FanPost

Transitive Rankings Post Week 10-Stability at the Top

 

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

The top group remains at size 8, as everyone in it either won last week or lost to TCU.   

 

1 Auburn 114-0 (10-0)

Chattanooga? Really?

 

2 Oregon 113-0 (9-0)

2 TCU 113-0 (10-0)

TCU got an elusive win over a top group member from beating Utah.  

 

4 LSU 113-1 (8-1)

LSU somewhat unexpectedly remains in the top group by beating Alabama.  

 

4 Boise State 112-0 (8-0)

6 Utah 112-1 (8-1)

Unlike other rankings, Utah won't get punished very much for losing to an excellent TCU team here.  

 

6 Stanford 112-1 (8-1)

8 Mississippi State 112-2 (7-2)

9 Wisconsin 109-10 (8-1)

10 Arkansas 107-12 (7-2)

11 Oklahoma State 106-13 (8-1)

12 Nebraska 105-14 (8-1)

13 Alabama 103-16 (7-2)

Alabama rises despite their loss.  In the some sense the loss was expected and already accounted for, since LSU was ranked higher.  Less expected was nearly every previous 'Bama opponent winning their game this week.  

 

14 Iowa 102-17 (7-2)

14 Arizona 102-17 (7-2)

14 Kansas State 102-17 (6-3)

KSU achieves a rather unusual feat this week: they are ranked in the BCS, but received effectively no votes in the polls.  Like transitive rankings, the computer rankings in the BCS like the Wildcats a lot more than the humans. 

 

17 Michigan State 101-18 (9-1)

18 Baylor 100-19 (7-3)

18 Oklahoma 100-19 (7-2)

20 Texas A&M 98-21 (6-3)

21 Ohio State 96-23 (8-1)

21 Missouri 96-23 (7-2)

21 Iowa State 96-23 (5-5)

24 UCLA 95-24 (4-5)

UCLA may have 5 losses, but they are to #2 Oregon, #6 Stanford, #14 Arizona, #14 Kansas State, and #30 California.  With decent wins against Texas, Oregon State, and Houston, UCLA manages to be the highest ranked team with a losing record.  

 

25 Texas 94-25 (4-5)

25 Texas Tech 94-25 (5-4)

There are only two ways to go with the cluster!@#$ that is the Big 12: either they are all good or they are all bad.  These rankings take the all good approach, leading to 10 Big 12 teams in the top 25. 

 

25 Florida 94-25 (6-3)

28 Southern California 91-28 (6-3)

29 South Carolina 90-29 (6-3)

30 Nevada 87-32 (8-1)

30 California 87-32 (5-4)

32 Oregon State 86-33 (4-4)

These rankings like the Pac-10 only slightly worse than the Big 12, with 7/10 in the top 32.

 

33 Air Force 84-35 (6-4)

33 Virginia Tech 84-35 (7-2)

35 Michigan 81-38 (6-3)

35 Illinois 81-38 (5-4)

37 Temple 79-40 (8-2)

37 Penn State 79-40 (6-3)

37 Northern Illinois 79-40 (7-2)

37 Florida State 79-40 (6-3)

37 North Carolina 79-40 (6-3)

42 North Carolina State 78-41 (6-3)

43 Hawaii 75-44 (7-3)

43 Washington 75-44 (3-6)

45 Arizona State 74-45 (4-5)

46 UCF 73-46 (7-2)

I hate to rain on a team ranked for the first time ever, but UCF's best wins are over decent-but-not-good ECU and Houston and they lost to a decidedly mediocre NC State.  

 

47 Miami (Fla.) 72-47 (6-3)

47 Kentucky 72-47 (5-5)

49 East Carolina 69-50 (5-4)

50 Brigham Young 68-51 (4-5)

50 Georgia 68-51 (5-5)

50 Clemson 68-51 (5-4)

53 San Diego State 67-52 (7-2)

54 Tennessee 62-57 (3-6)

54 Mississippi 62-57 (4-5)

56 Navy 61-58 (6-3)

57 Georgia Tech 60-59 (5-4)

57 Colorado 60-59 (3-6)

59 West Virginia 59-60 (5-3)

The best Big East team is sandwiched between the worst two Big 12 teams.  

