College Football Transitivity Rankings and Awards - Week 10

After a few upset bids fell just short, the top of the Transitivity Rankings lay mostly unchanged from last week. As always, if you're new here please check out the explanatory post found here. If you're a return reader, you may want to skim the following glossary of terminology specific to these posts:

• Win path: A transitive argument for one team over another. For example, you might argue that Kansas State is better than Western Michigan this season since K-State beat Iowa State, who in turn beat Toledo, who has beaten Western Michigan.
• Path length: The number of games in a transitive argument. The path in the above example has length 3.
• Loss path: Exactly like a win path, but reversed.
• Win Transitivity Rankings (WTR): A ranking of FBS teams calculated exclusively from win paths. It roughly measures the strength of a team's wins.
• Loss Transitivity Rankings (LTR): A ranking of FBS teams calculated exclusively from loss paths. It roughly measures how bad a team's losses have been.
• Combined Transitivity Rankings (CTR): The star of these posts. It's calculated by averages a team's rankings in the WTR and LTR.
• The cluster: After of sufficient number of games have been played, there is always a large group of teams in the middle of the rankings who all have win paths to each other. We call this group of teams the cluster.

After 10 weeks of play, the Combined Transitivity Rankings are as follows:

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	124	3.65	0	NaN	8	0
2	Auburn	-	3.0	2	4	123	3.30	1	1.00	7	1
3	LSU	-	5.0	3	7	121	3.55	2	1.00	6	2
4	Florida State	-	6.0	11	1	114	3.44	0	NaN	7	0
4	Kansas State	-	6.0	6	6	118	4.08	2	1.50	6	1
4	Mississippi	-	6.0	4	8	120	3.39	3	1.33	7	2
7	Alabama	-	7.0	5	9	119	3.64	4	2.00	7	1
8	Marshall	-	7.5	14	1	112	4.70	0	NaN	7	0
9	Notre Dame	-	8.0	12	4	112	3.43	1	1.00	7	1
10	Oklahoma	1	9.5	7	12	117	3.72	9	3.00	6	2
10	TCU	-	9.5	8	11	117	4.03	9	3.67	6	1
12	Baylor	-	11.5	10	13	117	4.35	9	2.89	6	1
12	Texas A&M	1	11.5	13	10	112	4.15	5	1.40	5	3
12	West Virginia	1	11.5	9	14	117	4.15	9	2.11	5	3
15	Louisiana Tech	-	15.5	16	15	112	4.89	10	3.30	6	2
15	Oklahoma State	-	15.5	15	16	112	4.74	11	2.00	4	4
17	Nebraska	-	18.5	20	17	111	3.56	119	9.04	7	1
18	Michigan State	-	19.5	21	18	111	3.66	119	8.10	6	1
18	Oregon	2	19.5	17	22	111	3.26	119	7.16	7	1
20	UCLA	1	21.5	18	25	111	3.36	119	7.02	7	2
21	Georgia	2	22.5	19	26	111	3.47	119	6.90	6	2
22	Arizona State	4	24.0	29	19	111	3.89	119	8.00	6	1
23	Colorado State	3	25.0	27	23	111	3.80	119	7.09	7	1
24	Clemson	2	26.0	32	20	111	3.95	119	7.78	5	2
