Sunday, September 27, 2009

Return of the Random Walkers!

It's still very early in the season to expect anything accurate from the random walker rankings, so apologies up front if your team isn't highly ranked. Let's concisely review the methodological essentials, so that you can rationalize why your team might not be where you want them to be at this point.

First and foremost, we're enormously grateful to Peter Wolfe for posting scores in an easy-to-parse format, and to Kenneth Massey for his College Football Ranking Comparison page. So with data to parse and a place to post results, what happens in the steps in between? We ignore margins of victory. We ignore the dates of games. And we collapse all non-FBS teams into a single representative node in our network (which we misname "FCS teams" below, though there are probably some DivII schools in there). Each of these could be easily handled differently; indeed, the last is a simple matter of considering the whole network and we've done this in recent years to try to predict the outcomes of bowl games (once turned out reasonably well and once not so much). The first two, however, require some modeling choices to specify how to handle these pieces of information, and our entire philosophy from the beginning has been to demonstrate what one gets from simple rankings.

Working solely from "but my team beat your team" arguments, we let loose two sets of random walkers on this network of teams: the "first-place votes" are biased to switch their votes to game winners 75% of the time, the "last-place votes" are biased to switch their votes to game losers 75% of the time, and we see how many votes on average each team gets (in reality, we solve the associated linear algebra problems). The RWFL ranking of a team is the number of first-place votes obtained minus the number of last-place votes (each expressed in the square brackets below in terms of the percentages of the respective totals).

Again, it's really early in the season to be making statements from such limited information. But the results below give a starting point for discussion and debate. Later in the week, we'll try to discuss the corresponding plots of rankings and violations across the bias value p (like we've produced in previous seasons) and perhaps also look at the rankings on a conference level.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday September 26th:
1. Alabama (4-0) [3.0342]
2. Virginia Tech (3-1) [2.4080]
3. Iowa (4-0) [2.4022]
4. LSU (4-0) [2.2689]
5. Houston (3-0) [2.0676]
6. Boise St (4-0) [1.9937]
7. Michigan (4-0) [1.7490]
8. Miami FL (2-1) [1.7174]
9. Cincinnati (4-0) [1.5009]
10. Florida (4-0) [1.3036]
11. Texas (4-0) [1.2741]
12. UCLA (3-0) [1.2486]
13. Oregon (3-1) [1.2442]
14. Georgia (3-1) [1.2347]
15. Auburn (4-0) [1.1884]
16. Georgia Tech (3-1) [1.1684]
17. Wisconsin (4-0) [1.0183]
18. TCU (3-0) [0.9325]
19. Kansas (4-0) [0.9044]
20. Arizona (3-1) [0.8854]
21. Oklahoma St (3-1) [0.8371]
22. Missouri (4-0) [0.7968]
23. Washington (2-2) [0.7779]
24. Nebraska (3-1) [0.7671]
25. South Carolina (3-1) [0.7105]
26. North Carolina (3-1) [0.6915]
27. Southern Cal (3-1) [0.6472]
28. Marshall (3-1) [0.6114]
29. Stanford (3-1) [0.6099]
30. California (3-1) [0.6062]
31. South Florida (4-0) [0.5924]
32. Penn State (3-1) [0.5889]
33. Brigham Young (3-1) [0.5620]
34. Minnesota (3-1) [0.5481]
35. Clemson (2-2) [0.5175]
36. Iowa St (3-1) [0.5102]
37. Connecticut (3-1) [0.5074]
38. Notre Dame (3-1) [0.5049]
39. Indiana (3-1) [0.4978]
40. Ohio State (3-1) [0.4843]
41. Idaho (3-1) [0.4233]
42. Utah (3-1) [0.4232]
43. Boston College (3-1) [0.3997]
44. Rutgers (3-1) [0.3321]
45. Arizona St (2-1) [0.2678]
46. Middle Tennessee St (3-1) [0.2601]
47. Florida St (2-2) [0.2566]
48. Mississippi St (2-2) [0.2308]
49. Texas A&M (3-0) [0.2218]
50. Central Michigan (3-1) [0.2208]
51. Baylor (2-1) [0.2136]
52. Kentucky (2-1) [0.2053]
53. North Carolina St (3-1) [0.2032]
54. Louisiana-Lafayette (2-2) [0.1960]
55. West Virginia (2-1) [0.1828]
56. Oklahoma (2-1) [0.1231]
57. Colorado St (3-1) [0.1121]
58. Oregon St (2-2) [0.0465]
59. Arkansas (1-2) [0.0341]
60. Wake Forest (2-2) [0.0169]
61. Mississippi (2-1) [-0.0033]
62. Pittsburgh (3-1) [-0.0462]
63. Tennessee (2-2) [-0.0467]
64. Air Force (3-1) [-0.0543]
65. Northern Illinois (2-2) [-0.0562]
66. Bowling Green (1-3) [-0.0636]
67. Southern Miss (3-1) [-0.0797]
68. Syracuse (2-2) [-0.1489]
69. Fresno St (1-3) [-0.1589]
70. Texas Tech (2-2) [-0.1620]
71. Western Michigan (2-2) [-0.1630]
72. Tulsa (3-1) [-0.1804]
73. Troy (2-2) [-0.1837]
74. Toledo (2-2) [-0.2178]
75. Louisiana-Monroe (2-2) [-0.2211]
76. East Carolina (2-2) [-0.2783]
77. Kansas St (2-2) [-0.2809]
78. Hawai`i (2-1) [-0.2944]
79. Wyoming (2-2) [-0.2952]
80. Vanderbilt (2-2) [-0.2972]
81. Purdue (1-3) [-0.2979]
82. Ohio U. (2-2) [-0.3529]
83. Kent St (2-2) [-0.3612]
84. Illinois (1-2) [-0.3999]
85. UNLV (2-2) [-0.4330]
86. San Jose St (1-3) [-0.4694]
87. SMU (2-1) [-0.4772]
88. Navy (2-2) [-0.4865]
89. Washington St (1-3) [-0.5129]
90. Colorado (1-2) [-0.5247]
91. Utah St (1-2) [-0.5517]
92. Louisville (1-2) [-0.5529]
93. Michigan St (1-3) [-0.5556]
94. Northwestern (2-2) [-0.5637]
95. San Diego St (1-3) [-0.5662]
96. Arkansas St (1-2) [-0.6476]
97. Akron (1-3) [-0.6534]
98. Tulane (1-2) [-0.6841]
99. Maryland (1-3) [-0.6868]
100. Central Florida (2-2) [-0.7041]
101. Memphis (1-3) [-0.7420]
102. Louisiana Tech (1-2) [-0.8184]
103. Duke (2-2) [-0.8396]
104. New Mexico St (2-2) [-0.9394]
105. North Texas (1-3) [-1.0065]
106. Nevada (0-3) [-1.0218]
107. Florida Int'l (0-3) [-1.0773]
108. Army (2-2) [-1.1548]
109. Florida Atlantic (0-3) [-1.1604]
110. UTEP (1-3) [-1.1829]
111. Alabama-Birmingham (1-3) [-1.2814]
112. Miami OH (0-4) [-1.4748]
113. Temple (1-2) [-1.4759]
114. FCS teams (XXX-XXX) [-1.5860]
115. Buffalo (1-3) [-1.7419]
116. New Mexico (0-4) [-2.1243]
117. Eastern Michigan (0-3) [-2.5679]
118. Rice (0-4) [-2.6886]
119. Western Kentucky (0-4) [-2.8495]
120. Virginia (0-3) [-2.9512]
121. Ball St (0-4) [-3.8851]

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