Sub-Subdivisions

Power howmany?
January 13, 2019

No conference declared they were a member of a "power 5" cabal, it was observed that division 1A seemed to be divided into two classes. These became known as "the Power 5 conferences (plus Notre Dame)" and "the Group of Five (plus Independents)."

The conventional definition would have the Power 5 be the ACC, B1G, Big 12, Pac 12 and SEC (plus Notre Dame) with the Group of 5 comprised of the AAC, CUSA, MAC, Mountain West and Sun Belt (plus the remaining Independents.) This is convenient since there are 65 teams in each collection, but whether it is the correct partition is subject to analysis.

We begin by noting again that the notion of conference quality has no inherent meaning: conferences don't play the games. We ascribe such by measuring the "quality" of conferences' constituent teams. There are a lot of possible ways to do that, but all of them can be subsumed by letting the 82 (as I write) computer rating systems curated by Ken Massey at the College Football Ranking Composite.

One of the pages I produce from Dr. Massey's compilation is Computer Rank Analysis by Conference Affiliation. It contains four reports that we can use to find a natural partition of the 130-team field into two subsets.

Rank Distribution by Conference

Assign each of the 10660 rank assignments to the conference with which the team is associated. Report the average and Bucklin Majority of the ranks assigned to each conference, and a histogram count of ranks in 25-rank-wide "buckets."
Note

• The average is not quite that reported on Dr. Massey's page for conferences because I only include computer systems that rank all 130 teams.
• "Bucklin Majority" is the best rank worse than 50 per cent of the ranks. For example, 82×14 = 1148 for the 14-team conferences so we take the 575^th-best rank.

#Tms #Ranks Buck Avg Conf 1-25 26-50 51-75 76-100 101-125 126+ 1 82 4 5.02 ND 82 0 0 0 0 0 14 1148 20 32.60 SEC 642 207 164 83 52 0 10 820 42 44.40 B12 223 290 184 88 35 0 14 1148 44 48.50 B1G 339 356 217 118 109 9 14 1148 48 52.20 ACC 163 464 301 98 118 4 12 984 54 55.07 P12 242 214 233 207 86 2 12 984 85 77.27 MW 163 85 122 264 343 7 12 984 86 80.00 AAC 110 80 196 294 226 78 5 410 100 84.06 Ind 40 49 75 42 176 28 10 819 92 84.25 SBC 40 140 108 219 287 25 12 984 90 91.42 MAC 1 76 211 279 325 92 14 1148 93 92.04 CUSA 5 90 242 356 291 164

There are five conferences (plus Notre Dame) where the average and Bucklin measures are ≤ 65, so qualify for being in "the top half." The difference between the worst of those and the best of the rest is large enough to qualify as a discriminator and if we use that criterion we get the conventional definition.

Conference Rank Distribution by "grade"

This is a pure histogram that counts the number of conference teams that fall within buckets that correspond to what would be expected if team quality as measured by the computer rankings is normally distributed.

1-3 4-9 10-21 22-40 41-90 91-109 110-121 122-127 128+ Conf A+ A B C+ C C− D E F ND 0 1 0 0 0 0 0 0 0 SEC 1 2 4 3 3 1 0 0 0 B1G 0 2 2 2 6 1 1 0 0 B12 0 1 1 3 4 1 0 0 0 ACC 1 0 1 2 8 2 0 0 0 P12 0 0 2 3 6 0 1 0 0 MW 0 0 1 2 4 2 3 0 0 Ind 0 0 0 1 1 2 0 1 0 AAC 0 0 1 1 4 3 2 0 1 SBC 0 0 0 1 4 2 2 1 0 CUSA 0 0 0 0 7 2 2 2 1 MAC 0 0 0 0 6 2 2 1 1

The only obvious discriminator in this report is number of teams who fall into the E and F buckets. Six conferences have none of those - the Power 5 and the Mountain West.

Team Consensus Ranks by Conference

Here we assign team ranks based upon the "Bucklin Majority" ranking for the team. With 82 computers "voting", for each team assign the team the 42^nd-best rank. Then characterize the conference by the n^th-best team rank, where n is the best rank worse than half the conferences' teams rank.