25	Arizona	1	28.0	24	32	111	3.73	119	6.18	6	2
26	Boise State	5	29.0	25	33	111	3.75	119	6.12	6	2
27	Utah	4	29.5	22	37	111	3.67	119	6.06	5	2
28	Duke	1	34.5	43	26	111	4.16	119	6.90	6	1
29	Florida	19	36.0	37	35	111	4.04	119	6.09	4	3
29	Miami (Fl)	1	36.0	30	42	111	3.90	119	5.92	5	3
29	Tennessee	21	36.0	42	30	111	4.13	119	6.82	3	5
32	South Carolina	6	37.0	33	41	111	3.98	119	5.95	3	5
33	Georgia Tech	9	38.5	28	49	111	3.86	119	5.62	6	2
33	Washington	2	38.5	53	24	111	4.48	119	7.03	5	3
35	Nevada	7	39.5	40	39	111	4.07	119	5.99	5	3
36	Iowa	3	40.5	31	50	111	3.91	119	5.61	5	2
37	Ohio State	2	41.5	23	60	111	3.72	119	5.21	7	1
37	Utah State	9	41.5	45	38	111	4.21	119	6.03	5	3
39	California	2	42.5	56	29	111	4.51	119	6.86	4	4
40	Stanford	4	43.5	53	34	111	4.48	119	6.10	4	4
40	Wisconsin	1	43.5	39	48	111	4.06	119	5.65	5	2
42	Maryland	2	45.0	34	56	111	3.99	119	5.30	5	3
43	Missouri	1	46.0	34	58	111	3.99	119	5.23	6	2
44	Arkansas	6	46.5	72	21	111	5.05	119	7.75	3	5
45	Kentucky	11	47.5	59	36	111	4.58	119	6.08	4	4
46	Louisville	7	50.5	47	54	111	4.24	119	5.45	5	3
46	Minnesota	7	50.5	49	52	111	4.29	119	5.50	5	2
48	Air Force	13	51.0	44	58	111	4.17	119	5.23	5	2
48	Iowa State	1	51.0	62	40	111	4.68	119	5.96	2	5
50	Boston College	18	52.0	26	78	111	3.77	119	4.61	5	3
51	USC	2	53.5	50	57	111	4.31	119	5.24	6	3
52	Rutgers	4	54.5	48	61	111	4.26	119	5.20	4	4
53	Michigan	15	56.0	57	55	111	4.54	119	5.39	4	5
54	Penn State	5	57.5	45	70	111	4.21	119	4.76	4	4
55	East Carolina	24	58.0	50	66	111	4.31	119	4.88	5	2
56	Arkansas State	7	59.0	71	47	111	5.04	119	5.66	4	3
56	UL Lafayette	5	59.0	90	28	111	5.66	119	6.88	4	3
58	BYU	1	60.0	38	82	111	4.05	119	4.59	5	4
59	Washington State	1	63.0	61	65	111	4.65	119	5.10	1	7
60	North Carolina	8	64.0	55	73	111	4.50	119	4.66	3	5
60	UTEP	7	64.0	97	31	111	5.91	119	6.58	5	3
62	Northwestern	4	64.5	58	71	111	4.56	119	4.74	2	5
62	Virginia Tech	9	64.5	36	93	111	4.02	119	4.24	3	5
64	Virginia	9	65.5	52	79	111	4.46	119	4.61	3	5
65	Texas	2	66.0	70	62	111	4.98	119	5.18	4	5
66	Texas Tech	15	69.5	93	46	111	5.77	119	5.72	2	6
66	Wyoming	9	69.5	60	79	111	4.60	119	4.61	3	5
68	Illinois	5	70.5	64	77	111	4.80	119	4.63	3	5
69	Oregon State	4	71.5	99	44	111	6.16	119	5.87	3	4
69	Pittsburgh	3	71.5	41	102	111	4.11	119	4.03	3	5
71	North Carolina State	17	72.0	82	62	111	5.32	119	5.18	4	4
72	Toledo	3	72.5	78	67	111	5.23	119	4.87	4	3
73	Northern Illinois	5	74.0	73	75	111	5.09	119	4.66	5	2
74	Indiana	2	74.5	66	83	111	4.90	119	4.52	2	5
74	Kansas	4	74.5	96	53	111	5.89	119	5.46	1	6
76	Colorado	5	76.5	102	51	111	6.25	119	5.60	2	7
76	Memphis	3	76.5	85	68	111	5.52	119	4.85	4	3
