What do the numbers say?

The Bradley-Terry method applied to college football.

A couple of notes regarding the calculations. I use the Bradley-Terry method for determining the ratings. This is an iterative, statistical rating that computes a hypothetical round-robin winning percentage if all teams played each other. Clearly, that's not the case in college football, and this method gives infinite results if teams are undefeated. This problem is 'solved' for the sake of comparison by adding a fictitious tie to each team's record.

Further notes:

• Game results are pulled from the NCAAFootball.com.
• Blogpoll results are pulled from SBNation.
• There are a lot of explanatory notes and links; I put those at the end of the post so people who don't care about them can skip them and get right to the results. There is also a link to all my results.
• For brevity, I only listed the top 20 here. For those who are interested, I also listed Michigan's position, FYI.
• I release this after all the major polls come out to avoid 'influencing' anybody's vote.

To the numbers...

Through games of 2010.11.06
	Team	Rating	Previous	Delta	Blogpoll
1	Auburn	85.581	1	0	2
2	Oregon	38.314	4	2	1
3	T-C-U	37.076	3	0	3
4	Boise State	28.029	2	-2	4
5	L-S-U	27.484	5	0	5
6	Stanford	15.449	13	7	6
7	Oklahoma State	15.175	12	5	10
8	Nebraska	14.947	8	0	8
9	Michigan State	12.443	9	0	11
10	Wisconsin	12.340	11	1	7
11	Utah	9.372	7	-4	15
12	Virginia Tech	8.671	14	2	20
13	Iowa	8.383	17	4	13
14	Alabama	8.000	16	2	12
15	Arkansas	7.989	20	5	14
16	Miss State	7.656	19	3	18
17	Ohio State	7.608	18	1	9
18	Missouri	7.282	6	-12	17
19	Arizona	6.162	15	-4	16
20	Oklahoma	5.663	10	-10	19
--	--	--	--	--	--
29	Michigan	2.621	41	12	NR

Auburn is pulling away as the number one team. Oregon has finally caught up with everybody's ranking due to strength of schedule, and Boise St. has begun to fall for the same reason. The bonus for being undefeated this far into the season is starting to balance out with perceived strength of schedule, as LSU is nipping at the Broncos heels.

As a point of comparison, it lines up really well with the blogpoll.  Two outliers:  blogpollers really like Ohio State, and they really dislike Virginia Tech (see discussion of limitations, below).

There's a pretty significant drop-off from #5 LSU to #6 Stanford, and another notable drop-off from #10 Wisconsin to #11 Utah. I think this supports the notion that a 16-team tournament would be sufficient to include all the top teams. If you're in the muddle around 16, there really isn't all that much to complain about if you're left out.

The conference breakdown in the top 10 and top 16 (non-BCS conferences in parentheses):

Conference	Top 10	Top 16
SEC:	2	5
Big Ten:	2	3
Big 12:	2	2
Pac 10:	2	2
(MWC):	1	2
ACC:	0	1
(WAC):	1	1
Big East:	0	0
(Conference USA):	0	0
(Independent):	0	0
(MAC):	0	0
(Sun Belt):	0	0

The top 10 has roughly equal representation from the BCS conferences. Looking at the top 16, a bias toward the SEC begins to emerge, with 5 teams, including those in spots 14-16. Not surprisingly, the Big East is absent, and the ACC is, well, underrepresented. TCU, Boise St. and Utah are ranked above all comers from these conferences, including Virginia Tech, who lost to Boise St. and, as we all know, James Madison. The nagging question remains: how do you compare the relative strengths of conferences when they don't play each other?

The next few weeks should be interesting.

Technical notes

I explained the mathematics of the calculations in much more detail last year. Wikipedia has a nice explanation of the foundation of the Bradley-Terry method.

Discussion of limitations

Many of the strengths of this method are addressed at U.S. College Hockey Online.

