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College Football Transitivity Rankings and Awards - Week 11

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There was a lot of movement all over the board in this week's Transitivity Rankings. Some big games had less impact than you might expect, while others had unanticipated consequences.

One Texas team's upset victory had a big effect on the Transitivity Rankings, and it wasn't the one you'd expect.
One Texas team's upset victory had a big effect on the Transitivity Rankings, and it wasn't the one you'd expect.
Erich Schlegel

Welcom back to the Transitivity Rankings. As always, if you're unfamiliar with how these posts work, please see this introductory post for an explanation. For the rest of you, let's jump straight to the rankings.

Combined Transitivity Rankings
Rank Team Change Avg Rank Win Rank Loss Rank Num Win Paths Avg Win Path Num Loss Paths Avg Loss Path FBS Wins FBS Losses
1 Mississippi State - 1.0 1 1 125 3.58 0 NaN 8 0
2 Auburn - 3.5 2 5 124 3.26 5 1.80 7 2
3 Alabama Arrow_up4 4.0 4 4 124 3.31 5 2.20 8 1
3 Florida State Arrow_up1 4.0 7 1 120 3.62 0 NaN 8 0
3 Mississippi Arrow_up1 4.0 2 6 124 3.26 5 1.60 7 2
6 Marshall Arrow_up2 4.5 8 1 120 4.86 0 NaN 8 0
7 LSU Arrow_down4 6.0 5 7 124 3.44 5 1.40 6 3
8 Texas A&M Arrow_up4 6.5 6 7 124 3.62 5 1.40 6 3
9 Notre Dame - 10.0 11 9 119 3.52 122 8.86 7 2
10 Arizona State Arrow_up12 13.0 14 12 119 3.57 122 7.95 7 1
11 Oregon Arrow_up7 13.5 10 17 119 3.29 122 7.05 8 1
11 UCLA Arrow_up9 13.5 9 18 119 3.18 122 6.97 8 2
13 Oklahoma Arrow_down3 16.0 16 16 119 3.66 122 7.55 6 3
14 Georgia Arrow_up7 17.5 14 21 119 3.57 122 6.80 7 2
15 Nebraska Arrow_up2 18.0 16 20 119 3.66 122 6.86 7 1
16 TCU Arrow_down6 18.5 23 14 119 3.87 122 7.66 7 1
17 Colorado State Arrow_up6 20.5 22 19 119 3.86 122 6.89 8 1
18 Utah Arrow_up9 21.0 12 30 119 3.54 122 6.00 5 3
19 Kansas State Arrow_down15 22.5 35 10 119 4.06 122 8.47 6 2
20 Arizona Arrow_up5 24.0 19 29 119 3.81 122 6.07 7 2
21 Boise State Arrow_up5 26.0 18 34 119 3.71 122 5.92 7 2
22 Clemson Arrow_up2 27.5 42 13 119 4.13 122 7.69 6 2
22 Michigan State Arrow_down4 27.5 19 36 119 3.81 122 5.89 6 2
24 Duke Arrow_up4 28.5 33 24 119 4.04 122 6.78 7 1
25 Baylor Arrow_down13 29.5 34 25 119 4.05 122 6.68 7 1
26 Miami (Fl) Arrow_up3 31.5 24 39 119 3.92 122 5.80 5 3
26 Nevada Arrow_up9 31.5 29 34 119 3.98 122 5.92 5 3
28 Georgia Tech Arrow_up5 33.0 21 45 119 3.82 122 5.49 7 2
29 Ohio State Arrow_up8 34.0 13 55 119 3.55 122 5.13 8 1
30 Tennessee Arrow_down1 34.5 41 28 119 4.12 122 6.40 3 5
31 West Virginia Arrow_down19 36.0 32 40 119 4.03 122 5.70 5 4
32 Florida Arrow_down3 36.5 42 31 119 4.13 122 5.99 5 3
33 South Carolina Arrow_down1 38.0 38 38 119 4.10 122 5.85 3 5
