National Transitive Rankings Post Week 7: Madness, or Possibly Sparta


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 when we must deal with cycles.  For instance, Rutgers beat Tulane who beat Army who beat Rutgers.  In these circumstances, the transitive win goes to the team with the shortest "path".  In this case, Rutgers beat Tulane directly (path length 1) so they get the transitive win over Tulane, even though Tulane beat Army who beat Rutgers (path length 2).  

An unfortunate by-product is that teams can be ranked below teams they beat.  However, this will only occur if a cycle exists involving the two teams. 



1 Michigan State 105-0 (6-0)

The win over Illinois is nice, but the previous win over Wisconsin looks much better after the Badger beat-down of OSU.  Add the win over Michigan and the Spartans are the new #1.


2t Oklahoma 103-0 (6-0)

Oklahoma got a big boost from Texas beating Nebraska.  Curiously, Iowa State remains their second best win (contributing 26 transitive wins).  


2t Wisconsin 104-1 (5-1)

Wisconsin's wins over OSU and Arizona State (who beat Washington) pushes them into a tie at #2.


2t Louisiana State 103-0 (6-0)

LSU has to be the most criticized 6-0 team ever (remember, no FCS games count here).  Usually, an SEC team with that record who played a remarkably respectable out of conference slate (WVU, UNC) would be praised as "zomg best ever".  However, that's what happens when the most memorable play is a bouncing ball on a fake field goal.


5t Boise State 102-0 (6-0)

Boise State is going to get the same line here for the rest of the season.  The win against VT has held up remarkably well (again, no FCS games here), while Oregon State still has the quality win over Arizona.  Toledo even appears to be the class of the MAC, if such a thing exists.  


5t Oregon 102-0 (5-0)

Oregon's win over Stanford is worth an incredible 71 transitive wins.  Arizona State is less helpful to the Ducks than the Badgers because Stanford beat USC directly, while ASU beat Washington who beat USC.  In this situation, all of the credit from USC goes through Stanford.


5t Missouri 102-0 (5-0)

Missouri hasn't gotten much love from the pollsters, but it's easy to see why: their best win is Colorado.  If they beat Oklahoma, they will shoot up both the polls and the transitive rankings.  


5t Auburn 102-0 (7-0)

The Auburn-LSU game this week is likely for the #1 ranking.  


9t TCU 101-0 (6-0)

TCU's wins over Baylor and Oregon State account for 60 of their transitive wins.  


9t Florida State 102-1 (5-1)

As long as a team keeps winning and they don't have bad losses, they will continue to rise.  FSU's only decent win is over a good-but-not-great Miami.  


9t Oklahoma State 101-0 (6-0)

Another team that has risen this far by not having a bad loss and having wins over moderately respectable opponents (Texas A&M, Texas Tech)


9t Ohio State 103-2 (6-1)

OSU is the highest rated team that has a loss to a not-undefeated team (Wisconsin).  


9t Utah 101-0 (6-0)

I'm not sold on Utah still.  If they beat TCU in a couple weeks, I'll be more convinced.  


14 West Virginia 101-1 (4-1)

14 Stanford 101-1 (4-1)

14 Virginia Tech 101-1 (5-1)

17 Mississippi State 101-2 (4-2)

3rd best team in the SEC?  Probably not, but they have only lost to the undefeated teams in conference.  


18 Illinois 101-4 (2-3)

19 Miami (FL) 101-5 (3-2)


There's a big gap between #19 and #20.  #19 and above have no losses to anyone #20 and below.  Almost everyone after that is involved in a cycle with almost everyone else, so the cycle breaking mechanism affects the rankings a lot.  

20 Nebraska 92-22-5 (4-1)

21 Kansas State 91-25-3 (4-1)

22 Baylor 88-29-2 (4-2)

23 Texas 85-27-7 (4-2)

24 Nevada 84-28-7 (5-1)

25 Texas Tech 84-32-3 (3-3)

26 East Carolina 82-33-4 (4-2)

27 Alabama 79-33-7 (6-1)

27 Arizona 80-34-5 (4-1)

29 California 78-33-8 (2-3)

30 Iowa State 78-34-7 (2-4)

31 Arkansas 78-35-6 (3-2)

31 Iowa 78-35-6 (4-1)

33 Colorado 77-36-6 (3-3)

33 Maryland 78-37-4 (3-2)

35 Florida 76-36-7 (4-3)

35 Air Force 76-36-7 (4-2)

35 South Carolina 76-36-7 (3-2)

38 UCLA 75-36-8 (3-3)

39 Northwestern 76-38-5 (4-1)

40 Texas A&M 75-38-6 (2-3)

The Big 12 has 11 teams in the top 40, more than any other conference.  (SEC 8/12, Big Ten 7/11)


41 North Carolina State 75-39-5 (4-2)

41 North Carolina 75-39-5 (4-2)

43 Arizona State 75-40-4 (1-3)

43 Southern California 72-37-10 (5-2)

45 Michigan 73-39-7 (4-2)

46 Notre Dame 72-40-7 (4-3)

47 Oregon State 74-43-2 (3-3)

47 Hawaii 72-41-6 (4-2)

49 Northern Illinois 70-42-7 (4-2)

50 Washington 71-44-4 (3-3)

Washington is the most inexplicable team.  They beat USC (who's not as good as they have been, but still decent) and Oregon State (who beat Arizona), but lost to a bad BYU and a suspect Arizona State (1-3 against an admittedly tough schedule).