 

60 Kansas 58-61 (3-6)

60 Northwestern 58-61 (6-3)

62 Maryland 57-62 (6-3)

63 Pittsburgh 56-63 (5-3)

64 Notre Dame 55-64 (4-5)

64 Fresno State 55-64 (6-2)

66 Syracuse 53-66 (6-3)

66 Tulsa 53-66 (6-3)

68 South Florida 52-67 (5-3)

69 Duke 51-68 (3-6)

69 Army 51-68 (5-4)

69 Boston College 51-68 (4-5)

72 Louisville 50-69 (5-4)

72 Southern Mississippi 50-69 (6-3)

74 Houston 49-70 (5-4)

75 Virginia 48-71 (4-5)

76 Connecticut 47-72 (4-4)

76 Southern Methodist 47-72 (5-5)

78 Utah State 43-76 (3-6)

79 Cincinnati 42-77 (3-5)

79 Vanderbilt 42-77 (2-7)

81 Indiana 39-80 (4-5)

81 Toledo 39-80 (6-3)

81 Rutgers 39-80 (4-4)

81 Wake Forest 39-80 (2-7)

81 Purdue 39-80 (4-5)

86 Marshall 34-85 (3-6)

87 UAB 32-87 (3-6)

88 Tulane 31-88 (3-6)

89 Ohio 30-89 (7-3)

90 Texas-El Paso 29-90 (6-4)

90 Miami (Ohio) 29-90 (5-4)

92 Florida Atlantic 28-91 (3-5)

92 Rice 28-91 (2-7)

92 Kent State 28-91 (4-5)

95 Troy 26-93 (5-3)

96 Louisiana-Monroe 25-94 (4-5)

96 Wyoming 25-94 (2-8)

98 Colorado State 24-95 (3-7)

98 Arkansas State 24-95 (4-5)

98 Florida International 24-95 (3-5)

101 Louisiana Tech 23-96 (3-6)

102 UNLV 21-98 (1-8)

102 Bowling Green 21-98 (2-7)

102 Buffalo 21-98 (2-7)

105 Minnesota 18-101 (1-9)

105 Idaho 18-101 (4-5)

107 Memphis 17-102 (1-8)

108 New Mexico 15-104 (1-8)

New Mexico leaps out of the cellar by beating a Wyoming team with at least one decent win (Toledo).  

 

109 North Texas 14-105 (2-7)

110 Middle Tennessee 13-106 (3-5)

111 New Mexico State 12-107 (2-7)

112 La.-Lafayette 10-109 (2-7)

112 Ball State 10-109 (3-7)

114 Western Kentucky 9-110 (1-8)

115 Western Michigan 6-113 (3-6)

116 Eastern Michigan 5-114 (1-8)

116 Washington State 5-114 (1-9)

116 San Jose State 5-114 (1-8)

119 Central Michigan 4-115 (3-7)

How bad are CMU's wins?  They're ranked lower that two teams with one win each over an FCS team (SJSU and Washington State).  

 

120 Akron 0-119 (0-10)

 

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.  

Rank Team Shortest Connection Record
1 Auburn 72-0
2 TCU 68-0
3 LSU 65-1
3 Boise State 64-0
5 Nebraska 64-2
5 Stanford 63-1
7 Oregon 61-0
8 Oklahoma State 57-1
8 Oklahoma 62-6
10 Utah 56-1
10 Alabama 58-3
12 Arizona 59-5
13 Missouri 60-7
14 Wisconsin 52-1
15 Michigan State 52-3
16 Ohio State 49-2
16 Iowa 54-7
18 Kansas State 49-4
19 Arkansas 46-3
20 Baylor 46-8
21 Mississippi State 39-2
21 Virginia Tech 40-3
21 Texas A&M 44-7
24 South Carolina 40-4
25 Florida 39-4

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