34 California Arrow_up5 38.5 55 22 119 4.48 122 6.79 4 4
35 Washington Arrow_down2 39.0 56 22 119 4.53 122 6.79 5 4
36 Louisville Arrow_up10 39.5 28 51 119 3.97 122 5.27 6 3
37 Utah State - 40.0 44 36 119 4.15 122 5.89 6 3
37 Wisconsin Arrow_up3 40.0 37 43 119 4.09 122 5.53 6 2
39 Louisiana Tech Arrow_down24 40.5 70 11 119 4.90 122 8.39 7 2
40 Minnesota Arrow_up6 41.5 36 47 119 4.08 122 5.44 6 2
41 Missouri Arrow_up2 42.5 30 55 119 4.01 122 5.13 6 2
41 Stanford Arrow_down1 42.5 54 31 119 4.46 122 5.99 4 4
43 Arkansas Arrow_up1 44.5 74 15 119 5.03 122 7.66 3 5
43 Penn State Arrow_up11 44.5 24 65 119 3.92 122 4.77 5 4
45 Iowa Arrow_down9 47.0 40 54 119 4.11 122 5.20 5 3
46 Kentucky Arrow_down1 47.5 62 33 119 4.74 122 5.94 4 5
46 Michigan Arrow_up7 47.5 47 48 119 4.27 122 5.42 5 5
48 Maryland Arrow_down6 48.5 38 59 119 4.10 122 5.07 5 3
48 Rutgers Arrow_up4 48.5 44 53 119 4.15 122 5.20 4 4
50 Boston College - 49.5 26 73 119 3.93 122 4.48 5 4
50 Oklahoma State Arrow_down35 49.5 72 27 119 4.97 122 6.49 4 4
52 Air Force Arrow_down4 53.0 46 60 119 4.23 122 5.05 6 2
53 USC Arrow_down2 54.0 50 58 119 4.39 122 5.11 6 3
54 Washington State Arrow_up5 55.5 51 60 119 4.40 122 5.05 2 7
55 BYU Arrow_up3 57.0 27 87 119 3.96 122 4.18 5 4
56 Arkansas State - 57.5 71 44 119 4.92 122 5.52 5 3
57 Texas Arrow_up8 58.0 52 64 119 4.41 122 4.80 5 5
58 Iowa State Arrow_down10 59.5 67 52 119 4.87 122 5.25 2 6
58 Northwestern Arrow_up4 59.5 53 66 119 4.44 122 4.66 2 6
58 Virginia Tech Arrow_up4 59.5 31 88 119 4.03 122 4.16 3 5
61 UL Lafayette Arrow_down5 60.0 94 26 119 5.62 122 6.52 5 3
62 East Carolina Arrow_down7 63.0 49 77 119 4.34 122 4.35 5 2
63 North Carolina Arrow_down3 64.0 57 71 119 4.55 122 4.53 3 5
64 Illinois Arrow_up4 64.5 59 70 119 4.62 122 4.57 3 5
65 Northern Illinois Arrow_up8 65.0 63 67 119 4.76 122 4.63 6 2
66 Virginia Arrow_down2 68.0 60 76 119 4.63 122 4.41 3 6
67 Wyoming Arrow_down1 69.5 61 78 119 4.65 122 4.29 3 6
68 Indiana Arrow_up6 70.0 66 74 119 4.80 122 4.42 2 6
68 Kansas Arrow_up6 70.0 85 55 119 5.44 122 5.13 2 6
70 Texas Tech Arrow_down4 70.5 91 50 119 5.59 122 5.38 2 6
71 North Carolina State - 72.0 81 63 119 5.33 122 4.93 4 5
72 Rice Arrow_up4 72.5 73 72 119 5.02 122 4.49 6 3
73 Pittsburgh Arrow_down4 73.0 48 98 119 4.29 122 3.90 3 5
74 Toledo Arrow_down2 74.0 79 69 119 5.27 122 4.60 5 3
75 Oregon State Arrow_down6 74.5 103 46 119 6.24 122 5.48 3 5
76 Memphis - 75.5 68 83 119 4.88 122 4.23 5 3
77 Cincinnati Arrow_up2 76.0 84 68 119 5.43 122 4.61 5 3
78 Colorado Arrow_down2 76.5 104 49 119 6.30 122 5.41 2 8
79 Bowling Green Arrow_up10 78.0 64 92 119 4.78 122 4.07 5 3
80 South Alabama Arrow_up1 78.5 115 42 119 7.05 122 5.61 5 4
81 Georgia Southern Arrow_up4 79.5 118 41 119 7.37 122 5.69 7 2
82 Purdue Arrow_up2 80.5 80 81 119 5.32 122 4.26 2 7