76	Rice	1	76.5	81	72	111	5.30	119	4.71	5	3
79	Cincinnati	5	77.5	86	69	111	5.54	119	4.84	5	3
80	Central Florida	15	78.0	63	93	111	4.70	119	4.24	4	3
81	South Alabama	11	78.5	114	43	111	7.78	119	5.91	5	3
81	Temple	27	78.5	65	92	111	4.89	119	4.26	4	3
83	Syracuse	10	79.5	95	64	111	5.84	119	5.17	2	6
84	Purdue	2	80.0	76	84	111	5.19	119	4.51	2	6
85	Georgia Southern	3	81.5	118	45	111	8.66	119	5.76	6	2
86	Western Michigan	1	83.5	78	89	111	5.23	119	4.34	5	3
87	Middle Tennessee State	7	84.0	83	85	111	5.48	119	4.50	4	4
87	San Jose State	3	84.0	87	81	111	5.55	119	4.60	2	5
89	Akron	-	85.5	68	103	111	4.95	119	4.00	3	4
89	Bowling Green	3	85.5	74	97	111	5.11	119	4.15	4	3
91	Navy	8	86.5	77	96	111	5.20	119	4.16	3	5
92	Central Michigan	5	87.0	68	106	111	4.95	119	3.92	5	4
92	Houston	3	87.0	75	99	111	5.14	119	4.13	4	3
94	Western Kentucky	4	88.5	67	110	111	4.94	119	3.86	3	5
95	Hawaii	3	90.0	89	91	111	5.58	119	4.28	1	7
96	Vanderbilt	5	92.0	108	76	111	7.06	119	4.65	2	6
97	San Diego State	-	92.5	98	87	111	6.13	119	4.37	3	4
98	Florida Atlantic	5	94.0	84	104	111	5.50	119	3.98	3	6
98	UL Monroe	2	94.0	115	73	111	7.86	119	4.66	3	5
100	UAB	6	94.5	88	101	111	5.56	119	4.09	4	4
100	UTSA	4	94.5	94	95	111	5.81	119	4.20	2	6
102	Connecticut	25	95.5	91	100	111	5.68	119	4.11	1	6
103	Ball State	8	96.0	80	112	111	5.25	119	3.71	2	4
104	New Mexico	2	97.0	104	90	111	6.51	119	4.29	3	5
105	Wake Forest	2	97.5	109	86	111	7.13	119	4.39	1	6
106	Ohio	8	98.5	92	105	111	5.69	119	3.96	3	5
107	Texas State	3	99.0	111	87	111	7.55	119	4.37	4	3
108	Tulane	16	102.0	106	98	111	6.67	119	4.13	1	6
109	Old Dominion	7	105.0	101	109	111	6.19	119	3.87	2	6
110	Fresno State	1	106.5	107	106	111	6.77	119	3.92	2	6
110	South Florida	8	106.5	105	108	111	6.62	119	3.89	2	6
112	Florida International	5	107.0	103	111	111	6.34	119	3.76	2	5
113	Army	8	108.5	100	117	111	6.17	119	3.38	2	5
114	Tulsa	7	112.5	112	113	111	7.63	119	3.69	1	7
115	UNLV	3	113.5	113	114	111	7.75	119	3.48	1	7
116	Kent State	5	114.5	110	119	111	7.14	119	3.27	1	7
117	Miami (Oh)	5	116.0	116	116	111	8.05	119	3.39	2	7
118	Buffalo	3	117.0	119	115	111	9.03	119	3.41	1	5
119	Massachusetts	5	118.0	116	120	111	8.05	119	3.21	2	7
120	Eastern Michigan	4	119.0	120	118	111	10.00	119	3.36	1	7
121	Southern Miss	4	121.0	121	121	6	1.83	120	4.59	2	6
122	Appalachian State	3	122.5	122	123	3	1.33	121	4.40	2	4
122	Idaho	3	122.5	123	122	2	1.50	120	3.87	1	7
124	North Texas	2	124.5	125	124	1	1.00	121	3.96	1	6
124	Troy	1	124.5	123	126	2	1.50	122	3.96	1	7
126	New Mexico State	-	126.0	125	127	1	1.00	124	3.44	1	7
126	SMU	1	126.0	127	125	0	NaN	122	4.15	0	7
128	Georgia State	-	127.5	127	128	0	NaN	125	3.66	0	8

