Sunday, November 23, 2008

Random Walker Rankings through November 22nd

The random walker rankings are back again for 2008! 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. 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.


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.



2008 Random Walker Rankings (p=0.75)
Games Through Saturday November 22nd

RW
RWFL
RankTeam (Wins-Losses)% of Total Votes
Team (Wins-Losses)%(First)-%(Last)
1Texas (10-1)2.3680Texas (10-1)2.1289
2Alabama (11-0)2.3317Alabama (11-0)2.0357
3Oklahoma (10-1)2.2593Oklahoma (10-1)1.9523
4Florida (10-1)2.1220Florida (10-1)1.8241
5Texas Tech (10-1)2.0932Utah (12-0)1.7469
6Utah (12-0)2.0743Texas Tech (10-1)1.7235
7Southern Cal (9-1)1.8659Southern Cal (9-1)1.5516
8Penn State (11-1)1.8156Penn State (11-1)1.4866
9Boise St (11-0)1.6526Georgia (9-2)1.3229
10Georgia (9-2)1.6402Boise St (11-0)1.2815
11Ohio State (10-2)1.4787Ohio State (10-2)1.1402
12Oklahoma St (9-2)1.4079Oklahoma St (9-2)1.0301
13Ball St (11-0)1.3948Missouri (9-2)0.9975
14Florida St (8-3)1.3799Cincinnati (9-2)0.9851
15Cincinnati (9-2)1.3796Ball St (11-0)0.9535
16Georgia Tech (8-3)1.3728Oregon St (8-3)0.9187
17Missouri (9-2)1.3498Florida St (8-3)0.9140
18Oregon St (8-3)1.3426TCU (10-2)0.9134
19TCU (10-2)1.3296Georgia Tech (8-3)0.8761
20Boston College (8-3)1.3090Boston College (8-3)0.8371
21North Carolina (7-4)1.2789Michigan St (9-3)0.8355
22Michigan St (9-3)1.2113North Carolina (7-4)0.7594
23Virginia Tech (7-4)1.2067Virginia Tech (7-4)0.6781
24Miami FL (7-4)1.1360Brigham Young (10-2)0.6749
25Mississippi (7-4)1.1321Miami FL (7-4)0.6520
26Brigham Young (10-2)1.1250Pittsburgh (7-3)0.6514
27Maryland (7-4)1.1248Mississippi (7-4)0.6096
28Pittsburgh (7-3)1.1176California (7-4)0.5878
29Connecticut (7-3)1.0744Connecticut (7-3)0.5803
30Wake Forest (6-5)1.0609Nebraska (7-4)0.5760
31California (7-4)1.0447Northwestern (9-3)0.5545
32South Carolina (7-4)1.0347Oregon (8-3)0.5461
33Northwestern (9-3)1.0346South Carolina (7-4)0.5386
34Nebraska (7-4)1.0150Maryland (7-4)0.5209
35Iowa (8-4)0.9956Wake Forest (6-5)0.5143
36Oregon (8-3)0.9875Iowa (8-4)0.4846
37West Virginia (7-3)0.9865West Virginia (7-3)0.4800
38Clemson (6-5)0.9655LSU (7-4)0.4221
39LSU (7-4)0.9587Central Michigan (8-3)0.4151
40Virginia (5-6)0.9320Western Michigan (9-2)0.4057
41Vanderbilt (6-5)0.9316Clemson (6-5)0.3429
42Central Michigan (8-3)0.9146Vanderbilt (6-5)0.3040
43Western Michigan (9-2)0.8979Air Force (8-4)0.2855
44Navy (6-4)0.8395Kansas (6-5)0.2638
45Air Force (8-4)0.8357Virginia (5-6)0.2488
46Kansas (6-5)0.8274Tulsa (9-2)0.2112
47Rutgers (6-5)0.8252Kentucky (6-5)0.2027
48North Carolina St (5-6)0.8227Rice (8-3)0.1945
49Tulsa (9-2)0.8186Rutgers (6-5)0.1927
50East Carolina (7-4)0.8100Navy (6-4)0.1916
51Kentucky (6-5)0.8029Wisconsin (7-5)0.1885
52Rice (8-3)0.7830East Carolina (7-4)0.1581
53Wisconsin (7-5)0.7715South Florida (6-4)0.1424
54South Florida (6-4)0.7555North Carolina St (5-6)0.1287
55Hawai`i (6-5)0.7231Buffalo (7-4)0.1171
56Notre Dame (6-5)0.7169Minnesota (7-5)0.0495
57Colorado (5-6)0.7095Notre Dame (6-5)0.0448
