College Football Transitivity Rankings and Awards - Week 12

Welcome back to the Transitivity Rankings, where we use transitive arguments as a basis for ranking every FBS team. If this is your first time here, you'll want to check out this introductory post. Otherwise, let's dive into this week's results.

Combined Transitivity Rankings - Week 12

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	2	1.0	1	1	126	3.51	0	NaN	9	0
2	Marshall	4	1.5	2	1	126	4.52	0	NaN	9	0
3	Alabama	-	4.5	5	4	125	3.14	122	8.57	9	1
4	Mississippi	1	5.0	5	5	125	3.14	122	7.59	7	2
5	LSU	2	6.5	7	6	125	3.30	122	7.57	6	4
5	Mississippi State	4	6.5	10	3	125	3.39	122	9.55	8	1
7	Auburn	5	8.0	4	12	125	3.11	122	6.66	7	3
8	Georgia	6	8.5	3	14	125	3.06	122	6.62	8	2
9	Oregon	2	9.5	8	11	125	3.34	122	6.79	8	1
10	UCLA	1	12.0	9	15	125	3.35	122	6.55	8	2
11	Oklahoma	2	13.0	17	9	125	3.55	122	6.95	7	3
12	TCU	4	15.5	24	7	125	3.70	122	7.47	8	1
13	Arkansas	30	16.0	19	13	125	3.65	122	6.63	4	5
14	Texas A&M	6	17.5	13	22	125	3.48	122	5.81	6	4
15	Arizona State	5	19.5	19	20	125	3.65	122	6.03	7	2
16	Michigan State	6	20.0	15	25	125	3.54	122	5.68	7	2
17	Nebraska	2	21.5	13	30	125	3.48	122	5.61	7	2
18	Utah	-	23.0	15	31	125	3.54	122	5.58	6	3
19	Kansas State	-	23.5	39	8	125	3.95	122	7.00	6	2
19	South Carolina	14	23.5	22	25	125	3.66	122	5.68	4	5
21	Arizona	1	24.5	26	23	125	3.72	122	5.80	8	2
22	Tennessee	8	25.5	33	18	125	3.82	122	6.24	4	5
23	Notre Dame	14	26.0	12	40	125	3.45	122	5.12	7	3
24	Florida	8	26.5	29	24	125	3.76	122	5.71	5	4
25	Baylor	-	27.5	39	16	125	3.95	122	6.48	7	1
26	Colorado State	9	28.0	39	17	125	3.95	122	6.43	8	1
27	Wisconsin	10	29.0	19	39	125	3.65	122	5.13	7	2
28	Ohio State	1	30.0	11	49	125	3.42	122	4.93	9	1
29	Missouri	12	32.5	18	47	125	3.62	122	4.98	7	2
30	Boise State	9	34.5	36	33	125	3.86	122	5.46	8	2
31	Iowa	14	35.0	22	48	125	3.66	122	4.94	6	3
32	Michigan	14	35.5	29	42	125	3.76	122	5.07	5	5
33	Miami (Fl)	7	36.5	38	35	125	3.94	122	5.19	5	4
34	Rutgers	14	37.0	28	46	125	3.75	122	4.98	5	4
34	West Virginia	3	37.0	42	32	125	3.96	122	5.50	5	4
36	California	2	38.0	47	29	125	4.15	122	5.66	4	5
37	Georgia Tech	9	38.5	35	42	125	3.83	122	5.07	8	2
38	Clemson	16	39.0	51	27	125	4.22	122	5.67	6	3
39	Washington	4	39.5	60	19	125	4.38	122	6.04	5	5
40	Louisiana Tech	1	40.0	70	10	125	4.66	122	6.94	7	2
41	Minnesota	1	41.5	31	52	125	3.77	122	4.85	6	3
42	Kentucky	4	42.0	57	27	125	4.32	122	5.67	4	6
43	Penn State	-	42.5	24	61	125	3.70	122	4.56	6	4
44	Nevada	18	43.5	46	41	125	4.12	122	5.11	5	4
45	Louisville	9	44.5	44	45	125	4.06	122	5.06	6	3
45	Maryland	3	44.5	34	55	125	3.82	122	4.75	5	4
47	Northwestern	11	46.5	27	66	125	3.74	122	4.31	3	6
48	Duke	24	49.5	45	54	125	4.06	122	4.84	7	2
48	Utah State	11	49.5	49	50	125	4.18	122	4.91	7	3
50	Stanford	9	50.5	63	38	125	4.42	122	5.14	4	5
51	Oregon State	24	51.5	61	42	125	4.39	122	5.07	4	5
52	Oklahoma State	2	52.0	70	34	125	4.66	122	5.38	4	5
53	Air Force	1	52.5	48	57	125	4.17	122	4.68	7	2
54	USC	1	53.0	54	52	125	4.30	122	4.85	7	3
55	Boston College	5	54.5	37	72	125	3.86	122	4.23	5	4
56	Texas	1	56.5	54	59	125	4.30	122	4.61	6	5
57	Washington State	3	57.5	57	58	125	4.32	122	4.65	2	7
58	Iowa State	-	58.0	65	51	125	4.46	122	4.89	2	6
59	Virginia Tech	1	58.5	32	85	125	3.78	122	3.96	4	5
60	Northern Illinois	5	59.0	53	65	125	4.27	122	4.33	7	2
61	UL Lafayette	-	60.5	100	21	125	5.68	122	6.00	6	3
62	BYU	7	61.0	43	79	125	3.97	122	4.04	6	4