That said, there's always a bit of resistance when I post this rating. It's one additional data point. It's not even my opinion, and it doesn't mean your team is better or worse than you think it is. It attempts to look objectively at how teams would fare, should they play every other team. There are some limitations, namely the infinite results, and incomparability, of undefeated teams. As with any statistical calculation, sample size is important; while there are only ~12 games per team, there are ~120 teams. One could argue the merits of using any sort of statistical calculation on said sample. Also, it should be pointed out that games against FCS teams are ignored. This is a double-edged sword: teams don't get credit for beating up on FCS teams, but Virginia Tech effectively gets a pass for losing to James Madison.

Brian pointed out another interesting anomaly (it's the double star at the very bottom) in last year's end-of-season college hockey KRACH. A similar effect can be seen in this rating, as discussed above. So, why does this happen? Like college football, there's little overlap between conferences, teams tend to get compartmentalised.

As with any tool, it's only as good as its user; we can't blindly take the results as fact. One possible solution is to take the top 30 teams at the end of the season and run a KRACH on only those teams. Although, for any hypothetical tournament, I would strongly support the inclusion of all conference champions.

What if I want to see the entire rating, and results for each week?

All the results are available, if you'd like to see the numbers yourself. As I said last year, John Whelan freely gave me the perl script in 1998 to calculate KRACH for ACHA club hockey teams, so I'm happy to share the script and input data if you don't want to write it yourself. And I am fallible. There's a lot of data to crunch, and I copied and pasted from the NCAA site; there may be errors. If you find one, please bring it to my attention and I'll make the fix posthaste.

Not much movement at the top:

• Texas overtakes TCU
• Oregon and Georgia Tech swap
• LSU jumps 7 spots after a similar fall last week.
• USC jumps 7 spots after beating UCLA
• BYU is up 10 spots after knocking off Utah
• Pittsburgh drops 10 spots after losing to West Virginia

If you're interested in checking out different scenarios for this week's games, I put together a script that lets you pick the games and see the resultant effects on the ratings.  The script can be found at http://quakk.co.cc/cfb/pick.php. 

Interestingly, I don't think there's any way Florida or Alabama falls further than 4th;  and they end up with the top 2 SOS rankings by a significant margin (the SEC takes 6 of the top 7 spots here).  EDIT:  If all the underdogs win this week, Alabama and Florida end up 1 and 2, respectively.

This week's top 20:

Team	Pvs	+/-	Rank	KRACH	RRWP	Record Rank	W	L	T	Win %	SOS Rank	SOS
Alabama	1	0	1	63.764	0.960	1	11	0	0	1.000	6	2.772
Florida	2	0	2	54.767	0.955	1	11	0	0	1.000	11	2.381
Cincinnati	3	0	3	36.668	0.937	1	10	0	0	1.000	32	1.746
Texas	5	1	4	31.291	0.929	1	12	0	0	1.000	52	1.252
TCU	4	-1	5	29.027	0.925	1	11	0	0	1.000	50	1.262
Boise State	6	0	6	27.779	0.922	1	11	0	0	1.000	53	1.208
Oregon	8	1	7	11.106	0.851	3	9	2	0	0.818	4	2.923
Georgia Tech	7	-1	8	7.822	0.814	3	9	2	0	0.818	19	2.058
LSU	16	7	9	7.745	0.813	5	9	3	0	0.750	5	2.853
Ohio State	10	0	10	6.409	0.791	2	10	2	0	0.833	37	1.526
Virginia Tech	11	0	11	6.347	0.790	5	9	3	0	0.750	12	2.339
Iowa	12	0	12	6.256	0.788	3	9	2	0	0.818	33	1.646
USC	20	7	13	5.493	0.771	6	8	3	0	0.727	14	2.262
Miami (FL)	15	1	14	5.280	0.766	6	8	3	0	0.727	16	2.174
Oregon State	19	4	15	5.262	0.765	7	7	3	0	0.700	9	2.456
Penn State	13	-3	16	5.011	0.759	3	9	2	0	0.818	46	1.319
Brigham Young	27	10	17	4.956	0.757	2	10	2	0	0.833	55	1.180
California	21	3	18	4.769	0.752	7	7	3	0	0.700	15	2.226
Pittsburgh	9	-10	19	4.674	0.749	4	8	2	0	0.800	44	1.375
Oklahoma State	14	-6	20	4.301	0.738	6	8	3	0	0.727	30	1.771

Apologies for the tardiness of this post - I meant to post this when the blogpoll came out, but I missed that, then it was the weekend.  And there's not much change at the top. 