58Houston (7-4)0.7084Colorado (5-6)0.0268
59Louisiana Tech (7-4)0.6892Fresno St (7-4)0.0156
60Nevada (6-5)0.6880Houston (7-4)0.0077
61Minnesota (7-5)0.6875Hawai`i (6-5)-0.0255
62Buffalo (7-4)0.6827Colorado St (6-6)-0.0312
63Fresno St (7-4)0.6774Arizona (6-5)-0.0435
64Arizona (6-5)0.6697Louisiana Tech (7-4)-0.0650
65Duke (4-7)0.6647Nevada (6-5)-0.0687
66Arkansas (4-7)0.6582Illinois (5-7)-0.0941
67Colorado St (6-6)0.6474Stanford (5-7)-0.1306
68Stanford (5-7)0.6448Troy (7-4)-0.1358
69Tennessee (4-7)0.6293Baylor (4-7)-0.1373
70Troy (7-4)0.6231Arkansas (4-7)-0.1444
71Illinois (5-7)0.6139Duke (4-7)-0.1629
72Baylor (4-7)0.6079Louisville (5-6)-0.1888
73Louisville (5-6)0.5817Auburn (5-6)-0.1988
74Auburn (5-6)0.5803Tennessee (4-7)-0.2157
75Mississippi St (4-7)0.5786Purdue (4-8)-0.2561
76Texas A&M (4-7)0.5640UCLA (4-6)-0.2629
77Arizona St (4-6)0.5611Arizona St (4-6)-0.2670
78Purdue (4-8)0.5534Kansas St (5-7)-0.2879
79Kansas St (5-7)0.5454Northern Illinois (6-5)-0.2879
80UCLA (4-6)0.5346San Jose St (6-6)-0.3183
81San Jose St (6-6)0.5318Texas A&M (4-7)-0.3321
82Bowling Green (5-6)0.5309Mississippi St (4-7)-0.3505
83UNLV (5-7)0.5276UNLV (5-7)-0.3954
84Arkansas St (5-5)0.5211UTEP (5-6)-0.4084
85Northern Illinois (6-5)0.5176Southern Miss (5-6)-0.4176
86Southern Miss (5-6)0.5091Arkansas St (5-5)-0.4875
87Michigan (3-9)0.5050New Mexico (4-8)-0.4933
88UTEP (5-6)0.4995Florida Atlantic (5-6)-0.5143
89New Mexico (4-8)0.4808Akron (5-6)-0.5158
90Syracuse (3-8)0.4766Syracuse (3-8)-0.5307
91Middle Tennessee St (5-6)0.4740Michigan (3-9)-0.5500
92Indiana (3-9)0.4662Bowling Green (5-6)-0.5758
93Florida Atlantic (5-6)0.4612Memphis (5-6)-0.5924
94Akron (5-6)0.4541Indiana (3-9)-0.6045
95Marshall (4-7)0.4533Middle Tennessee St (5-6)-0.6172
96Wyoming (4-8)0.4444Marshall (4-7)-0.6215
97Memphis (5-6)0.4357Temple (4-7)-0.6548
98Temple (4-7)0.4187Central Florida (4-7)-0.6575
99Utah St (2-9)0.4138Wyoming (4-8)-0.6722
100Central Florida (4-7)0.4120Louisiana-Lafayette (5-6)-0.7191
101New Mexico St (3-8)0.3902Florida Int'l (4-6)-0.7652
102Florida Int'l (4-6)0.3897Utah St (2-9)-0.8625
103Louisiana-Lafayette (5-6)0.3715Ohio U. (3-8)-0.9288
104Washington St (2-10)0.3620Toledo (3-8)-0.9382
105Ohio U. (3-8)0.3557Washington St (2-10)-0.9981
106Toledo (3-8)0.3449New Mexico St (3-8)-1.0001
107San Diego St (2-10)0.3422Alabama-Birmingham (3-8)-1.0715
108Western Kentucky (2-9)0.3379Iowa St (2-10)-1.1016
109Washington (0-11)0.3354Louisiana-Monroe (4-8)-1.1863
110Army (3-8)0.3281Army (3-8)-1.2387
111Louisiana-Monroe (4-8)0.3259Kent St (3-8)-1.3300
112Tulane (2-9)0.3249Tulane (2-9)-1.3602
113Iowa St (2-10)0.3246San Diego St (2-10)-1.3729
114Alabama-Birmingham (3-8)0.3204Eastern Michigan (2-9)-1.4263
115Eastern Michigan (2-9)0.3171Miami OH (2-9)-1.4882
116Miami OH (2-9)0.3099Idaho (2-10)-1.4959
117Kent St (3-8)0.3094Western Kentucky (2-9)-1.5605
118FCS teams (XXX-XXX)0.3033Washington (0-11)-1.5963
119SMU (1-10)0.2953SMU (1-10)-1.7256
120Idaho (2-10)0.2927FCS teams (XXX-XXX)-1.9049
121North Texas (1-10)0.2182North Texas (1-10)-2.0391