50 Southern Mississippi 71-44-4 (4-2)

52 Clemson 68-42-9 (2-3)

53 Navy 69-44-6 (3-2)

54 Purdue 69-45-5 (3-2)

55 Brigham Young 67-47-5 (2-5)

56 San Diego State 64-47-8 (3-2)

57 Temple 64-48-7 (4-2)

58 Georgia Tech 65-50-4 (4-2)

58 Kentucky 63-48-8 (4-3)

60 Toledo 64-51-4 (4-3)

61 Mississippi 60-51-8 (3-2)

62 Kansas 62-54-3 (2-3)

I love dubious distinctions so here's another one: of the teams who are last in their conference, Kansas is the highest rated overall.  


63 Georgia 60-53-6 (3-4)

64 Utah State 57-55-7 (1-4)

65 Louisiana Tech 55-55-9 (2-4)

66 Tulsa 58-59-2 (3-3)

67 Wyoming 56-58-5 (1-5)

68 Southern Methodist 54-61-4 (4-3)

69 Penn State 53-62-4 (2-3)

70 Fresno State 50-63-6 (3-2)

71 Vanderbilt 50-64-5 (2-4)

72 Central Florida 49-67-3 (3-2)

73 Connecticut 46-66-7 (2-3)

Connecticut is the second highest ranked Big East team.  Just for comparison, only 4 teams total from the SEC (1), Big 12 (0), Big Ten (2), and Pac-10 (1) are below them.  The MWC and WAC each have 6 teams above; the MAC has 3.


74 Pittsburgh 47-71-1 (2-3)

75 Indiana 46-73 (3-2)

76 Rutgers 43-73-3 (3-2)

77 Tennessee 43-75-1 (1-4)

78 South Fla. 42-76-1 (2-3)

78 Syracuse 42-76-1 (2-2)

80 Houston 40-76-3 (2-3)

81 Minnesota 39-79-1 (1-5)

81 Army 38-78-3 (4-3)

83 Rice 36-80-3 (2-5)

84 Cincinnati 36-83 (2-3)

85 Louisville 35-83-1 (2-3)

85 Tulane 34-82-3 (1-4)

87 Texas-El Paso 32-85-2 (4-2)

87 Alabama-Birmingham 33-86 (2-4)

87 Florida International 33-86 (2-4)

90 Louisiana-Monroe 29-87-3 (2-3)

91 Troy 28-89-2 (4-2)

92 Florida Atlantic 27-89-3 (1-4)

93 Memphis 27-90-2 (1-6)

93 Louisiana-Lafayette 27-90-2 (2-4)

95 Middle Tennessee State 27-91-1 (1-4)

95 Arkansas State 26-90-3 (2-5)

97 North Texas 25-93-1 (1-6)


Like the #19-20 gap, a large divide exists between #97-98.  No one below this point has a win against anyone above it.  


98 Miami (OH) 10-97 (4-3)

This week's lowest ranked team with a winning record is Miami (OH).  Their wins are over the distinguished crowd of CMU, EMU, Kent State ("Kent Read, Kent Write, Kent State"), and Colorado State.  


99 Buffalo 7-97 (1-4)

100 Colorado State 7-98 (2-5)

101 Idaho 6-99 (2-3)

102 Bowling Green State 5-99 (1-6)

102 Marshall 5-99 (1-5)

102 Ohio 5-99 (3-3)

105 Boston College 2-97 (1-4)

106 Wake Forest 1-97 (1-5)

106 New Mexico State 1-97 (1-5)

108 Washington State 0-97 (0-6)

108 Western Kentucky 0-97 (0-6)

108 San Jose State 0-97 (0-5)

SJSU remains at least tied for the best transitive record by a winless team, though much lower the last week.  Nevada and Alabama both have moderately bad losses now (Alabama-South Carolina-Kentucky-Mississippi-Vanderbilt, Nevada-Hawaii).  If San Jose State could get a win against anyone, they could take back some of the losses by having a shorter path.  


108 Virginia 0-97 (0-4)

108 Western Michigan 3-100 (1-4)

113 Duke 0-98 (0-5)

113 Kent State 1-99 (1-4)

115 Nevada-Las Vegas 1-100 (1-6)

116 New Mexico 0-102 (0-6)

117 Akron 0-104 (0-6)

118 Eastern Michigan 1-106 (1-6)

118 Ball State 1-106 (1-4)

118 Central Michigan 1-106 (1-5)

EMU decided it felt lonely at the bottom, so they dragged the others down with them.  Beating Ball State created the "Cycle of Ineptitude", since Ball State beat CMU and CMU had beaten EMU.  The good news is that if any of the three win another game, they will all be lifted out.  


Longest Shortest Cycle:  Of the cycles which are the shortest for some team, which is the longest?

Pittsburgh gets this award.  Pitt beat Syracuse who beat USF who beat Florida Atlantic who beat Alabama-Birmingham 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 Brigham Young who beat Washington who beat Oregon State who beat Arizona who beat Iowa who beat Michigan who beat Notre Dame who beat Pittsburgh.  

In conference terms, it goes Big East-Sun Belt-CUSA-Big East-SEC-WAC-Pac 10-Big Ten-Indy-Big East.  

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