I'll post this week's results after the blogpoll comes out.

Here's the top 20 from last week (through games of 2009.11.22):

Team	Pvs	+/-	Rank	KRACH	RRWP	Record Rank	W	L	T	Win %	SOS Rank	SOS
Alabama	1	0	1	50.726	0.952	1	10	0	0	1.000	8	2.416
Florida	2	0	2	38.709	0.940	1	10	0	0	1.000	24	1.843
Cincinnati	3	0	3	35.500	0.936	1	9	0	0	1.000	22	1.868
TCU	4	0	4	30.850	0.928	1	10	0	0	1.000	42	1.469
Texas	5	0	5	29.226	0.925	1	11	0	0	1.000	53	1.271
Boise State	6	0	6	22.462	0.908	1	10	0	0	1.000	59	1.070
Georgia Tech	7	0	7	15.023	0.878	2	9	1	0	0.900	9	2.372
Oregon	9	1	8	10.346	0.843	5	9	2	0	0.818	2	2.723
Pittsburgh	10	1	9	8.102	0.817	3	8	1	0	0.889	44	1.430
Ohio State	11	1	10	7.223	0.804	4	10	2	0	0.833	29	1.720
Virginia Tech	13	2	11	7.074	0.801	7	8	3	0	0.727	1	2.913
Iowa	12	0	12	6.729	0.795	5	9	2	0	0.818	26	1.771
Penn State	15	2	13	6.109	0.783	5	9	2	0	0.818	35	1.608
Oklahoma State	14	0	14	5.917	0.779	6	8	2	0	0.800	28	1.740
Miami (FL)	19	4	15	5.415	0.768	8	7	3	0	0.700	5	2.527
LSU	8	-8	16	5.158	0.761	7	8	3	0	0.727	17	2.124
Clemson	20	3	17	4.903	0.755	8	7	3	0	0.700	10	2.288
North Carolina	26	8	18	4.783	0.751	9	6	3	0	0.667	3	2.575
Oregon State	16	-3	19	4.723	0.750	8	7	3	0	0.700	13	2.204
USC	17	-3	20	4.585	0.745	8	7	3	0	0.700	16	2.139

EDIT:  Added further justification to point 5.

I put a bit of effort in cleaning up my code to address some of the problems from last week:

1. Undefeated and winless teams:  I added the fictitious tie.  Now there's a path from every team to every other team.  While this is a hack, it's reasonable and about as far as I really care to go with it.  I also calculated the round-robin winning percentage (RRWP) and KRACH strength of schedule (SOS).  These are useful metrics for comparing teams that don't line up very well, as per John Whelan's KRACH site.  Now the undefeated and winless teams can be compared with multiple data elements.
2. Rasmus:  Open source:  The original Pairwise and KRACH code was freely given to me years ago by John Whelan.  This code is my own, based only on the information given in his KRACH site;  given that, I'm comfortable sharing my code, so long as the user gives due credit to John and Ken Butler.
3. joeyb:  Undefeated teams will always rate better than teams with losses:  To investigate this, I created a fictitious team that was 10-0 with wins against only the bottom ten teams.  It rated out at #37, well below several 1- and 2-loss teams.
4. SpartanDan:  Top teams are ranked backwards:  You are correct, sir.  I mistakenly assumed that a larger deviation from predicted meant a less accurate KRACH.  This has been fixed, as in 1) above, with the RRWP, SOS and fictitious tie.
5. Seth9:  The rating doesn't apply to college football:  You may be right on this. It's still curious, and now trivial, for me to crunch the numbers.  EDIT:  But is this any less applicable than any of the computer ratings used in the BCS?  And it certainly does not have the bias and politicking associated with opinion polls.

