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College Football Transitivity Rankings and Awards - Pre-Bowl Edition

With bowl season fast approaching, let's take a look at how the transitive property judges the regular season.

The Ducks are excited to move into the CTR top four
The Ducks are excited to move into the CTR top four
Kirby Lee-USA TODAY Sports

After Saturday's Army-Navy game, the regular season has now come to a close. As such, we're now ready for the final set of Transitivity Rankings before bowl season kicks off. We didn't post last week, so changes since last time are largely due to the happenings of conference championship week. If you've never seen one of these posts before, you'll want to check here first. Otherwise, let's proceed with the season's penultimate set of Transitivity Rankings (we'll check in again for a final time once bowls have been played and a national champion has been crowned).

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 Florida State - 1.0 1 1 127 2.85 0 NaN 12 0
2 Alabama - 3.0 3 3 126 3.00 123 6.78 11 1
3 Mississippi - 7.0 7 7 126 3.03 123 5.80 8 3
4 Oregon Arrow_up2 8.0 11 5 126 3.11 123 6.39 11 1
5 LSU - 8.5 9 8 126 3.07 123 5.79 7 4
6 Auburn Arrow_down2 9.5 4 15 126 3.01 123 5.37 7 4
7 UCLA Arrow_up1 11.0 10 12 126 3.10 123 5.41 9 3
8 Mississippi State Arrow_down1 11.5 19 4 126 3.29 123 6.76 9 2
9 Georgia - 13.0 2 24 126 2.98 123 4.84 8 3
10 Michigan State Arrow_up1 16.0 16 16 126 3.20 123 5.20 9 2
10 Oklahoma - 16.0 24 8 126 3.37 123 5.79 8 4
12 Clemson - 17.0 17 17 126 3.22 123 5.20 8 3
12 Georgia Tech - 17.0 5 29 126 3.02 123 4.61 9 3
14 Nebraska - 17.5 14 21 126 3.17 123 5.01 8 3
15 Arkansas - 18.5 13 24 126 3.17 123 4.84 5 6
16 TCU Arrow_up1 19.5 37 2 126 3.46 123 6.98 10 1
16 Texas A&M Arrow_up1 19.5 21 18 126 3.32 123 5.03 6 5
16 Utah - 19.5 18 21 126 3.27 123 5.01 7 4
19 Arizona State - 22.0 32 12 126 3.43 123 5.41 8 3
19 Louisville Arrow_up1 22.0 15 29 126 3.19 123 4.61 8 3
21 Arizona Arrow_up1 23.0 32 14 126 3.43 123 5.40 10 3
22 Ohio State Arrow_down2 23.5 8 39 126 3.06 123 4.46 12 1
23 Notre Dame Arrow_up1 26.0 6 46 126 3.02 123 4.24 7 5
24 Baylor Arrow_up1 28.0 50 6 126 3.67 123 6.00 10 1
25 Iowa Arrow_up3 31.0 29 33 126 3.42 123 4.54 6 5
25 USC Arrow_up4 31.0 27 35 126 3.41 123 4.50 8 4
27 Kansas State Arrow_down2 31.5 53 10 126 3.70 123 5.75 8 3
28 Missouri Arrow_down3 32.0 12 52 126 3.12 123 4.17 9 3
29 South Carolina - 33.5 35 32 126 3.44 123 4.59 5 6
30 Boise State Arrow_up1 34.0 40 28 126 3.52 123 4.65 10 2
31 Rutgers Arrow_up3 35.0 29 41 126 3.42 123 4.42 6 5
31 Washington - 35.0 59 11 126 3.79 123 5.58 7 5
33 Florida Arrow_up1 36.0 49 23 126 3.66 123 4.85 5 5
33 Wisconsin Arrow_down10 36.0 23 49 126 3.36 123 4.23 9 3
35 Colorado State Arrow_down1 37.0 48 26 126 3.60 123 4.82 9 2
35 Stanford Arrow_down1 37.0 47 27 126 3.59 123 4.80 6 5
37 West Virginia Arrow_down3 38.0 56 20 126 3.77 123 5.02 6 5
38 Tennessee Arrow_down5 38.5 46 31 126 3.58 123 4.60 5 6
39 Oklahoma State Arrow_up9 40.0 61 19 126 3.83 123 5.02 5 6
40 Minnesota Arrow_down1 41.0 37 45 126 3.46 123 4.27 7 4
41 Duke - 42.0 29 55 126 3.42 123 4.11 8 3
41 Penn State Arrow_down1 42.0 27 57 126 3.41 123 4.08 6 6
43 North Carolina State - 42.5 45 40 126 3.57 123 4.45 6 5
44 Maryland Arrow_down2 43.5 44 43 126 3.56 123 4.36 6 5
45 Boston College - 46.5 25 68 126 3.37 123 3.89 6 5
46 BYU Arrow_down2 47.0 20 74 126 3.31 123 3.75 7 4
47 Michigan Arrow_down2 48.5 43 54 126 3.55 123 4.14 5 7
48 Illinois Arrow_down1 49.5 32 67 126 3.43 123 3.90 5 6
49 Utah State Arrow_up1 51.0 42 60 126 3.54 123 4.05 8 4
50 North Carolina Arrow_down1 51.5 26 77 126 3.40 123 3.67 5 6
51 Northwestern - 53.0 36 70 126 3.45 123 3.80 4 7
51 Oregon State - 53.0 68 38 126 4.15 123 4.46 4 7
53 Nevada Arrow_up1 53.5 55 52 126 3.73 123 4.17 6 5
54 Iowa State Arrow_down3 54.5 73 36 126 4.23 123 4.49 2 9
55 Kentucky - 55.0 66 44 126 4.10 123 4.33 4 7
55 Miami (Fl) Arrow_up2 55.0 39 71 126 3.47 123 3.80 5 6
57 Texas Arrow_down2 55.5 65 46 126 3.98 123 4.24 6 6
