Sunday, November 30, 2008

Random Walker Rankings through November 29th

We remain grateful to both Kenneth Massey for maintaining his comparisons page and to Peter R. Wolfe for making game results available online.

Below we list rankings according to the Random Walker (RW) system of first-place votes and the Random Walker First-Last (RWFL) system at our selected p=0.75. We use the random walkers to rank all 120 Football Bowl Subdivision teams, plus the extra made-up "team" representing their collective Football Championship Subdivision opponents. The "votes" in the Random Walker (RW) system are all essentially first-place votes, teams with more votes ranked more highly. The Random Walker with First & Last (RWFL) system is a combination of "first-place" and "last-place" votes. We have determined that our bias parameter p=0.75 has nice properties for RWFL (near the minimum crossing probability when compared against round-robin standings), so we use p=0.75 for both RW and RWFL and are happy that this is coincidentally the same primary value we have used in the past for the RW rankings.

The breakdown of the top teams across different p values for both RW and RWFL can be seen in the figures below. Additionally, we plot the fraction of ranking violations---that is, the fraction of game outcomes that have been contrary to the rankings---for each system across the p values. Ranking violations like these are also included on Kenneth Massey's site, and can be used as one measure of the efficacy of a rank ordering; indeed, one could instead choose p to minimize such errors, but we are more comfortable at the selected fixed values for ease of explanation.




