63	Illinois	1	61.5	54	69	125	4.30	122	4.25	3	6
64	Texas Tech	6	62.5	89	36	125	5.25	122	5.16	2	7
65	East Carolina	3	65.5	52	79	125	4.22	122	4.04	5	3
66	Cincinnati	11	66.0	68	64	125	4.64	122	4.45	6	3
67	Indiana	1	67.0	66	68	125	4.46	122	4.27	2	7
68	North Carolina	5	68.5	61	76	125	4.39	122	4.11	4	5
69	Colorado	9	70.0	103	37	125	5.81	122	5.16	2	8
70	North Carolina State	1	71.5	87	56	125	5.18	122	4.71	5	5
71	Arkansas State	15	72.5	76	69	125	4.93	122	4.25	5	4
71	Virginia	5	72.5	72	73	125	4.68	122	4.20	3	6
73	Memphis	3	73.5	73	74	125	4.72	122	4.13	6	3
74	Kansas	6	74.0	88	60	125	5.23	122	4.58	2	7
75	Pittsburgh	2	74.5	50	99	125	4.19	122	3.58	3	6
76	Bowling Green	3	75.0	64	86	125	4.45	122	3.95	6	3
77	Wyoming	10	75.5	67	84	125	4.60	122	3.99	3	6
78	Rice	6	78.0	77	79	125	4.94	122	4.04	6	4
79	Toledo	5	79.5	85	74	125	5.11	122	4.13	5	4
80	Syracuse	2	80.0	97	63	125	5.63	122	4.50	2	7
81	Purdue	1	80.5	78	83	125	4.96	122	4.00	2	7
82	UTEP	7	81.0	93	69	125	5.52	122	4.25	6	4
82	Western Kentucky	4	81.0	57	105	125	4.32	122	3.54	5	5
82	Western Michigan	-	81.0	85	77	125	5.11	122	4.09	6	3
85	Central Florida	-	81.5	69	94	125	4.66	122	3.73	5	3
86	Navy	2	85.0	79	91	125	5.02	122	3.76	4	5
87	South Alabama	7	86.5	112	61	125	6.10	122	4.56	6	4
88	UAB	8	88.0	84	92	125	5.10	122	3.75	4	5
89	Central Michigan	1	88.5	75	102	125	4.84	122	3.56	6	4
89	Temple	2	88.5	74	103	125	4.82	122	3.55	4	5
91	Akron	1	90.0	80	100	125	5.02	122	3.57	3	6
92	Georgia Southern	11	90.5	114	67	125	6.33	122	4.30	7	3
93	Hawaii	1	91.5	95	88	125	5.55	122	3.84	2	8
94	Vanderbilt	8	92.0	106	78	125	5.92	122	4.06	2	7
95	Middle Tennessee State	9	94.0	82	106	125	5.07	122	3.53	4	5
96	Ohio	2	94.5	97	92	125	5.63	122	3.75	4	5
97	Appalachian State	11	95.0	101	89	125	5.78	122	3.82	4	4
98	Houston	1	96.0	81	111	125	5.06	122	3.43	4	4
98	San Diego State	6	96.0	110	82	125	6.08	122	4.01	4	5
100	Florida Atlantic	1	97.0	82	112	125	5.07	122	3.37	3	7
101	Old Dominion	6	97.5	92	103	125	5.47	122	3.55	3	6
102	San Jose State	7	98.0	96	100	125	5.57	122	3.57	2	7
103	UTSA	-	100.0	91	109	125	5.43	122	3.49	3	7
104	Southern Miss	4	102.0	107	97	125	6.00	122	3.66	2	8
105	Ball State	4	104.0	90	118	125	5.34	122	3.13	2	6
106	Fresno State	1	104.5	111	98	125	6.09	122	3.66	3	6
106	New Mexico	2	104.5	113	96	125	6.16	122	3.67	3	7
106	Wake Forest	3	104.5	115	94	125	6.50	122	3.73	1	8
109	UL Monroe	2	105.0	123	87	125	7.26	122	3.87	3	7
110	Texas State	4	105.5	121	90	125	7.06	122	3.81	4	5
111	Tulane	3	106.0	102	110	125	5.79	122	3.46	2	7
112	North Texas	-	107.5	109	106	125	6.03	122	3.53	2	7
113	Florida International	2	108.0	104	112	125	5.85	122	3.37	3	6
114	Army	2	108.5	94	123	125	5.54	122	2.98	3	6
115	Buffalo	6	109.5	105	114	125	5.86	122	3.31	2	6
115	Connecticut	1	109.5	99	120	125	5.64	122	3.12	1	7
117	Massachusetts	6	112.5	107	118	125	6.00	122	3.13	3	7
117	South Florida	1	112.5	117	108	125	6.57	122	3.50	3	6
119	Miami (Oh)	-	116.5	119	114	125	6.77	122	3.31	2	8
120	Eastern Michigan	2	118.0	120	116	125	6.85	122	3.20	1	8
121	Kent State	3	119.0	116	122	125	6.52	122	3.03	1	9
121	Tulsa	4	119.0	118	120	125	6.74	122	3.12	2	8
123	UNLV	4	119.5	122	117	125	7.07	122	3.17	1	9
124	Troy	-	124.0	124	124	3	1.00	123	3.67	3	7
125	Idaho	-	125.5	125	126	2	1.50	124	3.15	1	9
126	SMU	-	126.0	127	125	0	NaN	123	3.28	0	9
127	New Mexico State	-	126.5	126	127	1	1.00	125	3.24	1	8
128	Georgia State	-	127.5	127	128	0	NaN	126	3.38	0	9