58 Marshall Arrow_up1 56.5 71 42 126 4.17 123 4.39 11 1
59 California Arrow_down2 57.0 63 51 126 3.96 123 4.19 4 7
59 Texas Tech Arrow_up2 57.0 81 33 126 4.41 123 4.54 3 8
61 Air Force Arrow_up1 57.5 51 64 126 3.67 123 3.93 8 3
61 Northern Illinois Arrow_up2 57.5 60 55 126 3.82 123 4.11 10 2
61 Virginia Tech Arrow_down2 57.5 22 93 126 3.33 123 3.48 5 6
64 East Carolina - 62.0 52 72 126 3.69 123 3.77 7 4
65 Louisiana Tech - 62.5 79 46 126 4.33 123 4.24 8 4
66 Cincinnati Arrow_down1 63.0 64 62 126 3.97 123 4.03 9 3
67 Virginia Arrow_up1 64.0 54 74 126 3.72 123 3.75 4 7
67 Washington State - 64.0 70 58 126 4.17 123 4.07 2 9
69 Memphis - 70.5 76 65 126 4.25 123 3.91 8 3
70 Pittsburgh Arrow_up1 71.0 40 102 126 3.52 123 3.35 5 6
71 Indiana Arrow_down1 73.5 58 89 126 3.79 123 3.52 3 8
72 UL Lafayette Arrow_up1 75.0 92 58 126 4.76 123 4.07 7 4
73 Central Florida Arrow_down1 75.5 57 94 126 3.78 123 3.46 8 3
73 Toledo Arrow_up1 75.5 88 63 126 4.63 123 3.96 7 4
75 Colorado - 76.5 117 36 126 5.36 123 4.49 2 10
75 Kansas Arrow_up2 76.5 103 50 126 4.98 123 4.20 2 9
77 Wyoming Arrow_down2 77.0 77 77 126 4.26 123 3.67 3 8
78 Rice Arrow_down1 77.5 86 69 126 4.52 123 3.82 7 5
79 San Diego State Arrow_up1 78.0 83 73 126 4.46 123 3.76 6 5
80 Purdue Arrow_down3 78.5 74 83 126 4.24 123 3.58 2 9
81 Wake Forest Arrow_up1 80.5 69 92 126 4.16 123 3.50 2 9
81 Western Kentucky - 80.5 62 99 126 3.95 123 3.41 7 5
83 UTEP - 81.0 97 65 126 4.80 123 3.91 7 5
84 Arkansas State Arrow_up1 82.0 75 89 126 4.25 123 3.52 6 5
85 Georgia Southern Arrow_down2 83.0 106 60 126 5.07 123 4.05 8 3
86 Bowling Green - 84.5 66 103 126 4.10 123 3.30 6 6
87 Fresno State Arrow_up1 85.5 83 88 126 4.46 123 3.54 5 6
88 Navy Arrow_up3 86.5 78 95 126 4.32 123 3.45 6 5
88 Temple Arrow_up1 86.5 72 101 126 4.21 123 3.36 5 6
88 Western Michigan Arrow_down1 86.5 89 84 126 4.64 123 3.57 7 4
91 Syracuse Arrow_down2 88.5 96 81 126 4.78 123 3.59 2 9
91 UAB - 88.5 91 86 126 4.72 123 3.54 5 6
93 Appalachian State - 90.5 99 82 126 4.84 123 3.59 6 4
93 Texas State Arrow_up2 90.5 92 89 126 4.76 123 3.52 6 5
95 Central Michigan Arrow_up1 91.0 82 100 126 4.44 123 3.37 6 5
96 UL Monroe Arrow_down2 92.0 104 80 126 5.02 123 3.61 4 8
97 South Alabama Arrow_down1 93.0 107 79 126 5.10 123 3.63 6 6
98 Akron - 94.0 80 108 126 4.36 123 3.27 4 7
99 Vanderbilt Arrow_down1 95.0 114 76 126 5.25 123 3.68 2 9
100 Ohio Arrow_up1 96.5 107 86 126 5.10 123 3.54 5 6
101 Middle Tennessee State Arrow_up1 97.5 90 105 126 4.71 123 3.28 5 6
102 Houston Arrow_down2 98.0 87 109 126 4.56 123 3.24 6 5
103 New Mexico Arrow_up1 98.5 102 95 126 4.92 123 3.45 4 8
104 Old Dominion Arrow_down1 99.0 100 98 126 4.91 123 3.44 5 6
104 Southern Miss - 99.0 114 84 126 5.25 123 3.57 2 9
106 Ball State - 100.0 83 117 126 4.46 123 3.00 4 6
107 Hawaii - 102.5 110 95 126 5.21 123 3.45 3 9
108 Florida Atlantic - 103.5 92 115 126 4.76 123 3.08 3 9
109 UTSA - 106.0 105 107 126 5.03 123 3.28 4 8
110 Connecticut Arrow_up2 106.5 92 121 126 4.76 123 2.87 1 10
111 San Jose State Arrow_down1 108.0 112 104 126 5.23 123 3.29 2 9
112 Army Arrow_down1 109.5 98 121 126 4.81 123 2.87 3 7
112 Buffalo - 109.5 109 110 126 5.13 123 3.22 3 6
114 Kent State Arrow_up1 110.5 100 121 126 4.91 123 2.87 2 9
115 North Texas Arrow_up2 111.5 111 112 126 5.22 123 3.20 3 8
115 Tulane Arrow_down1 111.5 113 110 126 5.24 123 3.22 2 9
117 South Florida Arrow_down1 113.0 121 105 126 5.71 123 3.28 3 8
118 Florida International Arrow_down1 116.0 119 113 126 5.53 123 3.14 3 7
119 Miami (Oh) Arrow_up1 117.0 120 114 126 5.66 123 3.09 2 9
119 UNLV - 117.0 118 116 126 5.44 123 3.02 1 11
121 Massachusetts - 120.0 116 124 126 5.27 123 2.82 3 9
121 SMU Arrow_up5 120.0 122 118 126 5.75 123 2.98 1 11
123 Eastern Michigan Arrow_down1 121.0 123 119 126 6.12 123 2.97 1 10
124 Tulsa Arrow_down1 122.0 124 120 126 6.21 123 2.93 2 10
125 Troy Arrow_down1 125.0 125 125 3 1.00 124 3.51 3 8
126 Idaho Arrow_down1 126.0 126 126 2 1.50 125 3.02 1 10
127 New Mexico State - 127.0 127 127 1 1.00 126 3.08 1 10
128 Georgia State - 128.0 128 128 0 NaN 127 3.17 0 11