2008 Random Walker Rankings (p=0.75)
Games Through Saturday November 29th

RW
RWFL
RankTeam (Wins-Losses)% of Total Votes Team (Wins-Losses)%(First)-%(Last)
1Oklahoma (11-1)2.4099Oklahoma (11-1)2.1205
2Texas (11-1)2.3095Texas (11-1)2.0672
3Alabama (12-0)2.1853Alabama (12-0)1.8886
4Florida (11-1)2.1021Florida (11-1)1.8138
5Texas Tech (11-1)2.0875Texas Tech (11-1)1.7311
6Utah (12-0)2.0415Utah (12-0)1.7200
7Southern Cal (10-1)1.9146Southern Cal (10-1)1.6069
8Penn State (11-1)1.7845Penn State (11-1)1.4542
9Boise St (12-0)1.7435Boise St (12-0)1.3941
10Georgia Tech (9-3)1.5604Ohio State (10-2)1.1365
11Boston College (9-3)1.5059Georgia Tech (9-3)1.1092
12Ball St (12-0)1.4819Boston College (9-3)1.0862
13Ohio State (10-2)1.4742Ball St (12-0)1.0593
14Cincinnati (10-2)1.4207Cincinnati (10-2)1.0225
15North Carolina (8-4)1.3617Georgia (9-3)0.9924
16Georgia (9-3)1.3532TCU (10-2)0.9175
17Florida St (8-4)1.3379North Carolina (8-4)0.8800
18Virginia Tech (8-4)1.3349Florida St (8-4)0.8793
19TCU (10-2)1.3303Michigan St (9-3)0.8527
20Oklahoma St (9-3)1.2467Oklahoma St (9-3)0.8479
21Pittsburgh (8-3)1.2451Virginia Tech (8-4)0.8474
22Michigan St (9-3)1.2219Pittsburgh (8-3)0.8159
23Oregon St (8-4)1.2017Missouri (9-3)0.7589
24Missouri (9-3)1.1565Oregon St (8-4)0.7492
25Wake Forest (7-5)1.1481Oregon (9-3)0.7319
26Oregon (9-3)1.1393Brigham Young (10-2)0.6765
27Mississippi (8-4)1.1306Wake Forest (7-5)0.6576
28Brigham Young (10-2)1.1200Nebraska (8-4)0.6532
29Maryland (7-5)1.1137Mississippi (8-4)0.6258
30Clemson (7-5)1.0949California (7-4)0.5957
31Nebraska (8-4)1.0698Northwestern (9-3)0.5499
32Miami FL (7-5)1.0589Clemson (7-5)0.5402
33California (7-4)1.0578Miami FL (7-5)0.5340
34Northwestern (9-3)1.0317Maryland (7-5)0.5020
35Iowa (8-4)0.9905Iowa (8-4)0.4786
36Connecticut (7-4)0.9656Kansas (7-5)0.4360
37North Carolina St (6-6)0.9596Connecticut (7-4)0.4255
38Kansas (7-5)0.9425South Carolina (7-5)0.3900
39South Carolina (7-5)0.9371South Florida (7-4)0.3525
40South Florida (7-4)0.9140North Carolina St (6-6)0.3518
41Virginia (5-7)0.9127West Virginia (7-4)0.3434
42Navy (7-4)0.9072Navy (7-4)0.3145
43West Virginia (7-4)0.8844Western Michigan (9-3)0.2932
44Rutgers (6-5)0.8548Air Force (8-4)0.2858
45East Carolina (8-4)0.8457Rice (9-3)0.2653
46Tulsa (10-2)0.8442Tulsa (10-2)0.2537
47Rice (9-3)0.8324East Carolina (8-4)0.2333
48Vanderbilt (6-6)0.8287Rutgers (6-5)0.2287
49Air Force (8-4)0.8269Virginia (5-7)0.2067
50Western Michigan (9-3)0.8235LSU (7-5)0.2004
51LSU (7-5)0.8144Wisconsin (7-5)0.1687
52Central Michigan (8-4)0.7642Vanderbilt (6-6)0.1540
53Wisconsin (7-5)0.7612Central Michigan (8-4)0.1065
54Nevada (7-5)0.7422Notre Dame (6-6)0.0633
55Hawai`i (7-5)0.7319Minnesota (7-5)0.0495
56Notre Dame (6-6)0.7305Nevada (7-5)0.0456
57Arkansas (5-7)0.7115Hawai`i (7-5)0.0343
58Kentucky (6-6)0.7061Kentucky (6-6)0.0147
59Minnesota (7-5)0.6905Fresno St (7-5)-0.0105
60Arizona (6-5)0.6647Arkansas (5-7)-0.0318
61Fresno St (7-5)0.6631Colorado St (6-6)-0.0410
62Duke (4-8)0.6574Arizona (6-5)-0.0573
63Tennessee (5-7)0.6493Colorado (5-7)-0.0653
64Colorado (5-7)0.6435Houston (7-5)-0.1004
65Houston (7-5)0.6432Illinois (5-7)-0.1229
66Stanford (5-7)0.6363Tennessee (5-7)-0.1315
67Colorado St (6-6)0.6362Buffalo (7-5)-0.1363
68Louisiana Tech (7-5)0.6345Stanford (5-7)-0.1375
69Baylor (4-8)0.6090Louisiana Tech (7-5)-0.1548
70Troy (7-4)0.6067Baylor (4-8)-0.1564
71Illinois (5-7)0.6008Duke (4-8)-0.1631
72Louisville (5-6)0.6001Arizona St (5-6)-0.1647
73Buffalo (7-5)0.5972Troy (7-4)-0.1684
74Arizona St (5-6)0.5903Louisville (5-6)-0.1894
75Bowling Green (6-6)0.5765Auburn (5-7)-0.2229
76Auburn (5-7)0.5758Purdue (4-8)-0.2730
77Texas A&M (4-8)0.5755Kansas St (5-7)-0.2828
78Kansas St (5-7)0.5495San Jose St (6-6)-0.2955
79Mississippi St (4-8)0.5427Texas A&M (4-8)-0.3155
80Purdue (4-8)0.5412Northern Illinois (6-6)-0.3458
81San Jose St (6-6)0.5395UNLV (5-7)-0.3609
82Southern Miss (6-6)0.5347Southern Miss (6-6)-0.3637
83UNLV (5-7)0.5344UCLA (4-7)-0.3818
84Arkansas St (6-5)0.5260Florida Atlantic (6-6)-0.4150
85Northern Illinois (6-6)0.5051Mississippi St (4-8)-0.4333
86Michigan (3-9)0.5000Arkansas St (6-5)-0.4496
87UCLA (4-7)0.4946Bowling Green (6-6)-0.4537
88Florida Atlantic (6-6)0.4883New Mexico (4-8)-0.4871
89Syracuse (3-9)0.4814Memphis (6-6)-0.5138
90New Mexico (4-8)0.4781UTEP (5-7)-0.5326
91Middle Tennessee St (5-6)0.4685Temple (5-7)-0.5366
92UTEP (5-7)0.4658Syracuse (3-9)-0.5480
93Memphis (6-6)0.4635Michigan (3-9)-0.5914
94Indiana (3-9)0.4618Akron (5-7)-0.6132
95Temple (5-7)0.4492Indiana (3-9)-0.6374
96Wyoming (4-8)0.4480Wyoming (4-8)-0.6389
97Utah St (3-9)0.4448Middle Tennessee St (5-6)-0.6552
98Akron (5-7)0.4369Marshall (4-8)-0.6637
99Marshall (4-8)0.4344Utah St (3-9)-0.6755
100Central Florida (4-8)0.3921Louisiana-Lafayette (5-6)-0.7116
101Eastern Michigan (3-9)0.3874Central Florida (4-8)-0.8008
102Louisiana-Lafayette (5-6)0.3768Ohio U. (4-8)-0.8346
103Kent St (4-8)0.3757Florida Int'l (4-7)-0.8643
104Ohio U. (4-8)0.3716Alabama-Birmingham (4-8)-0.8743
105New Mexico St (3-9)0.3711Kent St (4-8)-1.0386
106Florida Int'l (4-7)0.3698Washington St (2-11)-1.0620
107Washington St (2-11)0.3492Iowa St (2-10)-1.0879
108Alabama-Birmingham (4-8)0.3463New Mexico St (3-9)-1.1113
109San Diego St (2-10)0.3417Toledo (3-9)-1.1199
110Washington (0-11)0.3409Eastern Michigan (3-9)-1.1364
111Western Kentucky (2-9)0.3369Louisiana-Monroe (4-8)-1.1884
112Toledo (3-9)0.3279Army (3-8)-1.2521
113Army (3-8)0.3275San Diego St (2-10)-1.3513
114Iowa St (2-10)0.3237Idaho (2-10)-1.4577
115Louisiana-Monroe (4-8)0.3234Tulane (2-10)-1.4638
116FCS teams (XXX-XXX)0.3040Western Kentucky (2-9)-1.5812
117Tulane (2-10)0.2999Washington (0-11)-1.5971
118Miami OH (2-10)0.2969Miami OH (2-10)-1.6346
119Idaho (2-10)0.2923SMU (1-11)-1.8200
120SMU (1-11)0.2857FCS teams (XXX-XXX)-1.8933
121North Texas (1-11)0.2121North Texas (1-11)-2.1141