82 Syracuse Arrow_up1 80.5 99 62 119 5.82 122 5.04 2 7
82 Western Michigan Arrow_up4 80.5 82 79 119 5.37 122 4.28 5 3
85 Central Florida Arrow_down5 81.5 58 105 119 4.60 122 3.78 4 3
86 Middle Tennessee State Arrow_up1 85.5 87 84 119 5.47 122 4.20 4 4
86 Western Kentucky Arrow_up8 85.5 65 106 119 4.79 122 3.72 4 5
88 Navy Arrow_up3 86.5 78 95 119 5.24 122 4.04 3 5
89 UTEP Arrow_down29 87.0 100 74 119 6.00 122 4.42 5 4
90 Central Michigan Arrow_up2 87.5 75 100 119 5.11 122 3.87 5 4
91 Temple Arrow_down10 88.5 69 108 119 4.89 122 3.69 4 4
92 Akron Arrow_down3 90.0 77 103 119 5.13 122 3.80 3 5
92 Hawaii Arrow_up3 90.0 94 86 119 5.62 122 4.19 1 8
92 San Diego State Arrow_up5 90.0 101 79 119 6.18 122 4.28 4 4
95 San Jose State Arrow_down8 92.5 93 92 119 5.61 122 4.07 2 6
96 UAB Arrow_up4 93.0 89 97 119 5.55 122 3.95 4 5
97 Houston Arrow_down5 95.0 76 114 119 5.12 122 3.48 4 4
98 Ohio Arrow_up8 95.5 92 99 119 5.60 122 3.89 4 5
99 Florida Atlantic Arrow_down1 96.5 83 110 119 5.42 122 3.61 3 7
100 Southern Miss Arrow_up21 98.0 114 82 119 6.98 122 4.25 2 7
101 Ball State Arrow_up2 99.0 86 112 119 5.46 122 3.57 2 5
102 Vanderbilt Arrow_down6 100.0 111 89 119 6.64 122 4.14 2 7
103 UTSA Arrow_down3 100.5 98 103 119 5.81 122 3.80 2 7
103 Wake Forest Arrow_up2 100.5 107 94 119 6.45 122 4.05 1 7
105 Fresno State Arrow_up5 101.0 101 101 119 6.18 122 3.86 3 6
106 Texas State Arrow_up1 101.5 113 90 119 6.97 122 4.11 4 4
107 Old Dominion Arrow_up2 102.0 97 107 119 5.74 122 3.70 3 6
108 Appalachian State Arrow_up14 102.5 121 84 119 8.09 122 4.20 3 4
108 New Mexico Arrow_down4 102.5 109 96 119 6.48 122 4.02 3 6
108 Tulane - 102.5 96 109 119 5.73 122 3.68 2 6
111 UL Monroe Arrow_down13 103.5 117 90 119 7.19 122 4.11 3 6
112 Army Arrow_up1 104.0 88 120 119 5.49 122 3.30 3 5
112 North Texas Arrow_up12 104.0 106 102 119 6.37 122 3.84 2 6
114 Connecticut Arrow_down12 105.5 90 121 119 5.58 122 3.25 1 7
115 Florida International Arrow_down3 108.0 104 112 119 6.30 122 3.57 2 6
116 South Florida Arrow_down6 110.5 110 111 119 6.50 122 3.59 2 6
117 Tulsa Arrow_down3 114.0 112 116 119 6.68 122 3.36 2 7
118 Kent State Arrow_down2 115.0 108 122 119 6.46 122 3.20 1 8
119 Miami (Oh) Arrow_down2 117.0 119 115 119 7.38 122 3.40 2 7
119 UNLV Arrow_down4 117.0 116 118 119 7.17 122 3.32 1 8
121 Buffalo Arrow_down3 119.5 122 117 119 8.35 122 3.34 1 6
122 Eastern Michigan Arrow_down2 120.5 123 118 119 9.33 122 3.32 1 7
123 Massachusetts Arrow_down4 121.0 119 123 119 7.38 122 3.16 2 7
124 Troy - 124.0 124 124 2 1.00 123 3.90 2 7
125 Idaho Arrow_down3 125.5 125 126 2 1.50 123 3.35 1 8
126 SMU - 126.0 127 125 0 NaN 123 3.58 0 8
127 New Mexico State Arrow_down1 126.5 126 127 1 1.00 125 3.34 1 8
128 Georgia State - 127.5 127 128 0 NaN 126 3.52 0 9