Before this past weekend, the non-Arkansas SEC West teams had only lost games among themselves, and as a result were always among the top teams in the CTR. This week, Auburn, LSU, and Texas A&M lost to Georgia, Arkansas, and Missouri, respectively, ending the division's transitive dominance over the rest of the nation. But even with all these new win paths leading into the division, the SEC West continues to dominate the CTR top 10. Even Arkansas and Texas A&M are in the top 15. I was a little disappointed in this development, as I had hoped these losses might allow the CTR to spread the love a little more. But it appears the CTR is still impressed by the SEC's non-conference performances, and will likely continue to rate the conference highly unless they show poorly in their bowl matchups.

Other thoughts:

• Florida State survived another scare this weekend to remain undefeated. As their reward, the Seminoles find themselves in the top spot of this week's rankings.
• The week's biggest jump goes to Arkansas, whose upset over LSU moved them a surprising 30 spots up the rankings. The Razorbacks are now 13th in the CTR, which is... dumb. In general, the high rankings of mid-pack SEC teams LSU, Arkansas, Texas A&M, South Carolina, Tennessee, and Florida this late in the season represents my biggest gripe with this ranking system.
• The biggest drop this week belongs to Duke, who fell 24 spots after an upset loss to Virginia Tech. The Blue Devils, now ranked 48 in the CTR, actually still control their own destiny in the ACC Coastal, and will play Florida State for the conference championship should they beat UNC and Wake Forest in their final two games. Unseating a shaky Seminole team in the ACC championship would help gain back much of the ground Duke lost this week.

CLUSTER WATCH

The cluster is what we call 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 3 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 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.

For the second week in a row, we saw a large group of teams from the same conference drop from the super-cluster into the cluster. This week, it was the SEC. Going into the weekend, each of Auburn, LSU, and Texas A&M needed to win in order to keep themselves (plus Alabama and Ole Miss) in the super-cluster. As it turns out, all three of them lost. Mississippi State would have been spared a fall to the cluster had they beaten Alabama, but their loss to the Tide dropped Bulldogs along side their conference mates. As a result of the SEC's tumble, the super-cluster now consists of only two teams: Undefeated Marshall and Florida State.

In contrast to last week, however, the SEC's drop into the cluster was much less impactful on their rankings. Texas A&M was the worst off, falling six spots, but this drop is nothing compared to the 15-plus spot demotions many Big 12 teams faced last week. The reason is likely because the CTR prefers the SEC's non-conference performance to the Big 12's. Indeed, the Big 12 lost two non-conference matchups with the SEC. Had those games gone differently, the CTR might look quite different.

In the sub-cluster, only one team had the opportunity to enter the cluster over the weekend. That team was SMU, who blew a 13 point fourth quarter lead in a loss to South Florida. As a result, the sub-cluster stayed at five teams: Troy, Idaho, SMU, New Mexico State, and Georgia State.