Due to a smaller slate of games, this week's rankings saw very little movement. Here's what I noticed:

  • If the CTR were in charge of choosing teams for the College Football Playoff, three of its four selections would have matched the committee's selections. That's good! The fourth selection, however, would have sparked riots everywhere outside of Oxford. The CTR nailed the three obvious choices, but none of TCU (16), Ohio State (22), or Baylor (24) even sniffed the top four.
  • Speaking of Ohio State: The Buckeyes impressed a lot of eyeballs in the Big Ten championship game, whipping a solid Wisconsin team 59-0. And yet the CTR, which has been down on Ohio State all season, actually dropped the Buckeyes two spots for their effort. Given that, it's no surprise that Wisconsin suffered the worse downgrade of the week, falling 10 spots to number 33.
  • With the CTR focusing all of its ire on Ohio State, it apparently had none left over for Oklahoma. The Sooners have spent much of the back half of the season as the highest ranked Big 12 team, even through all of their recent slip ups. Indeed, the CTR sees their resume so unimpeachable that the Oklahoma State loss had no effect on their ranking. The Cowboys were rewarded for their victory, however, jumping nine spots to become the week's highest riser.
  • With bowl season coming up, be ready to see a lot of movement in the next set of Transitivity Rankings. Toward the end of conference play, it's hard to significantly change the lengths of your shortest win paths. As an example, let's look at Kansas State's last game and their next game. Both Baylor and UCLA are solid teams, and a win over either would be impressive to a pollster. But in terms of win paths, beating UCLA would be a bigger deal; Kansas State already owns a win path of length two over Baylor, so a win last week wouldn't have significantly shortened any K-State win paths. But the Cats' shortest path to UCLA is six games long. A drop from six to one would be a much bigger deal. Throw in 37 more games with similar stakes, and you see the impact bowl season can have.