Most of my analyses for this week fit better in the Cluster Watch section, but I do want to make one observation here: Ask anyone to name the biggest upset of the week, and they'd probably cite Texas A&M's win over Auburn. Yet, in the transitive world, this game had almost no effect on the teams involved. The Tigers aren't any worse off in the CTR for dropping that game, as they stayed tight at number 2. In fact, had you flipped the result of that game, both the Tigers and the Aggies would have wound up in the exact same spot.

CLUSTER WATCH

As the season progresses, we continue to see more and more teams enter the cluster, our term for the large mass of teams in the middle of the rankings with the same number of win and loss paths. This week, the cluster covers all teams ranked between 9 and 123. The defining characteristic of the cluster is that every cluster team has a win path to every other cluster team. The super-cluster (teams ranked 1-8) is the group of teams with no losses to cluster teams, and the sub-cluster teams (ranked 124-128) have no wins over cluster teams.

As you can see, there was a lot of movement among top 20 teams this week. The reason? Texas's upset victory over West Virginia. That's right, a game largely ignored on the national stage was the primary mover in this week's CTR. Before this game, West Virginia was in the super-cluster. The loss to the Longhorns moved them to the cluster, along with every super-cluster team the Mountaineers owned win paths over: Oklahoma, Oklahoma State, Baylor, TCU, and Louisiana Tech. When Kansas State lost to TCU later that night, the Wildcats were also thrown into the cluster. So a number of teams that were in the top 15 last week lost their transitive dominance over many teams, and as a result some saw their rankings plummet.

Once in the cluster, the only things separating you from the rest of the pack are your average win and loss path lengths. If you've had good wins and no bad losses, you will stay relatively clean, as was the case with Oklahoma and TCU. If you've lost too may games or don't have any impressive wins, the situation is less rosy. This accounts for most of the big drops of the week, as Kansas State, West Virginia, Louisiana Tech, and Oklahoma State fell 15, 19, 24, and 35 spots, respectively. (Notre Dame also fell from the super-cluster this week due to their loss to Arizona State, but despite this they didn't lose any ground in the rankings.)

On the flip side, any sub-cluster team which beats a cluster team is rewarded by moving up to the cluster. Two sub-cluster teams were able to do just that on Saturday, as North Texas rolled Florida Atlantic and Appalachian State squeaked by UL Monroe. The Mean Green and Mountaineers were rewarded with 12 and 14 spot improvements in the CTR, respectively. However, the biggest beneficiary of these developments was actually Southern Miss. The Golden Eagles had beaten both North Texas and Appalachian State earlier in the season. As a result, they were awarded their own one-way ticket out of the sub-cluster, to the tune of a 21 spot rise over last week. That's good for the biggest jump of any team this week, and can perhaps help soothe the pain from the 63-17 shellacking they took from Marshall on Saturday.

Next week brings a handful of opportunities for the cluster to absorb a few sub-cluster or super-cluster teams. On the sub-cluster side, only SMU has a chance for promotion, through their tilt with South Florida. From the super-cluster side, the following matchups could see the cluster grow:

  • LSU at Arkansas
  • Auburn at Georgia
  • Florida State at Miami (Fl)
  • Marshall vs. Rice
  • Texas A&M vs. Missouri
Keep an eye on the SEC matchups. Should any of those games go against the super-cluster team, then LSU, Auburn, Texas A&M, Alabama, and Ole Miss will all fall to the cluster.

