 21-0 (#31t)

MSU's best win in transitive terms is still FAU (worth 8 wins).  Notre Dame hasn't exactly impressed while Wisconsin hasn't beaten anyone of note.  

Next Week: Michigan, worth 30 wins or 1 loss


7 Ohio State 20-0 (#33t)

OSU's wins over EMU, Marshall, and Ohio are worth 3 transitive wins total.  In other words, those teams haven't beaten anyone but each other.  Their would-be signature win over Miami hasn't been particularly helpful, as the Hurricanes have only beaten dismal Pitt and mediocre Clemson.

Next Week: Indiana, worth 2 wins or 2 losses


8 Illinois 15-2 (#42t)

Illinois losses are to still undefeated teams.  Their lone win against Northern Illinois has held up better than one might expect from a MAC team.  

Next Week: Penn State, worth 27 wins or 1 loss


9 Wisconsin 4-1 (#59)

Wisconsin's loss to MSU doesn't hurt that much.  However, their wins are over teams whose combined FBS record is 1-10.  

Next Week: Minnesota, worth 13 wins or 30 losses


10 Indiana 2-1 (#64t)

Indiana has beaten two teams win no wins and lost to one team with no losses.  Transitively speaking, not much can be said.  

Next Week: Ohio State, worth 20 wins or 1 loss


11 Purdue 3-14 (#85)

Purdue didn't play last week, but Toledo lost to 2-3 Wyoming, making the Boilermakers loss that much worse.  

Next Week: Northwestern, worth 36 wins or 1 loss


12 Minnesota 12-28 (#95)

Minnesota is on the other end of the Connecticut/Vanderbilt chain.  USC losing to 2-2 Washington (who lost to 1-4 BYU) stings a bit.  Fortunately for the Gophers, I am not including FCS games in these calculations: South Dakota lost to UCF who lost to NC State who lost to Virginia Tech who lost to.... James Madison.  

Next Week: Wisconsin, worth 5 wins or 2 losses.


The next set of rankings devalues common transitive wins.  For example, Ohio State is the only team with a transitive win over Miami, so that's worth 100.0 win shares to OSU.  However, 85 different teams have transitive wins over EMU, so that only gives (100/85)~=1.2 win shares to OSU (and each of the 84 other teams to transitively beat EMU).  

National Rank Team Weighted Transitive Win-Loss Record
9 Michigan 326-0
10 Iowa 318-1
14 Ohio State 257-0
15 Michigan State 232-0
16 Penn State 200-5
23 Northwestern 152-0
33 Nebraska 88-0
45 Wisconsin 52-4
47 Illinois 38-7
59 Indiana 9-2
90 Purdue 12-80
95 Minnesota 17-98


The final set of rankings (aka "The Evil 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.  This method also allows predictions which I've included below with some explanations.  

National Rank Team Record in Marginal Wins
3 Iowa 104-15
13 Michigan 94-25
16 Nebraska 91-28
20 Ohio State 88-31
27 Michigan State 82-37
35 Penn State 75-44
35 Wisconsin 75-44
48 Indiana 65-54
48 Northwestern 65-54
50 Illinois 64-55
87 Minnesota 42-77
93 Purdue 36-83

Purdue -6.5 @ Northwestern

Purdue beat Ball State by 11.  Ball State beat CMU by 14.  CMU lost to Northwestern by 5.  (11+14-5)/(3 games) ~= 6.5


Michigan State +0.5 @ Michigan

MSU beat ND by 3, Michigan beat ND by 4 (I probably should fix it to consider an overtime game as a tie).  (4-3)/2=.5


Illinois +1.5 @ Penn State

Indiana +1.5 @ Ohio State

Minnesota +1.5 @ Wisconsin

Nebraska -4 @ Kansas State

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