#Tms Conf #Top10 #Top25 Maj Team Consensus Ranks 1 ND 1 1 4 4                           14 SEC 4 9 24 2 5 9 10 11 14 19 24 25 38 52 63 72 106 10 B12 1 3 46 5 16 23 33 40 46 55 61 67 98         14 B1G 2 4 47 4 8 18 20 29 38 43 47 50 65 66 73 101 116 14 ACC 1 2 51 1 18 32 38 41 42 45 51 53 55 69 70 104 107 12 P12 0 3 60 14 16 25 29 36 51 60 67 82 85 88 110     12 MW 0 2 90 17 25 26 72 80 81 90 91 108 112 113 119     12 AAC 0 1 91 13 29 57 69 76 77 91 97 103 113 114 129     12 MAC 0 0 91 48 58 72 77 82 83 91 109 112 121 125 128     14 CUSA 0 0 92 44 63 67 72 75 86 90 92 101 116 117 122 127 130 10 SBC 0 0 96 27 45 47 71 89 96 101 118 120 123         5 Ind 0 0 101 26 58 101 108 124

A reasonable criterion for a partition would be that at least half the conference's teams fall in the top half of the field - ranked 65^th or better. For the 2018 season we get the conventional composition.

Pairwise Comparison of Teamranks by Conference

This is the most comprehensive of the reports, as it is a true "top to bottom" measurement. For each team in each conference compare its rank to every team not in its conference and count the number of times it has a better rank. The value in (row,column) is 1000× the percentage that row-conference's team is ranked better than column-conference's team.

All% ND SEC B12 B1G ACC P12 MW AAC Ind SBC MAC CUSA 981 ND ∗ 929 1000 964 929 1000 1000 1000 1000 1000 1000 1000 794 SEC 71 ∗ 646 656 702 738 857 857 871 871 926 923 683 B12 0 354 ∗ 529 575 592 775 800 800 810 900 904 652 B1G 36 344 471 ∗ 546 568 726 759 750 771 857 857 624 ACC 71 298 425 454 ∗ 515 720 747 743 754 875 857 590 P12 0 262 408 432 485 ∗ 698 712 717 750 795 824 392 MW 0 143 225 274 280 302 ∗ 514 567 575 608 613 368 AAC 0 143 200 241 253 288 486 ∗ 533 525 583 589 357 Ind 0 129 200 250 257 283 433 467 ∗ 470 575 564 347 SBC 0 129 190 229 246 250 425 475 530 ∗ 583 561 267 MAC 0 74 100 143 125 205 392 417 425 417 ∗ 515 260 CUSA 0 77 96 143 143 176 387 411 436 439 485 ∗

The All% column represents the number of times out of a thousand trials that a random choice from the row-conference would be expected to have a better rank than a random choice from all the teams not in that conference. Again, there's a natural criterion for inclusion in the "power" category, namely All% > 500.

So in all of the ways we've characterized conferences we have a natural dividing line between "power" and non-"power" conferences. In all cases we get the same "power" five, and by any of these criteria the AAC isn't even the best of the rest!

More Granularity

ConfDiv	Best
ND	4
SEC West	2	9	11	19	25	72	106
SEC East	5	10	14	24	38	52	63
P12 North	14	16	25	36	60	110
B1G East	4	8	18	43	65	66	116
ACC Atlantic	1	18	32	45	53	69	107
B12	5	16	23	33	40	46	55	61	67	98
B1G West	20	29	38	47	50	73	101
SBC East	27	45	47	101	120
ACC Coastal	38	41	42	51	55	70	104
P12 South	29	51	67	82	85	88
MW Western	17	72	81	90	108	119
CUSA West	44	72	86	90	122	127	130
AAC East	13	29	57	91	114	129
MW Mountain	25	26	80	91	112	113
MAC West	72	82	83	91	112	128
CUSA East	63	67	75	92	101	116	117
SBC West	71	89	96	118	123
AAC West	69	76	77	97	103	113
Ind	26	58	101	108	124
MAC East	48	58	77	109	121	125

