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College Football Transitivity Rankings & Awards - Week 9

After toiling away in Fanposts for a few weeks, we've taken notice of Jeff's fantastic work. We welcome him to the BOTC staff with his Transitivity Rankings following week 9.

The Cats are tied for fourth in this week's version of the rankings.
The Cats are tied for fourth in this week's version of the rankings.
Peter G. Aiken-US PRESSWIRE

It was a relatively calm week in the world of college football, but that doesn't mean all was peaceful in Transitive Land. This week, we see LSU rise, Minnesota tumble, and our Wildcats pull themselves into a three-way tie for fourth in the CTR. If you're new to the Transitivity Rankings, you'll want to read this introductory post to get the basics. For the rest of you, here's the quick glossary in case your memory needs jogging:

  • 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.

Now that everyone's (re)calibrated, let's take a look at this week's Combined Transitivity 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 1 124 3.847 0 NaN 7 0
2 Auburn Arrow_up1 3.0 2 4 123 3.537 1 1.000 6 1
3 LSU Arrow_up11 5.0 3 7 121 3.810 2 1.000 6 2
4 Florida State Arrow_up1 6.0 11 1 114 3.737 0 NaN 6 0
4 Kansas State Arrow_up2 6.0 6 6 118 4.390 2 1.500 5 1
4 Mississippi Arrow_down2 6.0 4 8 120 3.517 3 1.667 7 1
7 Alabama Arrow_down3 7.0 5 9 119 3.882 4 2.250 7 1
8 Marshall - 7.5 14 1 112 4.848 0 NaN 7 0
9 Notre Dame Arrow_down2 8.0 12 4 112 3.884 1 1.000 6 1
10 TCU Arrow_down2 9.0 7 11 117 4.325 9 3.667 5 1
11 Oklahoma Arrow_down1 10.0 8 12 117 4.402 9 3.000 5 2
12 Baylor Arrow_down1 11.0 10 12 117 4.504 9 3.000 5 1
13 Texas A&M Arrow_down1 11.5 13 10 112 4.330 5 1.600 4 3
13 West Virginia Arrow_down1 11.5 9 14 117 4.427 9 2.333 5 2
15 Louisiana Tech Arrow_up2 15.5 16 15 112 5.839 10 3.300 5 2
15 Oklahoma State Arrow_up1 15.5 15 16 112 4.902 11 2.545 4 3
17 Nebraska Arrow_up3 19.5 21 18 111 3.811 115 9.139 6 1
18 Michigan State - 20.0 19 21 111 3.694 115 8.200 6 1
19 Georgia Arrow_up2 21.5 18 25 111 3.595 115 7.365 6 1
20 Oregon Arrow_down2 22.5 17 28 111 3.477 115 7.261 6 1
21 UCLA - 24.5 20 29 111 3.766 115 7.200 6 2
22 Clemson Arrow_up1 26.0 32 20 111 4.279 115 8.226 5 2
23 Utah Arrow_up6 31.0 26 36 111 4.126 115 6.548 5 1
24 Arizona Arrow_up1 32.0 22 42 111 3.964 115 6.296 6 1
24 Georgia Tech Arrow_up10 32.0 27 37 111 4.135 115 6.452 5 2
26 Arizona State Arrow_up4 33.0 43 23 111 4.622 115 8.165 5 1
26 Colorado State Arrow_down2 33.0 34 32 111 4.324 115 7.096 6 1
26 South Carolina Arrow_up6 33.0 25 41 111 4.099 115 6.383 3 4
29 Duke Arrow_down4 33.5 43 24 111 4.622 115 7.391 5 1
30 Miami (Fl) Arrow_up5 36.0 33 39 111 4.288 115 6.409 4 3
31 Boise State Arrow_up6 37.0 29 45 111 4.216 115 6.122 6 2
31 East Carolina Arrow_up5 37.0 47 27 111 4.667 115 7.330 5 1