The lack of movement at the top is pretty impressive, especially considering what could have been. Both Mississippi State and Florida State came very close to dropping games to cluster teams. Had Arkansas or Louisville, respectively, pulled off the upset, these rankings would look much different. An Arkansas upset would have been particularly impactful, but we'll touch on that in the next section. As it stands, the top 18 teams from last week either stood pat or saw their rankings improve this week (possible because of ties). This includes Ole Miss, West Virginia, and Oklahoma State, all losers on Saturday who nevertheless developed no chinks in their transitive armor (losing to highly ranked Auburn, TCU, and Kansas State, respectively). Some other thoughts:

• Georgia was the highest ranked team from last week to drop in this week's rankings, though perhaps not as far as you would expect. After a loss to Florida, the Bulldogs check in at number 21 in the CTR, down two spots from last week. In contrast, the AP voters dropped them eight spots from 9 to 17.
• The biggest jump of the week belongs to Temple, who shot up 27 spots after taking down East Carolina. The Owls check in at number 81 this week.
• The Temple-East Carolina game is also responsible for the biggest drop of the week, as the Pirates slid 24 spots. The CTR was already less enthusiastic about ECU than most polls, but after that result the Pirates find themselves at number 55.
• The worst drop among last week's top 25 belongs to Georgia Tech, who fell nine spots from 24 to 33. What did the Yellow Jackets do on Saturday to deserve this fate? Lose to Virginia by negative 25 points. Which is to say, they beat Virginia by 25 points. So despite the decisive victory, their transitive resume became worse. This probably has to do with some of their earlier results becoming less impressive due to other outcomes. It probably also means that the CTR has no idea what to make of the ACC Coastal, just like the rest of America.

CLUSTER WATCH

The cluster is the large group of teams in the middle of the CTR who all have win paths to each other. This week, this group consists of the teams ranked between 17 and 120. As teams in the cluster have win paths and loss paths to the same number of teams, different rankings depend entirely on average path lengths.

Teams not in the cluster fall into one of two categories, the sub-cluster teams or the super-cluster teams. It is impossible to find a win path from a team in the sub-cluster to a team in the cluster. Similarly, it is impossible to find a win path from a cluster team to a team in the super-cluster. This week, the sub-cluster consists of teams ranked 121 through 128, and the super-cluster contains teams with rankings 1 through 16.

No teams fell from the super-cluster into the cluster this week. We came very close though, as Mississippi State, Florida State, Notre Dame, and Texas A&M all found themselves in tight games against opponents from the cluster. In fact, had Mississippi State lost, the super-cluster would have shrunk from 16 teams to just three! In this scenario, we would have seen Florida State as the number 1 team, followed by Notre Dame and Marshall. The rest of the current super-cluster would have fallen into the cluster with Mississippi State, with only average path lengths to separate themselves from the rest of the pack. Such a scenario would be great for highly-ranked cluster teams (e.g. Nebraska, Michigan State, and Oregon) who would likely be able to slip into the top 10.

On the flip side, four teams were able to escape the sub-cluster this week, all owing to a single result from Saturday. UConn, which ranked a second-to-last 127 in last week's rankings, pulled an upset over UCF to shoot up to 102 this week. This victory also served to pull Tulane and South Florida out of the sub-cluster, by virtue of these teams' victories over the Huskies earlier this year. Tulsa also benefited, as the Golden Hurricane's lone victory on the year came against Tulane.

Looking forward to next week, a handful of fixtures pit cluster teams against non-cluster teams. The following is a list of games involving sub-cluster teams (listed first) with an opportunity to pull themselves into a cluster by beating a cluster team:

• SMU at Tulsa
• New Mexico State vs. UL Lafayette
• North Texas vs. Florida Atlantic
• Idaho at San Diego State
• Appalachian State vs. UL Monroe

Next is a list of super-cluster teams trying to fight off cluster teams. The list is pretty short, as many of the SEC and Big 12 cluster teams are playing each other, while the Mississippi schools are playing games against FCS teams, which the CTR ignores.

• Florida State vs. Virginia
• Notre Dame at Arizona State
• West Virginia at Texas
• Louisiana Tech at UAB

Lastly, we have a rare (for this late in the season) matchup of a super-cluster team against a sub-cluster team. If you were waiting for Marshall's undefeated run to come to an end, I wouldn't bet on it happening this week.

• Marshall at Southern Miss

AWARDS

On to the awards section, where we acknowledge Transitivity Ranking performance worthy of recognition.

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:
The Eagles have had a nice season in their first year as an FBS member, sitting at 7-2 on the year. Those two losses came in competitive away games against ACC teams NC State and Georgia Tech. Neither of those are really bad losses, and this is reflected in Georgia Southern's LTR of 45.

However, none of their wins have been particularly impressive. The Eagles own six FBS victories (half of them over teams in their first or second year as FBS institutions), but still sit at only 118 in the WTR. This difference of 73 spots was enough for the award, just ahead of South Alabama (WTR 114, LTR 43, difference of 71).