Mrnk

Brnk

ConfDiv

Teams

4

4

ND

Notre Dame

19

2

SEC West

Alabama

LSU

Texas A&M

Mississippi State

Auburn

Mississippi

Arkansas

24

5

SEC East

Georgia

Florida

Kentucky

Missouri

South Carolina

Vanderbilt

Tennessee

36

14

P12 North

Washington State

Washington

Stanford

Oregon

California

Oregon State

43

4

B1G East

Ohio State

Michigan

Penn State

Michigan State

Maryland

Indiana

Rutgers

45

1

ACC Atlantic

Clemson

Syracuse

North Carolina State

Boston College

Wake Forest

Florida State

Louisville

46

5

B12

Oklahoma

Texas

West Virginia

Iowa State

Oklahoma State

TCU

Baylor

Texas Tech

Kansas State

Kansas

47

20

B1G West

Iowa

Northwestern

Wisconsin

Minnesota

Purdue

Nebraska

Illinois

47

27

SBC East

Appalachian State

Troy

Georgia Southern

Coastal Carolina

Georgia State

51

38

ACC Coastal

Duke

Pittsburgh

Virginia

Miami-Florida

Georgia Tech

Virginia Tech

North Carolina

82

29

P12 South

Utah

Arizona State

Southern California

Arizona

UCLA

Colorado

90

17

MW Western

Fresno State

Nevada

San Diego State

Hawaii

UNLV

San Jose State

90

44

CUSA West

UAB

North Texas

Louisiana Tech

Southern Miss

Texas-San Antonio

Rice

UTEP

91

13

AAC East

UCF

Cincinnati

Temple

South Florida

East Carolina

Connecticut

91

25

MW Mountain

Utah State

Boise State

Wyoming

Air Force

Colorado State

New Mexico

91

72

MAC West

Northern Illinois

Eastern Michigan

Toledo

Western Michigan

Ball State

Central Michigan

92

63

CUSA East

Marshall

Middle Tenn State

Florida Intl

Florida Atlantic

UNC-Charlotte

Old Dominion

Western Kentucky

96

71

SBC West

Arkansas State

UL Lafayette

UL Monroe

South Alabama

Texas State

97

69

AAC West

Memphis

Houston

Tulane

SMU

Navy

Tulsa

101

26

Ind

Army

BYU

Liberty

Massachusetts

New Mexico State

109

48

MAC East

Ohio

Buffalo

Miami-Ohio

Akron

Bowling Green

Kent State

Suppose we ignore the computers and just look at inter-conference division records. The AAC East actually performed better in 2018 than three of the P5 conference divisions …

%	W	L	Cdiv	ND	SEC E	B12	SEC W	ACC A	P12 N	SBC E	B1G E	AAC E	B1G W	MW M	MW W	Ind	ACC C	CUSA E	P12 S	MAC E	CUSA W	AAC W	MAC W	SBC W
0.923	12	1	ND		1-0	0-0	0-0	3-1	1-0	0-0	1-0	0-0	1-0	0-0	0-0	0-0	2-0	0-0	1-0	0-0	0-0	1-0	1-0	0-0
0.735	36	13	SEC East	0-1		0-4	9-6	2-1	0-0	1-0	2-0	0-0	1-0	2-0	1-0	1-0	1-1	4-0	0-0	1-0	1-0	1-0	1-0	0-0
0.722	26	10	B12	0-0	4-0		0-3	0-1	1-1	0-0	1-2	0-0	0-1	1-0	0-0	1-0	0-1	1-0	2-0	1-0	2-0	3-0	1-0	1-0
0.714	35	14	SEC West	0-0	6-9	3-0		2-2	1-0	0-0	0-0	1-0	1-1	0-1	0-0	1-0	1-0	0-0	0-0	1-0	5-1	1-0	0-0	5-0
0.708	34	14	ACC Atlantic	1-3	1-2	1-0	2-2		0-0	2-0	0-0	3-0	0-1	0-0	0-0	1-0	9-6	2-0	0-0	0-0	1-0	2-0	2-0	0-0
0.688	33	15	P12 North	0-1	0-0	1-1	0-1	0-0		0-0	1-2	0-0	0-0	1-0	3-1	2-0	2-0	0-0	16-9	1-0	0-0	0-0	0-0	0-0
0.651	28	15	SBC East	0-0	0-1	0-0	0-0	0-2	0-0		0-1	0-0	1-0	0-1	0-0	3-1	0-0	2-0	0-0	1-0	1-0	0-1	1-1	14-7
0.617	29	18	B1G East	0-1	0-2	2-1	0-0	0-0	2-1	1-0		0-1	12-10	1-0	0-0	0-0	2-0	1-0	0-1	2-1	0-0	2-0	3-0	1-0
0.587	27	19	AAC East	0-0	0-0	0-0	0-1	0-3	0-0	0-0	1-0		1-0	0-1	0-0	1-1	4-1	2-1	1-0	2-1	0-0	11-8	0-0	0-0
0.542	26	22	B1G West	0-1	0-1	1-0	1-1	1-0	0-0	0-1	10-12	0-1		1-0	1-0	1-1	2-1	1-0	1-1	2-1	0-0	0-0	1-1	0-0
0.523	23	21	MW Mountain	0-0	0-2	0-1	1-0	0-0	0-1	1-0	0-1	1-0	0-1		9-10	5-2	0-0	0-1	0-1	0-0	1-0	1-0	0-0	0-0
0.521	25	23	MW Western	0-0	0-1	0-0	0-0	0-0	1-3	0-0	0-0	0-0	0-1	10-9		0-3	0-0	0-0	3-1	0-1	2-1	1-0	2-1	1-1
0.500	25	25	Ind	0-0	0-1	0-1	0-1	0-1	0-2	1-3	0-0	1-1	1-1	2-5	3-0		0-2	2-1	1-1	2-1	1-1	2-0	2-1	0-2
0.500	24	24	ACC Coastal	0-2	1-1	1-0	0-1	6-9	0-2	0-0	0-2	1-4	1-2	0-0	0-0	2-0		2-1	0-0	2-0	0-0	0-0	1-0	0-0
0.478	22	24	CUSA East	0-0	0-4	0-1	0-0	0-2	0-0	0-2	0-1	1-2	0-1	1-0	0-0	1-2	1-2		0-0	1-0	9-6	0-0	2-0	0-0
0.422	19	26	P12 South	0-1	0-0	0-2	0-0	0-0	9-16	0-0	1-0	0-1	1-1	1-0	1-3	1-1	0-0	0-0		0-0	1-0	0-1	1-0	0-0
0.422	19	26	MAC East	0-0	0-1	0-1	0-1	0-0	0-1	0-1	1-2	1-2	1-2	0-0	1-0	1-2	0-2	0-1	0-0		0-0	0-0	9-10	0-0
0.413	19	27	CUSA West	0-0	0-1	0-2	1-5	0-1	0-0	0-1	0-0	0-0	0-0	0-1	1-2	1-1	0-0	6-9	0-1	0-0		2-1	1-0	2-1
0.404	19	28	AAC West	0-1	0-1	0-3	0-1	0-2	0-0	1-0	0-2	8-11	0-0	0-1	0-1	0-2	0-0	0-0	1-0	0-0	1-2		0-0	2-1
0.404	19	28	MAC West	0-1	0-1	0-1	0-0	0-2	0-0	1-1	0-3	0-0	1-1	0-0	1-2	1-2	0-1	0-2	0-1	10-9	0-1	0-0		0-0
0.395	17	26	SBC West	0-0	0-0	0-1	0-5	0-0	0-0	7-14	0-1	0-0	0-0	0-0	1-1	2-0	0-0	0-0	0-0	0-0	1-2	1-2	0-0