33 Iowa Arrow_down6 38.0 24 52 111 4.054 115 5.904 4 2
34 Kentucky Arrow_down3 39.0 53 25 111 4.739 115 7.365 4 3
35 Ohio State Arrow_up2 40.0 23 57 111 4.045 115 5.748 6 1
35 Washington Arrow_up4 40.0 49 31 111 4.703 115 7.104 4 3
37 California Arrow_down4 41.0 49 33 111 4.703 115 6.957 3 4
38 Arkansas Arrow_up7 43.5 66 21 111 5.180 115 8.200 3 4
39 Louisville Arrow_up2 44.0 37 51 111 4.495 115 5.939 5 2
39 Minnesota Arrow_down24 44.0 40 48 111 4.595 115 6.017 5 2
39 Wisconsin Arrow_up28 44.0 38 50 111 4.586 115 5.957 4 2
42 Missouri - 45.0 28 62 111 4.162 115 5.609 5 2
42 Nevada Arrow_down3 45.0 41 49 111 4.604 115 6.009 3 3
44 Maryland Arrow_down16 45.5 35 56 111 4.477 115 5.800 4 3
44 Stanford Arrow_up3 45.5 48 43 111 4.685 115 6.217 4 3
46 Utah State Arrow_down4 46.5 49 44 111 4.703 115 6.183 4 3
47 Iowa State Arrow_down5 47.5 55 40 111 4.811 115 6.400 2 4
48 Florida Arrow_up1 48.0 58 38 111 5.018 115 6.435 3 3
49 USC Arrow_down4 51.0 36 66 111 4.486 115 5.322 5 3
50 Tennessee Arrow_down1 52.0 74 30 111 5.514 115 7.113 2 5
51 Texas Tech Arrow_down3 52.5 86 19 111 5.982 115 8.704 2 5
52 North Carolina Arrow_up7 54.5 45 64 111 4.631 115 5.557 3 4
53 UTEP Arrow_up3 56.0 95 17 111 6.468 115 9.478 4 3
53 Virginia Tech Arrow_up1 56.0 30 82 111 4.252 115 4.783 3 4
55 Virginia Arrow_down6 57.0 38 76 111 4.586 115 5.061 3 4
56 Rutgers Arrow_up8 58.0 63 53 111 5.144 115 5.878 4 3
57 BYU Arrow_down4 59.0 42 76 111 4.613 115 5.061 4 4
58 Northwestern Arrow_up9 61.0 46 76 111 4.658 115 5.061 2 4
59 Penn State Arrow_down3 61.5 54 69 111 4.766 115 5.243 4 3
60 Washington State Arrow_up1 62.5 62 63 111 5.099 115 5.574 1 6
61 Air Force Arrow_up5 63.5 56 71 111 4.955 115 5.226 4 2
61 UL Lafayette Arrow_up54 63.5 92 35 111 6.369 115 6.870 3 3
63 Arkansas State Arrow_down11 65.0 75 55 111 5.541 115 5.843 3 3
63 Illinois Arrow_up30 65.0 57 73 111 4.982 115 5.157 3 4
65 Central Florida - 66.0 67 65 111 5.198 115 5.391 4 2
66 Pittsburgh Arrow_down8 66.5 30 103 111 4.252 115 4.148 3 4
67 Texas Arrow_up3 68.0 75 61 111 5.541 115 5.617 3 5
68 Boston College Arrow_down6 68.5 52 85 111 4.730 115 4.722 4 3
68 Michigan Arrow_down6 68.5 77 60 111 5.550 115 5.626 3 5
70 Kansas Arrow_up7 69.5 85 54 111 5.955 115 5.870 1 5
70 South Alabama Arrow_up3 69.5 106 33 111 7.865 115 6.957 5 2
72 Indiana Arrow_up3 70.0 60 80 111 5.072 115 4.852 2 4
73 Oregon State Arrow_down1 70.5 94 47 111 6.414 115 6.035 3 3
73 Syracuse Arrow_down13 70.5 83 58 111 5.901 115 5.722 2 5
75 Toledo Arrow_up5 72.0 70 74 111 5.243 115 5.104 4 3
75 Wyoming Arrow_down2 72.0 63 81 111 5.144 115 4.800 2 5
77 Rice Arrow_down7 73.0 78 68 111 5.766 115 5.270 4 3
78 Northern Illinois Arrow_up1 73.5 65 82 111 5.171 115 4.783 5 2
79 Memphis Arrow_up4 75.5 82 69 111 5.883 115 5.243 3 3
80 Middle Tennessee State Arrow_down13 76.5 81 72 111 5.856 115 5.217 4 3
81 Colorado - 77.5 96 59 111 6.505 115 5.643 2 6