CLUSTER WATCH

Looking back over the rankings, you'll see that every team between 2 and 124 has win paths (and loss paths) to the same number of teams. We call this mass of teams the cluster. Championship Saturday brought us two games with the potential to change cluster membership: Florida State trying to stay above the cluster in the ACC championship against Georgia Tech, and SMU ending its regular season against UConn with the chance to enter the cluster from the bottom.

As I'm sure you're aware, FSU was able to hold off the Yellow Jackets and maintain their transitive dominance over the rest of the country. What you may not have noticed was the Mustangs picking up their only win of the season against the cluster-residing Huskies. So congratulations to SMU, who escapes the ignominy of being the only non-Sunbelt team to finish the season in the sub-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:
Largest difference between WTR and LTR.

Winner:
Colorado

Notes:
Not much to talk about here, as the back-to-back-to-back Jekyll and Hyde champion Buffaloes were off last week, as were all of their closest competitors.

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, TCU

Notes:
Another repeat winner from last week (that's going to be a theme today). The Eagles need 11 games to reach TCU on a win path. A representative argument looks like this: Eastern Michigan > Buffalo > Massachusetts > Kent State > Army > Connecticut > Central Florida > BYU > Texas > West Virginia > Baylor > TCU.

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:
Tulsa

Notes:
Yet another repeat winner. Tulsa owns win paths over 126 other teams, and the shortest paths sum to 782 games. Eastern Michigan is once again in second place, with 126 paths summing to 771 games.

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:
Boise State (Atlas), Vanderbilt (Coattails)

Notes:
Finally, a winner that's not a retread from last week! And even then it was close, as Boise State's rank of 30 is 45.92 spots better than the MWC's average rank, while reigning Atlas Florida State is 45.29 spots higher than the ACC average. Vanderbilt, of course, is steady as ever in the Coattails race. Here's the conference-by-conference breakdown:

Conference Avg Conference Rank Atlas Atlas Rank Atlas Difference Coattail Hanger Coattail Rank Coattail Difference
AAC 95.36 East Carolina 64 31.36 Tulsa 124 28.64
ACC 46.29 Florida State 1 45.29 Syracuse 91 44.71
Big 12 39.80 Oklahoma 10 29.80 Kansas 75 35.20
Big Ten 39.79 Michigan State 10 29.79 Purdue 80 40.21
CUSA 93.46 Marshall 58 35.46 Florida International 118 24.54
MAC 99.69 Northern Illinois 61 38.69 Eastern Michigan 123 23.31
MWC 75.92 Boise State 30 45.92 UNLV 119 43.08
Pac-12 34.17 Oregon 4 30.17 Colorado 75 40.83
SEC 24.71 Alabama 2 22.71 Vanderbilt 99 74.29
Sun Belt 102.36 UL Lafayette 72 30.36 Georgia State 128 25.64
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:
Baylor

Notes:
Last week, Baylor and Kansas State were numbers one and two for this award. I said that whoever won that game would get enough of a CTR boost to be out of the running this week. I was wrong. The Bears were number 4 in the final AP ranking, but only gained one spot in the CTR this week , moving up to 24. This difference of 20 was slightly above second place Ohio State (AP 5, CTR 22, difference of 17) and brings the award to Waco for the third week in a row.

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:
Arkansas

Notes:
Depending on bowl results, its possible that the CTR's conference-wide crush on the SEC will fade a bit. For now, the CTR continues to value Arkansas (15) and Texas A&M (16) more than any living human does.

KANSAS STATE WIN PATHS

K-State lost their last game to Baylor, but it didn't hurt them too much, sliding just two spots to number 27. More importantly, the Wildcats drew a bowl opponent in UCLA that can really help them in the CTR. The Bruins sit at number 7 in the current rankings and, as noted earlier, are only reachable via a fairly long win path of length six. In fact, as the win path diagram shows, all of the Pac-12 is pretty distant from Kansas State right now (Pac-12 teams are shaded light blue). A win over the Bruins would give K-State a short path out to the west coast, and could be big for their CTR. The full diagram and depth list is found below.

Click to embiggen. - jeffp171/Bring on the Cats

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