As points of comparison, I've included the latest BlogPoll results and BCS standings.

Again, this rating includes all D-IA games through 15 November 2009:

Team	BlogPoll	BCS	Rank	KRACH	RRWP	Record Rank	W	L	T	Win %	SOS Rank	SOS
Alabama	1	2	1	50.413	0.953	1	10	0	0	1.000	10	2.401
Florida	3	1	2	43.477	0.946	1	9	0	0	1.000	15	2.288
Cincinnati	5	5	3	36.050	0.937	1	9	0	0	1.000	23	1.897
TCU	4	4	4	29.380	0.926	1	9	0	0	1.000	35	1.546
Texas	2	3	5	26.406	0.920	1	10	0	0	1.000	52	1.257
Boise State	6	6	6	21.243	0.906	1	9	0	0	1.000	59	1.118
Georgia Tech	7	7	7	13.464	0.870	2	9	1	0	0.900	18	2.126
LSU	11	8	8	9.599	0.837	5	8	2	0	0.800	2	2.823
Oregon	9	11	9	9.141	0.832	5	8	2	0	0.800	3	2.688
Pittsburgh	8	9	10	8.655	0.826	3	8	1	0	0.889	37	1.527
Ohio State	10	10	11	7.289	0.807	4	9	2	0	0.818	22	1.918
Iowa	14	13	12	6.292	0.789	5	8	2	0	0.800	24	1.851
Virginia Tech	16	15	13	6.103	0.785	8	7	3	0	0.700	1	2.848
Oklahoma State	12	12	14	5.436	0.770	6	7	2	0	0.778	26	1.812
Penn State	15	14	15	5.061	0.761	5	8	2	0	0.800	40	1.489
Oregon State	19	19	16	4.967	0.758	9	6	3	0	0.667	4	2.675
USC	21	18	17	4.954	0.758	8	7	3	0	0.700	14	2.312
Wisconsin	17	16	18	4.574	0.747	6	7	2	0	0.778	38	1.525
Miami (FL)	20	20	19	4.544	0.746	9	6	3	0	0.667	8	2.447
Clemson	18	23	20	4.393	0.741	9	6	3	0	0.667	12	2.365
Rutgers			21	4.372	0.741	7	5	2	0	0.714	20	1.987
Utah	23	21	22	3.965	0.727	5	8	2	0	0.800	56	1.166
Stanford	13	17	23	3.825	0.721	8	7	3	0	0.700	27	1.785
California		25	24	3.679	0.716	9	6	3	0	0.667	21	1.981
Temple			25	3.607	0.713	3	8	1	0	0.889	88	0.636
North Carolina	25		26	3.504	0.708	11	5	3	0	0.625	16	2.230
Arizona			27	3.496	0.708	11	5	3	0	0.625	17	2.224
Georgia			28	3.049	0.687	14	5	4	0	0.556	7	2.494
South Florida			29	3.048	0.687	13	4	3	0	0.571	11	2.370
Navy			30	3.001	0.685	8	7	3	0	0.700	46	1.400
Brigham Young	22	22	31	2.900	0.680	5	8	2	0	0.800	71	0.853
Boston College			32	2.855	0.677	9	6	3	0	0.667	36	1.537
Arkansas			33	2.826	0.675	14	5	4	0	0.556	13	2.312
Houston	24	24	34	2.817	0.675	6	7	2	0	0.778	63	0.939
West Virginia			35	2.665	0.666	9	6	3	0	0.667	41	1.435
Auburn			36	2.379	0.648	12	6	4	0	0.600	31	1.647
Notre Dame			37	2.252	0.639	12	6	4	0	0.600	33	1.559
Mississippi			38	2.228	0.637	11	5	3	0	0.625	43	1.418