82 Georgia Southern Arrow_up1 79.0 112 46 111 8.748 115 6.078 5 2
82 Purdue Arrow_up13 79.0 69 89 111 5.225 115 4.626 2 5
84 Cincinnati Arrow_up2 79.5 84 75 111 5.937 115 5.096 4 3
85 Western Michigan Arrow_up2 81.0 72 90 111 5.306 115 4.565 4 3
86 Bowling Green Arrow_down4 82.0 68 96 111 5.216 115 4.409 4 3
87 Central Michigan Arrow_up1 82.5 58 107 111 5.018 115 4.035 4 4
88 North Carolina State Arrow_up1 84.0 101 67 111 7.081 115 5.313 3 4
89 Akron Arrow_down11 84.5 61 108 111 5.090 115 4.017 3 4
90 San Jose State Arrow_down35 86.0 87 85 111 6.027 115 4.722 2 4
90 Western Kentucky Arrow_up5 86.0 70 102 111 5.243 115 4.270 3 4
92 Hawaii Arrow_down1 88.5 89 88 111 6.099 115 4.652 1 5
93 Florida Atlantic Arrow_down4 90.0 79 101 111 5.811 115 4.339 3 5
94 UAB - 90.5 88 93 111 6.045 115 4.470 3 4
95 Ball State Arrow_up6 91.0 73 109 111 5.333 115 3.800 2 4
95 Houston Arrow_up4 91.0 91 91 111 6.360 115 4.539 3 3
97 San Diego State Arrow_up1 92.0 97 87 111 6.568 115 4.696 3 3
98 Ohio Arrow_down1 92.5 79 106 111 5.811 115 4.078 3 5
99 Navy Arrow_up10 95.0 93 97 111 6.378 115 4.400 3 4
100 UL Monroe Arrow_down25 95.5 107 84 111 7.946 115 4.765 3 4
101 Vanderbilt Arrow_up1 96.0 113 79 111 9.045 115 4.913 1 6
102 Old Dominion Arrow_down11 97.0 99 95 111 6.649 115 4.461 2 5
103 Wake Forest Arrow_down20 97.5 102 93 111 7.207 115 4.470 1 6
104 UTSA Arrow_down4 100.0 100 100 111 6.892 115 4.374 2 6
105 Army Arrow_up2 100.5 90 111 111 6.252 115 3.548 2 4
106 New Mexico Arrow_down2 101.0 105 97 111 7.784 115 4.400 2 5
107 Florida International Arrow_down5 101.5 98 105 111 6.640 115 4.087 2 4
108 Temple Arrow_down2 103.0 115 91 111 9.703 115 4.539 3 3
109 Fresno State Arrow_down4 104.0 104 104 111 7.261 115 4.139 2 5
110 Texas State Arrow_up8 105.0 111 99 111 8.649 115 4.391 3 3
111 Kent State Arrow_down2 109.0 103 115 111 7.225 115 3.296 1 7
112 Miami (Oh) - 110.0 108 112 111 8.135 115 3.530 2 6
112 UNLV Arrow_down4 110.0 110 110 111 8.243 115 3.670 1 6
114 Massachusetts Arrow_down3 112.0 108 116 111 8.135 115 3.252 2 7
115 Buffalo Arrow_down2 114.0 114 114 111 9.108 115 3.400 1 5
116 Eastern Michigan Arrow_down2 114.5 116 113 111 10.081 115 3.452 1 6
117 Southern Miss Arrow_down1 117.0 117 117 6 2.167 116 5.241 2 5
118 South Florida Arrow_down1 118.0 118 118 3 1.333 116 4.716 2 5
119 Appalachian State - 119.5 119 120 3 2.000 117 4.897 1 4
119 Idaho Arrow_up3 119.5 120 119 2 1.500 116 3.879 1 6
121 Tulsa Arrow_up2 121.0 120 122 2 1.500 117 3.897 1 6
122 North Texas Arrow_down2 122.0 123 121 1 1.000 117 4.162 1 6
123 Troy Arrow_down3 122.5 120 125 2 1.500 118 4.178 1 6
124 Tulane Arrow_up1 123.5 123 124 1 1.000 118 4.381 1 5
125 SMU Arrow_down1 124.5 126 123 0 NaN 118 4.390 0 7
126 New Mexico State - 125.0 123 127 1 1.000 120 3.567 1 6
127 Connecticut - 126.0 126 126 0 NaN 119 4.168 0 6
128 Georgia State - 127.0 126 128 0 NaN 121 3.876 0 7