Looking forward to next week, the following five games have the potential to alter cluster membership:

• Florida State vs. Boston College
• Marshall at UAB
• SMU at Central Florida
• Georgia State at Clemson
• New Mexico State vs. UL Monroe

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:
Louisiana-Lafayette

Notes:
Georgia Southern is out after a two-week run, and in their place are the Ragin' Cajuns. UL Lafayette holds an unfortunate WTR of 100, but a respectable LTR of 21. That 79 spot spread is 13 spots wider than that of their closest competitor, Colorado (WTR 103, LTR 37, difference 66).

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:
South Alabama, Mississippi State

Notes:
The number of the week is 14, which is the length of the shortest win path to Mississippi State from Georgia Southern, UL Monroe, South Alabama, and Texas State. The tiebreaker gives the nod to South Alabama, whose path to Mississippi State covers 9709 miles, or just over 250 miles longer than Georgia Southern's path to the Bulldogs. A representative path looks like this:

South Alabama > Appalachian State > Arkansas State > Utah State > Wyoming > Florida Atlantic > Western Kentucky > Bowling Green > Indiana > Missouri > Texas A&M > Auburn > Mississippi > Alabama > Mississippi State

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:
Louisiana-Monroe

Notes:
After a four week reign, Eastern Michigan has finally been unseated for this award. UL Monroe wins by virtue of their 125 win paths covering 908 total games. Coming in second place was UNLV, whose 125 win paths sum to 884 total 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:
Marshall (Atlas), Vanderbilt (Coattails)

Notes:
New week, same story for the Atlas and Coattail-Rider Awards. Here's the conference-by-conference breakdown, in which we see the Big Ten gaining ground on the Big 12 in terms of lowest average rank.

Conference	Avg Conference Rank	Atlas	Atlas Rank	Atlas Difference	Coattail Hanger	Coattail Rank	Difference
AAC	96.91	East Carolina	65	31.91	SMU	126	29.09
ACC	56.14	Florida State	1	55.14	Wake Forest	106	49.86
Big 12	40.50	Oklahoma	11	29.50	Kansas	74	33.50
Big Ten	40.86	Michigan State	16	24.86	Purdue	81	40.14
CUSA	84.62	Marshall	2	82.62	Florida International	113	28.38
MAC	97.69	Northern Illinois	60	37.69	Kent State	121	23.31
MWC	75.50	Colorado State	26	49.50	UNLV	123	47.50
Pac-12	35.75	Oregon	9	26.75	Colorado	69	33.25
SEC	20.64	Alabama	3	17.64	Vanderbilt	94	73.36
Sun Belt	102.82	UL Lafayette	61	41.82	Georgia State	128	25.18

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:
USC

Notes:
The AP brought the Trojans back into the rankings this week, allowing USC to win this award for the first time since week 8. Compared to their AP ranking of 24, Southern Cal's CTR rank of 54 represents a 30 spot difference. Their closest competition for the award was Duke, who is sitting at 25 in the AP but 48 in the CTR, a difference of 23.

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:
South Carolina

Notes:
The CTR's season-long love affair with the SEC West turned into a crush on the entire conference this week. CTR 19 South Carolina's two closest competitors are Tennessee (CTR 22) and Florida (CTR 24). I think it's safe to say the CTR got these ones wrong.

KANSAS STATE WIN PATHS

The Wildcats stood firm in the CTR this week, maintaining last week's ranking of 19. They come by this ranking via a strong LTR of 8, but a middling WTR of 39. Luckily, the Wildcats have a few opportunities to boost their WTR in the coming weeks, with games against West Virginia and Baylor.

You'll find K-State's shortest paths diagram below, along with the depth guide. Hopefully you know what to do with them by now. See you next week.

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, Illinois, Indiana, Kent State, Kentucky, 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, Florida, Fresno State, Georgia, Hawaii, Idaho, UL Monroe, Memphis, Miami (Oh), Minnesota, Missouri, Middle Tennessee State, Navy, Northern Illinois, Notre Dame, Ohio, Penn State, South Alabama, South Florida, Syracuse, TCU, Temple, Troy, Texas State, Vanderbilt, Virginia Tech, Wake Forest, Wisconsin, Wyoming

Level 5: Arkansas, Auburn, Boise State, Central Florida, Cincinnati, Clemson, Duke, Georgia Southern, Michigan, North Carolina, North Carolina State, Nebraska, Nevada, Ohio State, Rutgers, San Diego State, San Jose State, Stanford, Texas A&M, USC, Virginia

Level 6: Arizona, California, Colorado, Colorado State, Georgia Tech, Louisville, LSU, Michigan State, Miami (Fl), Mississippi, Oregon State, Washington, Washington State

Level 7: Alabama, Arizona State, Oregon, Utah

Level 8: Mississippi State, UCLA

No Path: Florida State, Marshall