Central Michigan			39	2.091	0.627	6	7	2	0	0.778	84	0.697
Nebraska			40	1.994	0.619	8	7	3	0	0.700	64	0.931
Florida State			41	1.985	0.618	16	4	5	0	0.444	9	2.426
South Carolina			42	1.748	0.597	15	5	5	0	0.500	28	1.748
Kentucky			43	1.717	0.594	14	5	4	0	0.556	44	1.405
Oklahoma			44	1.709	0.593	14	5	4	0	0.556	47	1.398
UCLA			45	1.680	0.590	15	5	5	0	0.500	29	1.680
Tennessee			46	1.648	0.587	15	5	5	0	0.500	30	1.648
Minnesota			47	1.549	0.576	15	5	5	0	0.500	34	1.549
Missouri			48	1.498	0.570	14	5	4	0	0.556	54	1.225
Troy			49	1.447	0.564	8	7	3	0	0.700	86	0.675
Texas Tech			50	1.400	0.559	14	5	4	0	0.556	57	1.145
Mississippi State			51	1.372	0.555	20	3	6	0	0.333	5	2.548
Connecticut			52	1.289	0.544	18	3	5	0	0.375	19	2.026
Air Force			53	1.239	0.537	12	6	4	0	0.600	70	0.858
Michigan State			54	1.223	0.535	15	5	5	0	0.500	55	1.223
Washington			55	1.187	0.530	21	3	7	0	0.300	6	2.543
Nevada			56	1.179	0.529	8	7	3	0	0.700	95	0.550
Fresno State			57	1.152	0.525	14	5	4	0	0.556	62	0.942
Northwestern			58	1.151	0.525	12	6	4	0	0.600	76	0.797
UCF			59	1.125	0.521	14	5	4	0	0.556	65	0.921
East Carolina			60	1.061	0.510	14	5	4	0	0.556	69	0.868
Duke			61	1.056	0.509	15	4	4	0	0.500	60	1.056
Arizona State			62	0.993	0.499	20	3	6	0	0.333	25	1.845
Idaho			63	0.961	0.493	10	7	4	0	0.636	92	0.577
Middle Tennessee State			64	0.943	0.490	8	7	3	0	0.700	102	0.440
Southern Methodist			65	0.924	0.486	14	5	4	0	0.556	80	0.756
Iowa State			66	0.874	0.477	15	5	5	0	0.500	67	0.874
Virginia			67	0.820	0.466	20	3	6	0	0.333	39	1.523
Southern Miss			68	0.787	0.459	14	5	4	0	0.556	87	0.644
Texas A&M			69	0.757	0.452	15	5	5	0	0.500	79	0.757
Wake Forest			70	0.757	0.452	21	3	7	0	0.300	32	1.622
Baylor			71	0.738	0.447	20	3	6	0	0.333	48	1.370
Purdue			72	0.736	0.447	19	4	7	0	0.364	53	1.227
Louisville			73	0.726	0.445	20	3	6	0	0.333	49	1.348
Kansas State			74	0.718	0.443	16	4	5	0	0.444	66	0.878
Kansas			75	0.683	0.434	16	4	5	0	0.444	73	0.835
Northern Illinois			76	0.675	0.432	9	6	3	0	0.667	108	0.364
Bowling Green			77	0.624	0.419	15	5	5	0	0.500	89	0.624
Ohio			78	0.624	0.419	9	6	3	0	0.667	113	0.336
Marshall			79	0.612	0.415	16	4	5	0	0.444	81	0.748