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, Louisiana-Lafayette

Notes:
The number of the week is 14, as all shortest paths this week involved 14 games or fewer. Further, each path of length 14 originates from Eastern Michigan, being the lengths of the Eagles' shortest paths to Arkansas, Clemson, Colorado State, UL Lafayette, and UTEP. My real-distance-if-you-road-trip-the-path tie-breaker gives the award to the Ragin' Cajuns, as the representative path covers 7772 miles, 460 miles more than the closest competitor. The particular argument looks like this:

Eastern Michigan > Buffalo > Miami (Oh) > Kent State > Army > Ball State > Central Michigan > Purdue > Illinois > Minnesota > San Jose State > Wyoming > Air Force > Boise State > UL Lafayette

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 is the Eagles' second win of the week, and the third week they've won this award. Eastern Michigan's 111 win paths sum up to 1110 total games, which is just over the 1001 game length of Buffalo's 111 win paths.

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 Commodores are keeping the perfect season alive, and the Thundering Herd have now won this award four weeks in a row. I have nothing else to add.

In the conference-by-conference breakdown, we see that the SEC has again expanded its lead over the Big 12 for lowest average rank.

Conference	Avg Conference Rank	Atlas	Atlas Rank	Atlas Difference	Coattail Hanger	Coattail Rank	Difference
AAC	93.00	East Carolina	55	38.00	SMU	126	33.00
ACC	52.00	Florida State	4	48.00	Wake Forest	105	53.00
Big 12	31.60	Kansas State	4	27.60	Kansas	74	42.40
Big Ten	48.79	Nebraska	17	31.79	Purdue	84	35.21
CUSA	84.92	Marshall	8	76.92	North Texas	124	39.08
MAC	100.00	Toledo	72	28.00	Eastern Michigan	120	20.00
MWC	70.25	Colorado State	23	47.25	UNLV	115	44.75
Pac-12	39.92	Oregon	18	21.92	Colorado	76	36.08
SEC	26.29	Mississippi State	1	25.29	Vanderbilt	96	69.71
Sun Belt	100.45	Arkansas State, UL Lafayette (tie)	56	44.45	Georgia State	128	27.55

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 own an AP rank of 13 and a CTR rank of 37, a full 24 spot difference, and have now won this award twice in a row. Their closest competition this week was Wisconsin, who was hardly within their range (AP 25, CTR 40, difference of 15). OSU has been near the top for this award for much of the season, but a win this week in East Lansing would likely change that for good.

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:
Louisiana Tech, Oklahoma State (tie)

Notes:
The Bulldogs and Cowboys are currently tied at 15 in the CTR. Given that they've only lost to super-cluster teams, they will remain in the top 16 until that changes. Among those outside the super-cluster, CTR 26 Boise State is the highest ranked team without a vote in the AP.

KANSAS STATE WIN PATHS

As no super-cluster teams lost last week, K-State didn't pick up win paths to any new teams. Their average path length decreased from 4.39 to 4.07 games. The shorter paths manifest themselves as a fatter win path diagram, which you can see below. As always, you can use the following depth list to help you find any team you choose.

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 International, Georgia State, Houston, Indiana, UL Lafayette, Maryland, Massachusetts, Northwestern, Pittsburgh, Purdue, Rice, South Carolina, SMU, Tulane, UNLV, Utah State, Western Kentucky, Western Michigan
• Level 4: Air Force, Akron, Army, Boston College, Bowling Green, Buffalo, BYU, Connecticut, East Carolina, Florida Atlantic, Fresno State, Georgia, Hawaii, Idaho, Illinois, Kent State, UL Monroe, Memphis, Miami (Oh), Missouri, Navy, Northern Illinois, Ohio, Penn State, South Alabama, South Florida, Syracuse, TCU, Temple, Troy, Texas State, UAB, Vanderbilt, Virginia Tech, Wake Forest, Wisconsin
• 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, Wyoming
• Level 6: Arizona, Colorado, Colorado State, Georgia Southern, Georgia Tech, Louisville, Michigan, Nevada, Oregon State, Stanford, Washington State
• Level 7: California, Miami (Fl), Oregon, Utah, Washington
• Level 8: Duke, Michigan State, UCLA
• Level 9: Arizona State, Nebraska
• No Path: Alabama, Auburn, Florida State, LSU, Mississippi, Marshall, Mississippi State, Notre Dame, Texas A&M