Bradley-Terry Statistical Rating (KRACH) for FBS Football

Bradley-Terry Statistical Rating (KRACH) for FBS Football

Submitted by quakk on November 10th, 2010 at 7:17 PM

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.

Modified Terry-Bradley Statistical Ranking for Week Ending 2009.11.29

Modified Terry-Bradley Statistical Ranking for Week Ending 2009.11.29

Submitted by quakk on December 3rd, 2009 at 10:35 AM
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

Modified Terry-Bradley Statistical Ranking for Week Ending 2009.11.22

Modified Terry-Bradley Statistical Ranking for Week Ending 2009.11.22

Submitted by quakk on November 29th, 2009 at 6:32 AM

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

KRACH 19 Nov 2009 - Addresses most of the problems from last week

KRACH 19 Nov 2009 - Addresses most of the problems from last week

Submitted by quakk on November 18th, 2009 at 4:06 PM
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

KRACH applied to Division I-A college football

KRACH applied to Division I-A college football

Submitted by quakk on November 11th, 2009 at 3:37 PM
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