Louisiana-Monroe			80	0.578	0.406	14	5	4	0	0.556	99	0.473
Michigan			81	0.577	0.406	17	4	6	0	0.400	74	0.833
Wyoming			82	0.564	0.402	16	4	5	0	0.444	85	0.689
UAB			83	0.511	0.385	15	5	5	0	0.500	97	0.511
North Carolina State			84	0.510	0.385	22	2	6	0	0.250	50	1.326
Syracuse			85	0.476	0.374	23	2	7	0	0.222	42	1.428
Indiana			86	0.407	0.349	21	3	7	0	0.300	68	0.872
Colorado			87	0.390	0.342	21	3	7	0	0.300	72	0.835
Illinois			88	0.380	0.338	23	2	7	0	0.222	58	1.140
UNLV			89	0.363	0.331	21	3	7	0	0.300	78	0.777
Toledo			90	0.324	0.313	17	4	6	0	0.400	100	0.468
Colorado State			91	0.314	0.309	23	2	7	0	0.222	61	0.943
San Diego State			92	0.303	0.303	20	3	6	0	0.333	93	0.562
Kent State			93	0.298	0.301	16	4	5	0	0.444	107	0.364
Louisiana-Lafayette			94	0.273	0.289	16	4	5	0	0.444	114	0.334
Western Michigan			95	0.243	0.272	17	4	6	0	0.400	111	0.351
Florida Atlantic			96	0.242	0.271	20	3	6	0	0.333	101	0.449
Maryland			97	0.226	0.262	26	1	8	0	0.111	51	1.282
Hawaii			98	0.223	0.260	20	3	6	0	0.333	103	0.413
Washington State			99	0.222	0.259	27	1	9	0	0.100	45	1.403
Tulsa			100	0.205	0.248	20	3	6	0	0.333	106	0.380
Louisiana Tech			101	0.204	0.248	23	2	7	0	0.222	90	0.611
Buffalo			102	0.185	0.235	23	2	7	0	0.222	94	0.555
UTEP			103	0.165	0.220	21	3	7	0	0.300	110	0.353
Army			104	0.162	0.218	20	3	6	0	0.333	116	0.300
Florida International			105	0.155	0.213	21	3	7	0	0.300	115	0.332
Tulane			106	0.136	0.197	23	2	7	0	0.222	104	0.407
Memphis			107	0.126	0.189	26	1	8	0	0.111	83	0.713
Vanderbilt			108	0.124	0.187	27	1	9	0	0.100	77	0.787
Utah State			109	0.117	0.180	23	2	7	0	0.222	112	0.350
Akron			110	0.107	0.171	26	1	8	0	0.111	91	0.606
Arkansas State			111	0.106	0.170	25	1	7	0	0.125	96	0.528
Miami (OH)			112	0.105	0.169	28	1	10	0	0.091	82	0.734
New Mexico State			113	0.079	0.141	23	2	7	0	0.222	118	0.236
Rice			114	0.076	0.138	27	1	9	0	0.100	98	0.479
North Texas			115	0.064	0.123	24	2	8	0	0.200	119	0.218
San Jose State			116	0.048	0.101	29	0	8	0	0.000	75	0.815
Ball State			117	0.032	0.074	26	1	8	0	0.111	120	0.179
New Mexico			118	0.019	0.049	29	0	10	0	0.000	105	0.395
Western Kentucky			119	0.019	0.049	29	0	9	0	0.000	109	0.353
Eastern Michigan			120	0.012	0.033	29	0	10	0	0.000	117	0.250

