Transitive Rankings Post Week 11: Chaos Returns After Its Bye Week

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).


This week was the wildest in quite awhile.  Before last Saturday, the Big Ten seemed to have separated into 4 well-defined bands: Top 4, Next 3, Next 3, and Minnesota.  This week saw two crossover wins, which shook up the ratings much more than I thought was possible this late in the season.  

I go back and forth on allowing ties.  This week, they're included.  


1 Wisconsin 107-11-1 (#10 nationally)

Wisconsin still stays on top.  In a week of crazy, not much changed for the Badgers.

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


2 Ohio State 106-12-1 (#11)

Ohio State gets a nice bump from the Penn State win.  

Next Week: At Iowa.  Ohio State beat Penn State who beat Northwestern who beat Iowa.  


3 Nebraska 102-14-3 (#13)

Nebraska keeps winning, but Texas keeps losing.  The Longhorns haven't lost to particularly bad teams, but at some point the quantity just is too much.

Next Week: At Texas A&M.  Nebraska beat Oklahoma State who beat Texas A&M, while Texas A&M beat Oklahoma who beat Texas who beat Nebraska.  


4 Michigan State 101-17-1 (#15)

MSU's win over Notre Dame became substantially more valuable this weekend after ND's shocking victory over Utah.  

Next Week: Purdue.  MSU beat Illinois who beat Purdue.  


5 Iowa 90-24-5 (#23)

Obviously neither one helps, but in terms of transitive record, the out-of-conference loss to Arizona hurts more (14.5 vs 11, with ties counting for .5).  Arizona has to lost to USC (who lost to Washington) and Oregon State (who somehow lost to Washington State).  

Next Week: Ohio State.  Iowa beat MSU who beat Wisconsin who beat Ohio State.  


6 Michigan 83-32-4 (#30)

Michigan got nice bumps both from ND and from their Connecticut win; the Huskies now have wins over Pitt and WVU (or WFVU if you prefer).  

Next Week: Wisconsin.  Michigan beat Purdue who beat Northwestern who beat Iowa who beat MSU who beat Wisconsin.  


7 Penn State 76-41-2 (#38)

Is Penn State's win over now 8-2 Temple the conference's best out-of-conference win?  It's at least in the top 5 (Miami, ND, ISU, Arizona State).  It's not enough to completely overcome losing to a now-toxic Illinois though.  

Next Week: At Indiana.  Penn State beat Northwestern who beat Indiana.  


8 Northwestern 73-44-2 (#42)

Northwestern gets a huge boost from the annual win over Ioa and the hurt from Purdue seems to have stabilized.  However, as much as I hate to say it, the coaches are crazy if they really think Northwestern deserves a top 25 spot.  

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


Illinois 59-57-3 (#62)

Illinois losing to Minnesota was probably the most shocking result of the conference season.  The general consensus before this week was Illinois as a solid second tier team and Minnesota as one of the worst conference teams in recent memory.

Next Week: At Northwestern.  Illinois beat Penn State who beat Northwestern.  


10 Purdue 41-72-6 (#79)

Purdue is still riding the win over Northwestern as far as it will take them.  Right now, it's good for 25 wins.  

Next Week: At MSU.  Purdue beat Northwestern who beat Iowa who beat MSU.  


11 Minnesota 34-83-2 (#87)

To recap: Minnesota lost to a now 4-7 FCS team and beat a now 5-5 Illinois.  

Next Week: Bye


12 Indiana 31-84-4 (#88)

The loss to Illinois looks much worse today and the Hoosier best win is still over now #105 Arkansas State.  Their other vanquished opponents have a combined 3 wins:  Western Kentucky over ULL and the aforementioned Arkansas State, Towson over Coastal Carolina.  Akron remains the only FBS team with no wins.  

Next Week: Penn State.  Indiana beat Arkansas State who beat Louisiana-Monroe who beat Southeastern Louisiana who beat Texas State-San Marcos who beat Southern Utah who beat South Dakota who beat Minnesota who beat Illinois who beat Penn State.  


Transitive rankings obviously aren't perfect.  One issue is that they unreasonably value long chains.  In some sense, the best information comes from the closest connection.  As an alternative, here are rankings according closest connection record.  These rankings consider only the shortest connection of the type "Team A played Team B played Team C".  If Team A beat Team B who beat Team C, then Team A gets a win over Team C.  If Team A beat Team B, but Team B lost to Team C, then the Team A vs Team B match-up is considered a no-result.  Confused?  Consider Purdue and South Carolina.  The shortest connection is Purdue-Northwestern-Vanderbilt-South Carolina.  Purdue beat Northwestern who beat Vanderbilt, but Vanderbilt lost to South Carolina.  So Purdue (and South Carolina) get a transitive tie.  

National Rank Team Shortest Connection Record
4 Nebraska 66-2
12 Michigan State 57-3
13 Wisconsin 54-1
15 Ohio State 50-2
19 Michigan 50-11
21 Iowa 47-9
46 Penn State 31-18
53 Northwestern 25-15
61 Illinois 23-20
73 Indiana 9-19
75 Purdue 18-32
90 Minnesota 6-34


I'm still a little iffy on these rankings.  I think one issue with them is that losing to a good non-conference opponent (e.g. Arizona) effectively means that a team cannot get a win over any team in that conference.  For instance, the shortest connection between Iowa and Washington State is that they both lost to Arizona, which gives them both a transitive tie.  


The final set of rankings looks at the closest connection and takes the net score along that path to determine the winner.  Home field advantage is considered as 3 points and victories have a max margin of 28 points.  

National Rank Team Margin Win/Loss Record
11 Ohio State 99-20
13 Nebraska 95-24
15 Iowa 93-26
24 Michigan State 87-32
25 Wisconsin 86-33
29 Michigan 83-36
38 Illinois 77-42
46 Penn State 71-48
66 Northwestern 56-63
85 Purdue 40-79
89 Indiana 37-82
89 Minnesota 37-82


These rankings are, as usual, rather different.  The biggest movers are Wisconsin ("We Beat Indiana by Eleventy, but still only beat ASU by 1 point") and Northwestern ("All We Do Is Win... by Less Than a Touchdown, Except When We Don't").  


Penn State -.5 at Indiana

Purdue +14.5 at Michigan State

Illinois -4.5 at Northwestern

Wisconsin -4.5 at Michigan

Ohio State -.5 at Iowa

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