AWARDS

Jekyll and Hyde Award

Description:
For the team whose performances in the WTR and LTR are most divergent. This one's for the team which has experienced the highest highs and the lowest lows. Or perhaps the highest lows and the lowest highs.

Measure:
Maximum length shortest win path.

Winner:
Georgia Southern

Notes:
This is the second consecutive Jekyll and Hyde award for the Eagles, who sit at spots 118 and 41 in the WTR and LTR, respectively. This difference of 77 spots is just clear of South Alabama (WTR 115, LTR 42, difference of 71), who once again came up just short.

Are We There Yet Award

Description:
Not all shortest paths are created equal. Sometimes, teams have to work very hard to claim a win path, meandering tirelessly among the season's results before the path is earned. This one goes to a pair of teams for whom the shortest win path between them is longer than all other shortest paths.

Measure:
Maximum length shortest win path.

Winners:
Eastern Michigan, Notre Dame

Notes:
For the second week in a row, Eastern Michigan is on the source end for this award. Four teams were in contention on the destination end, as the shortest path from the Eagles to each of Arkansas, Clemson, Colorado State, and Notre Dame is 14 games long. My questionably accurate tie breaking system says the path to Notre Dame covers 9312 miles, about 2500 miles longer than any of the others. For reference, here's what the path looks like:

Eastern Michigan > Buffalo > Miami (Oh) > Kent State > Army > Ball State > Akron > Pittsburgh > Boston College > USC > Arizona > Oregon > UCLA > Arizona State > Notre Dame

Frequent Flyer Award

Description:
If you took all of one team's shortest win paths, and made them actual travel itineraries, for which team would you be making the most stops? To win this one, you need to have a lot of win paths, but you don't want them to be too short.

Measure:
Largest sum of shortest win path lengths.

Winner:
Eastern Michigan

Notes:
This makes four straight weeks that the Eagles have won this award. Their 119 win paths sum to 1110 total games, which is leaps and bounds ahead of anyone else.

Conference Atlas & Coattail-Rider Awards

Description:
There are two awards here, one for the team which does the most to carry its conference's reputation on its shoulders (Atlas), and another for the conference black sheep who most disgraces his comrades (Coattail-Rider).

Measure:
The team whose CTR is highest above/farthest below the average among teams in its conference.

Winner:
Marshall (Atlas), Vanderbilt (Coattails)

Notes:
The race for these awards continues to be uninteresting, as Marshall has held the Atlas award for five weeks now, and Vanderbilt is keeping their wire-to-wire Coattail Rider bid intact. What's more interesting is the conference-by-conference breakdown. The Pac-12 has surpassed the Big 12 to become the second best conference by lowest CTR average, another development that can be traced back to West Virginia's loss to Texas.

Conference Avg Conference Rank Atlas Atlas Rank Atlas Difference Coattail Hanger Coattail Rank Difference
AAC 97.18 East Carolina 62 35.18 SMU 126 28.82
ACC 50.36 Florida State 3 47.36 Wake Forest 103 52.64
Big 12 40.70 Oklahoma 13 27.70 Texas Tech 70 29.30
Big Ten 46.07 Nebraska 15 31.07 Purdue 82 35.93
CUSA 85.38 Marshall 6 79.38 Florida International 115 29.62
MAC 98.77 Northern Illinois 65 33.77 Massachusetts 123 24.23
MWC 69.25 Colorado State 17 52.25 UNLV 119 49.75
Pac-12 36.67 Arizona State 10 26.67 Colorado 78 41.33
SEC 26.07 Mississippi State 1 25.07 Vanderbilt 102 75.93
Sun Belt 100.64 Arkansas State 56 44.64 Georgia State 128 27.36
We Are Not Impressed Award

Description:
This award goes to the AP top 25 team whose reputation is most at odds with their transitive resume. Whatever human pollsters see in this team, the CTR is not buying the hype.