EDIT:  Fixed a typo and added section headers.

Background

A few years ago I applied Ken's Rating for American College Hockey (KRACH), or Bradley-Terry statistics, to ACHA club hockey teams.  At the time, participants for the national tournament were determined by an opinion poll, and there wasn't enough interplay for that to be meaningful (sound familiar?).

In an earlier post here, I intimated that I'd like to see someone crunch the numbers as a mechanism for rating Division I-A college football teams.  It's something I've been thinking about for quite some time, just to see what would happen.  So tonight I threw something together.

Brief Summary:

"The KRACH rating system is an attempt to combine the performance of each team with the strength of the opposition against which that performance was achieved, and to summarize the result as one number, a "rating", for each team. The higher the rating, the better the team."

"Interpreting the ratings

The ratings are given on an "odds scale": that is, if team A is rated at 400 and team B at 200, team A is reckoned to have odds of 2 to 1 of defeating team B when they meet (since 400 is twice 200). Equivalently, team A is reckoned to have probability 2/3 of defeating team B (since 400/(400+200) is 2/3)."

"There are two things we need to check, to make sure that the rating system is sensible:

1. If you win more against the same opposition as another team, your rating will be higher.
2. If you have the same record as another team, but against tougher opposition, your rating will be higher."

Methods

So, I took the season results from the official NCAA page.  I excluded results against FCS competition, as a matter of principle.

One caveat here - I haven't yet worked out what to do exactly with undefeated and winless teams.  This will become meaningful at the end of the season if there are multiple undefeated teams (I'm not sure I really care about the winless teams).  While I sort that out, I've done the following:

• Verified my calculated rating by calculating the predicted number of wins;
• Determining a percentage difference between the predicted and actual number of wins;

Teams with the same KRACH are ranked according to percentage difference, lower is better.  Interestingly, of the undefeated teams, Florida and Alabama rate near the bottom.  Woo!  SEC!  This should be sorted by the end of the season, when it IS important.

Results

Without further ado, the first KRACH rating for Division I-A college football:

		KRACH	Predicted Wins	Actual Wins	% Difference
1	Texas	200.000	8.937	9	0.702
2	TCU	200.000	7.928	8	0.898
3	Boise State	200.000	7.848	8	1.906
4	Cincinnati	200.000	7.830	8	2.131
5	Florida	200.000	7.752	8	3.104
6	Alabama	200.000	8.716	9	3.160
7	LSU	39.863	6.999	7	0.011
8	Georgia Tech	35.246	7.998	8	0.024
9	Oregon	32.752	6.998	7	0.021
10	Iowa	28.690	7.998	8	0.026
11	USC	21.015	6.999	7	0.021
12	Pittsburgh	17.119	6.998	7	0.024
13	Arizona	14.574	4.999	5	0.025
14	Oregon State	14.533	4.999	5	0.021
15	Miami (FL)	13.562	5.999	6	0.022
16	Ohio State	13.418	7.998	8	0.026
17	South Florida	12.804	3.999	4	0.021
18	Penn State	12.186	6.998	7	0.025
19	Virginia Tech	10.888	5.999	6	0.020
20	Clemson	9.944	4.999	5	0.023
21	Wisconsin	9.061	5.999	6	0.023
22	Oklahoma State	8.788	5.999	6	0.020
23	Temple	7.966	6.998	7	0.026
24	Stanford	7.682	5.999	6	0.021
25	Houston	7.679	6.998	7	0.024
26	Utah	7.215	7.998	8	0.024
27	California	7.194	4.999	5	0.024
28	Auburn	5.098	5.999	6	0.021
29	Navy	4.686	6.998	7	0.026
30	Georgia	4.627	3.999	4	0.019
31	Rutgers	4.399	3.999	4	0.022
32	Boston College	4.292	4.999	5	0.025
33	West Virginia	3.877	5.999	6	0.020
34	Tennessee	3.789	4.999	5	0.018
35	Notre Dame	3.761	5.999	6	0.022
36	Arkansas	3.534	3.999	4	0.022
37	UCLA	3.515	3.999	4	0.016
38	Florida State	3.103	2.999	3	0.019
39	North Carolina	3.030	3.999	4	0.020
40	Brigham Young	2.787	6.998	7	0.025
41	Washington	2.689	3.000	3	0.013
42	Central Michigan	2.345	5.999	6	0.024
43	South Carolina	2.315	4.999	5	0.017
44	Minnesota	2.130	4.999	5	0.023
45	Mississippi State	2.117	3.000	3	0.016
46	Fresno State	2.057	4.999	5	0.025
47	Kentucky	1.951	3.999	4	0.021
48	Mississippi	1.905	3.999	4	0.020
49	Arizona State	1.582	2.999	3	0.024
50	Texas Tech	1.541	4.999	5	0.020
51	Northwestern	1.260	4.999	5	0.023
52	Michigan State	1.219	3.999	4	0.022
53	Oklahoma	1.196	3.999	4	0.017
54	Nebraska	1.172	5.999	6	0.022
55	Wake Forest	1.133	3.000	3	0.015
56	Connecticut	1.010	2.999	3	0.023
57	Duke	0.905	3.999	4	0.025
58	Purdue	0.865	3.999	4	0.018
59	Syracuse	0.836	2.000	2	0.017
60	Air Force	0.729	4.999	5	0.025
61	Virginia	0.719	3.000	3	0.017
62	Missouri	0.718	3.999	4	0.020
63	Troy	0.690	6.998	7	0.022
64	North Carolina State	0.561	2.000	2	0.017
65	Kansas State	0.555	3.999	4	0.020
66	Michigan	0.545	3.999	4	0.023
67	Texas A&M	0.536	4.999	5	0.020
68	Baylor	0.476	2.999	3	0.025
69	Idaho	0.466	6.998	7	0.024
70	Iowa State	0.437	3.999	4	0.023
71	Kansas	0.434	3.999	4	0.020
72	East Carolina	0.413	3.999	4	0.024
73	Middle Tennessee State	0.363	5.999	6	0.022
74	Illinois	0.358	1.999	2	0.026
75	Southern Methodist	0.333	3.999	4	0.022
76	Louisville	0.305	2.000	2	0.020
77	Northern Illinois	0.304	4.999	5	0.024
78	Indiana	0.289	2.999	3	0.023
79	Nevada	0.287	5.999	6	0.022
80	Marshall	0.259	3.999	4	0.021
81	Southern Miss	0.240	3.999	4	0.020
82	UCF	0.223	3.999	4	0.018
83	Bowling Green	0.206	3.999	4	0.024
84	Colorado	0.203	2.999	3	0.025
85	Ohio	0.181	4.999	5	0.020
86	Louisiana-Monroe	0.177	3.999	4	0.018
87	Maryland	0.149	1.000	1	0.021
88	San Diego State	0.147	2.999	3	0.019
89	Wyoming	0.140	2.999	3	0.017
90	UAB	0.134	3.999	4	0.015
91	Toledo	0.117	3.999	4	0.020
92	Colorado State	0.115	2.000	2	0.020
93	UNLV	0.103	2.999	3	0.019
94	Kent State	0.092	3.999	4	0.020
95	Western Michigan	0.088	3.000	3	0.013
96	Washington State	0.074	1.000	1	0.013
97	Buffalo	0.050	2.000	2	0.019
98	Louisiana-Lafayette	0.048	3.999	4	0.016
99	Florida Atlantic	0.036	2.000	2	0.021
100	Tulane	0.035	2.000	2	0.013
101	UTEP	0.033	3.000	3	0.016
102	Memphis	0.031	1.000	1	0.019
103	Miami (OH)	0.031	1.000	1	0.020
104	Tulsa	0.031	3.000	3	0.015
105	Akron	0.030	1.000	1	0.025
106	Hawaii	0.028	2.000	2	0.023
107	Louisiana Tech	0.021	2.000	2	0.019
108	Arkansas State	0.019	1.000	1	0.021
109	Florida International	0.018	2.000	2	0.018
110	Army	0.015	3.000	3	0.013
111	New Mexico State	0.009	2.000	2	0.017
112	Utah State	0.008	1.000	1	0.007
113	North Texas	0.006	2.000	2	0.012
114	Vanderbilt	0.004	1.000	1	0.005
115	Ball State	0.002	1.000	1	0.007
116	Eastern Michigan	0.001	0.442	0	0.000
117	New Mexico	0.001	0.162	0	0.000
118	Rice	0.001	0.259	0	0.000
119	San Jose State	0.001	0.006	0	0.000
120	Western Kentucky	0.001	0.216	0	0.000