Some thoughts:

  • LSU is the big winner of the week, jumping up 11 spots to number 3 following their upset victory over Ole Miss. You may balk at a two-loss team so high in the rankings, and I don't necessarily disagree. But their only losses have come to Mississippi State and Auburn (CTR numbers 1 and 2), and they own perhaps the best victory of the season so far.
  • Minnesota was hurt badly by their loss to Illinois, dropping 24 spots from number 15 last week to this week's 39. This is actually pretty explainable when considering how the CTR works. More on this later.
  • Our biggest jumper of the week is Louisiana-Lafayette, whose win over Arkansas State had more impact than you may have anticipated. The victory moved the Ragin' Cajuns up from 115 to 61, a 54 spot jump. We'll come back to them as well.
  • The biggest drop was suffered by San Jose State, who fell 35 spots after a loss to Navy. The former Jekyll and Hyde Award winner is now much more Hyde, ranking 87 and 85 in the WTR and LTR, respectively.

CLUSTER WATCH

We're starting a new segment this week, which I'm calling the Cluster Watch. We're going to try to identify games that could have a large effect on the CTR, and along the way learn why the CTR has teams like Texas A&M and Oklahoma State ranked so highly.

Now, take another look at the rankings, and scroll somewhere towards the middle. See in the 7th and 9th columns, where every team displays the numbers 111 and 115? What's going on here? It's telling us that all of these teams have win paths to 111 different teams, and loss paths to 115 different teams. The teams in this group create what graph theorists call a strongly connected component. That is, choose any two teams in this group, and you will be able to find a win path from either team to the other. We'll call this group of teams the cluster.

Not every team is in the cluster, of course. The teams at the top of the rankings have more win paths and fewer loss paths than the cluster teams, and the opposite is true for teams at the bottom of the list. Then we can categorize every team into one of three groups: The cluster teams, the sub-cluster teams (teams with fewer win paths than the cluster teams), and the super-cluster teams (teams with more win paths than the cluster teams). In this weeks rankings, the super-cluster teams are the ones with rankings 1 through 15, while the sub-cluster teams are ranked 117 through 128.

A defining characteristic of the super-cluster teams is that they have beaten at least one cluster team, while no cluster team has beaten them. This means ultimately that every super-cluster team will always be ranked above the cluster teams. But, suppose a super-cluster team (call them Team A) loses to a cluster team (Team B). Then, not only does Team B earn a win path to Team A, but so does every other cluster team (since they all have paths to Team B, and Team B beat Team A). The result is that Team A (and any super-cluster team that has lost to Team A) is pulled into the cluster.

This phenomenon is responsible for a few different things. First, it tells us why Texas A&M and Oklahoma State are ranked so highly, even with three losses. Each of these losses came to a fellow super-cluster team, meaning they are safe from loss paths to cluster teams. Plus, they each own victories over every cluster team, so they also have more win paths than the cluster teams.

This also helps us understand why Minnesota fell so far. Their only loss prior to Saturday was to TCU, a fellow super-cluster team, so the Golden Gophers sat safely atop the cluster teams in the rankings. Once they lost to Illinois, they were thrust into the cluster where average path lengths are the only factor for separating teams. Their wins to date are decent but not excellent, so many stronger cluster teams jumped them in the rankings, explaining the large drop. Minnesota was the only super-cluster team to drop into the cluster this week.

A similar story explains Louisiana-Lafayette's rise. Last week they were the highest-ranked sub-cluster team. A victory over Arkansas State pushed them into the cluster, and above many of the lower-ranked cluster teams. Texas State similarly made the jump from sub-cluster to cluster this week. Incidentally, UL Lafayette beat the Bobcats earlier in the year, so the Cajuns would have left the sub-cluster with or without a victory on Saturday.