Measure:
The AP top 25 team whose ranking drops the most when compared to CTR.

Winner:
Ohio State

Notes:
The Buckeyes have now won this award three weeks in a row. Last week, I offered that a victory over Michigan State would improve Ohio State's CTR enough that they'd no longer be in contention for this award. I was wrong. The Buckeyes have a strong WTR (13), but in the LTR they still can't shake that Virginia Tech loss (which has looked worse and worse as the season progresses). Their mid-pack LTR ranking of 55 drags their CTR down to 29, 21 spots worse than their latest AP rank. Their closest competition this week comes from Baylor, who are 6th in the AP but only 25 in the CTR, a 19 spot difference.

Desserpmi Ton Era Ew Award

Description:
Like the We Are Not Impressed Award, but opposite. Indeed, the name of this award is "we are not impressed" backwards.

Measure:
The highest CTR among teams receiving no votes in the AP poll.

Winner:
Nevada

Notes:
The Wolf Pack currently occupy the 26 spot in the CTR with a record of 6-3 on the season. Those three losses have come to Arizona, Colorado State, and Boise State. Among those teams the first two are AP top 25 teams, while Boise State is receiving votes. Combine decent losses with a number of solid (if unspectacular) victories, and you have a recipe for an under appreciated team. Other contenders for this award were Tennessee (CTR 30) and Florida (32).

KANSAS STATE WIN PATHS

It wasn't a great weekend for Wildcat fans. Before Saturday's loss to TCU, the Cats owned win paths to every Big 12 team, while none of their conference-mates could say the same. The TCU loss changed that, while the Texas - West Virginia game gave every cluster team access to K-State as well. As a result, the Wildcats lost their transitive advantages over most teams. Where the CTR was higher on the Cats than other rankings early in the season, they are now barely in the top 20.

As is customary, I'll finish the post with a diagram illustrating all of Kansas State's shortest win paths. You can use the accompanying depth list to help find teams in the diagram.

Click to embiggen. - jeffp171/Bring on the Cats

  • Level 1: Iowa State, Oklahoma, Oklahoma State, Texas, Texas Tech, UTEP
  • Level 2: Iowa, Kansas, Louisiana Tech, New Mexico State, New Mexico, North Texas, Old Dominion, Southern Miss, Tennessee, Tulsa, Toledo, UTSA, West Virginia
  • Level 3: Arkansas State, Appalachian State, Ball State, Baylor, Central Michigan, Eastern Michigan, Florida Atlantic, Florida International, Georgia State, Houston, Indiana, Kent State, UL Lafayette, Maryland, Massachusetts, Northwestern, Pittsburgh, Purdue, Rice, South Carolina, SMU, Tulane, UAB, UNLV, Utah State, Western Kentucky, Western Michigan
  • Level 4: Air Force, Akron, Army, Boston College, Bowling Green, Buffalo, BYU, Connecticut, East Carolina, Fresno State, Georgia, Hawaii, Idaho, Illinois, UL Monroe, Memphis, Miami (Oh), Missouri, Navy, Northern Illinois, Ohio, Penn State, South Alabama, South Florida, Syracuse, TCU, Temple, Troy, Texas State, Vanderbilt, Virginia Tech, Wake Forest, Wisconsin, Wyoming
  • Level 5: Arkansas, Boise State, Central Florida, Cincinnati, Clemson, Florida, Kentucky, Minnesota, Middle Tennessee State, North Carolina, North Carolina State, Ohio State, Rutgers, San Diego State, San Jose State, USC, Virginia
  • Level 6: Arizona, Colorado, Colorado State, Georgia Southern, Georgia Tech, Louisville, Michigan State, Michigan, Nevada, Oregon State, Stanford, Washington State
  • Level 7: California, Miami (Fl), Nebraska, Oregon, Utah, Washington
  • Level 8: Duke, UCLA
  • Level 9: Arizona State
  • Level 10: Notre Dame
  • No Path: Alabama, Auburn, Florida State, LSU, Mississippi, Marshall, Mississippi State, Texas A&M