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