In the coming weeks, we'll use this space to track which teams have been absorbed into the cluster. We will also highlight games in the coming week whose results have a chance to relegate super-cluster teams to the cluster. This week, those games are:

  • Mississippi State vs. Arkansas
  • Florida State at Louisville
  • Notre Dame at Navy
  • Oklahoma at Iowa State
  • Baylor vs. Kansas
  • Texas A&M vs. Louisiana-Monroe
  • Louisiana Tech vs. Western Kentucky

Of course, these games aren't played in a vacuum, and the results of one game can send multiple teams down to the cluster. The most extreme example: Should Mississippi State lose it's game with Arkansas, the super-cluster will shrink from the current 16 teams to three! This is because the Bulldogs own win paths to every SEC school in the cluster (directly to Auburn, LSU, and TAMU, to Mississippi through LSU, and to Alabama through Mississippi), as well as to each Big 12 school through Auburn's win over K-State.

AWARDS

I spent a little more time than I wanted on that last section, so let's hustle through these 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:
UTEP

Notes:
The Miners take this award for the second week running. Their WTR of 95 and LTR of 17 make for a difference of 78 spots. This was just ahead of South Alabama's 73 spot difference between a WTR of 106 and LTR of 33.

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:
Temple, UTEP

Notes:
Both Eastern Michigan and Temple have shortest win paths to UTEP of length 16, longer than any other shortest paths this week. Temple's path takes the award by virtue of my questionably accurate tiebreaking system, which estimate's Temple's path at 7834 miles long, whereas Eastern Michigan's path was only 6669 miles. A representative path looks like this:

Temple > Vanderbilt > Massachusetts > Kent State > Army > Ball State > Central Michigan > Purdue > Western Michigan > Bowling Green > Indiana > Missouri > South Carolina > Georgia > Arkansas > Texas Tech > UTEP

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:
While the Eagles just missed out on the last award, they can rejoice in knowing that they've won the Frequent Flyer Award for the second week running. This week, their 111 paths total 1119 games. I'd be remiss if i didn't tie this back to our earlier discussion of cluster teams: we could probably redefine this award as going to the cluster team with the highest average win path length. In fact, just for fun, let's look at Eastern Michigan's win path diagram. We can see why their paths are so long, as we have to go seven layers down before getting to a level with more than two teams. Compare this with K-State's win path diagram (at the bottom of the article) to get a visual understanding of the difference between a good team and a not-so-good team, transitively speaking.

jeffp171/Bring on the Cats

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 Atlas trophy is starting to get comfortable in Huntington, where it's resided for the last three weeks. The Coattails trophy is starting to gather cobwebs in Nashville, where it's been since the first award was given in week 4. In the breakdown table, we see that the SEC has extended its lead on the Big 12 for smallest average conference ranking.

Conference Avg Conference Rank Atlas Atlas Rank Atlas Difference Coattail Hanger Coattail Rank Difference
AAC 97.91 East Carolina 31 66.91 Connecticut 127 29.09
ACC 50.43 Florida State 4 46.43 Wake Forest 103 52.57
Big 12 30.00 Kansas State 4 26.00 Kansas 70 40.00
Big Ten 48.79 Nebraska 17 31.79 Purdue 82 33.21
CUSA 81.69 Marshall 8 73.69 North Texas 122 40.31
MAC 97.00 Toledo 75 22.00 Eastern Michigan 116 19.00
MWC 73.92 Colorado State 26 47.92 UNLV 112 38.08
Pac-12 41.08 Oregon 20 21.08 Colorado 81 39.92
SEC 27.71 Mississippi State 1 26.71 Vanderbilt 101 73.29
Sun Belt 100.09 UL Lafayette 61 39.09 Georgia State 128 27.91
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 been within range for this award for most of the season, and have finally broken through. Their CTR rank of 35 is 22 spots below their AP ranking of 13. Their closest competition here is Oregon, whose CTR rank of 20 is 15 spots off of their number 5 AP rank. I imagine Ohio State may well retain this award should they beat Illinois next week, but their game in two weeks against Michigan State may do a lot to bring their AP and CTR rankings in line.

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:
Texas A&M

Notes:
I think we explained this one well enough in the Cluster Watch section. The number 13 Aggies take this award in front of fellow super-cluster member Louisiana Tech (15). The only other CTR top 25 team without a vote in the AP is Georgia Tech (24).

KANSAS STATE WIN PATHS

The Wildcats didn't pick up win paths to any new teams this week, but their average path length did improve from last week's 4.585 to this week's 4.390. Below, you will find the customary win path diagram, along with the handy depth guide. Have fun with it, and I'll see you next week.

jeffp171/Bring on the Cats

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