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