W%	W	L	Conf	ND	SEC	B12	ACC	B1G	P12	SBC	MW	IND	AAC	CUSA	MAC
0.923	12	1	ND		1-0	0-0	5-1	2-0	2-0	0-0	0-0	0-0	1-0	0-0	1-0
0.824	56	12	SEC	0-1		3-4	6-4	4-1	1-0	6-0	3-1	2-0	3-0	10-1	3-0
0.722	26	10	B12	0-0	4-3		0-2	1-3	3-1	1-0	1-0	1-0	3-0	3-0	2-0
0.652	43	23	ACC	1-5	4-6	2-0		1-5	0-2	2-0	0-0	3-0	6-4	5-1	5-0
0.647	33	18	B1G	0-2	1-4	3-1	5-1		3-3	2-1	3-0	1-1	2-2	2-0	8-3
0.628	27	16	P12	0-2	0-1	1-3	2-0	3-3		0-0	6-4	3-1	0-2	1-0	2-0
0.545	24	20	SBC	0-0	0-6	0-1	0-2	1-2	0-0		1-2	5-1	1-3	4-2	2-1
0.537	29	25	MW	0-0	1-3	0-1	0-0	0-3	4-6	2-1		5-5	3-0	3-2	2-2
0.500	25	25	Ind	0-0	0-2	0-1	0-3	1-1	1-3	1-5	5-5		3-1	3-2	4-2
0.491	27	28	AAC	0-1	0-3	0-3	4-6	2-2	2-0	3-1	0-3	1-3		3-3	2-1
0.419	26	36	CUSA	0-0	1-10	0-3	1-5	0-2	0-1	2-4	2-3	2-3	3-3		4-0
0.352	19	35	MAC	0-1	0-3	0-2	0-5	3-8	0-2	1-2	2-2	2-4	1-2	0-4

All hail the "Power 8"!

I don't blame them for recognizing that "We're about the same as CUSA" doesn't carry the same weight as "we're one of the power 6", but that latter bit is just wishful thinking, and false advertising.