Sunday, October 18, 2009

Rankings through October 17th

Some quick, probably insufficiently thought out comments about the new rankings... It seems fairly typical (in an unscientifically sampled way) to see algorithmic rankings start to make more sense here in the middle part of the season, as there is more information available and, in particular, as the number of undefeateds dwindles. The big end-of-season controversies usually don't start to make themselves clearer until later, because there are so many games left to play with so many different possible outcomes between now and then. Still, if you want, you can definitely start to guess at possible controversies to come, if the game outcomes align certain ways, particularly as more of the remaining undefeateds eventually lose.

Looking at the one-loss teams in the top 10 or top 12, along with two-loss Virginia Tech, one could certainly quibble over ordering; but each team's appearance there seems reasonable enough at this stage. LSU lost to Florida. Oregon's only loss was to Boise State (and helps to make the Broncos look subsequently better). But how does two-loss VT stay ranked so high? It's all about who they lost to, and who those teams lost to. Taken as a 3-team unit, ignoring their games against each other, the GT-VT-Miami triangle have only one loss: VT's loss to Alabama. The other three losses on their combined schedules are the three times one of them beat another. So in the "but my team beat your team" arguments, there are a lot of victories drawing some votes towards these teams, only the one loss to Alabama draining them away, and a lot of votes cycling around the triangle made up of these three teams.

And just in case you think there's an ACC bias here (there isn't), take a look at the conference rankings at the bottom of this post (told you).

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 17th:
1. Florida (6-0) [2.7889]
2. Alabama (7-0) [2.5812]
3. Iowa (7-0) [2.3490]
4. Texas (6-0) [1.9274]
5. Cincinnati (6-0) [1.7367]
6. Boise St (6-0) [1.7106]
7. LSU (5-1) [1.6075]
8. Georgia Tech (6-1) [1.5798]
9. Virginia Tech (5-2) [1.4777]
10. TCU (6-0) [1.4662]
11. Miami FL (5-1) [1.4501]
12. Oregon (5-1) [1.3937]
13. Southern Cal (5-1) [1.3706]
14. Arizona (4-2) [0.9424]
15. Houston (5-1) [0.8916]
16. Pittsburgh (6-1) [0.8087]
17. Wisconsin (5-2) [0.7842]
18. South Carolina (5-2) [0.7816]
19. Notre Dame (4-2) [0.7693]
20. Oklahoma St (5-1) [0.7482]
21. Penn State (6-1) [0.7235]
22. West Virginia (5-1) [0.7054]
23. Ohio State (5-2) [0.6803]
24. Georgia (4-3) [0.6789]
25. Washington (3-4) [0.6633]
26. Oregon St (4-2) [0.6617]
27. Kansas (5-1) [0.6232]
28. Utah (5-1) [0.6163]
29. Idaho (6-1) [0.6050]
30. California (4-2) [0.5798]
31. Brigham Young (6-1) [0.5688]
32. Arizona St (4-2) [0.5329]
33. Kentucky (3-3) [0.5328]
34. Auburn (5-2) [0.5222]
35. Arkansas (3-3) [0.5151]
36. Nebraska (4-2) [0.5019]
37. Boston College (5-2) [0.4647]
38. Michigan (5-2) [0.4579]
39. Central Michigan (6-1) [0.4220]
40. South Florida (5-1) [0.3967]
41. Stanford (4-3) [0.3564]
42. Texas Tech (5-2) [0.3335]
43. Troy (4-2) [0.2902]
44. UCLA (3-3) [0.2691]
45. Minnesota (4-3) [0.2675]
46. Mississippi (4-2) [0.2595]
47. Connecticut (4-2) [0.2587]
48. Clemson (3-3) [0.2447]
49. Tennessee (3-3) [0.2421]
50. Oklahoma (3-3) [0.2386]
51. Louisiana-Monroe (4-2) [0.2129]
52. North Carolina (4-2) [0.2005]
53. Michigan St (4-3) [0.1703]
54. Missouri (4-2) [0.1654]
55. Navy (5-2) [0.1533]
56. Rutgers (4-2) [0.1225]
57. Fresno St (3-3) [0.0799]
58. Louisiana-Lafayette (4-2) [0.0288]
59. Iowa St (4-3) [0.0141]
60. Wake Forest (4-3) [0.0076]
61. Colorado St (3-4) [0.0069]
62. Marshall (4-3) [-0.0084]
63. Mississippi St (3-4) [-0.0512]
64. Ohio U. (5-2) [-0.0572]
65. Florida St (2-4) [-0.0702]
66. Colorado (2-4) [-0.1013]
67. Air Force (4-3) [-0.1065]
68. Kansas St (4-3) [-0.1351]
69. Tulsa (4-2) [-0.1379]
70. Northern Illinois (3-3) [-0.1729]
71. East Carolina (4-3) [-0.1880]
72. Nevada (3-3) [-0.1923]
73. Baylor (3-3) [-0.2273]
74. Wyoming (4-3) [-0.2399]
75. Indiana (4-3) [-0.2487]
76. Southern Miss (4-3) [-0.2644]
77. SMU (3-3) [-0.2732]
78. Purdue (2-5) [-0.2974]
79. Central Florida (3-3) [-0.3155]
80. Virginia (3-3) [-0.3174]
81. Toledo (4-3) [-0.3289]
82. North Carolina St (3-4) [-0.3388]
83. Louisville (2-4) [-0.3594]
84. Middle Tennessee St (3-3) [-0.3620]
85. Louisiana Tech (3-3) [-0.3830]
86. Syracuse (2-4) [-0.3991]
87. Bowling Green (3-4) [-0.4010]
88. Texas A&M (3-3) [-0.4198]
89. UTEP (2-4) [-0.4266]
90. Northwestern (4-3) [-0.4289]
91. Duke (3-3) [-0.4764]
92. San Diego St (2-4) [-0.5287]
93. Western Michigan (3-4) [-0.5348]
94. Buffalo (3-4) [-0.5741]
95. Arkansas St (1-4) [-0.5934]
96. UNLV (2-5) [-0.6491]
97. Tulane (2-4) [-0.6502]
98. Washington St (1-5) [-0.6666]
99. San Jose St (1-5) [-0.6679]
100. Temple (4-2) [-0.6850]
101. Maryland (2-5) [-0.7816]
102. Hawai`i (2-4) [-0.8064]
103. Alabama-Birmingham (2-4) [-0.8168]
104. Kent St (3-4) [-0.8451]
105. Florida Atlantic (1-4) [-0.8665]
106. New Mexico St (3-4) [-0.8706]
107. Memphis (2-5) [-0.9384]
108. Illinois (1-5) [-0.9454]
109. Vanderbilt (2-5) [-0.9860]
110. Florida Int'l (1-5) [-1.0750]
111. Army (3-4) [-1.2312]
112. Akron (1-5) [-1.2534]
113. Utah St (1-5) [-1.2864]
114. North Texas (1-5) [-1.5233]
115. FCS teams (XXX-XXX) [-1.6214]
116. Miami OH (0-7) [-1.8190]
117. New Mexico (0-6) [-2.2315]
118. Rice (0-7) [-2.2360]
119. Eastern Michigan (0-6) [-2.7336]
120. Western Kentucky (0-6) [-2.7543]
121. Ball St (0-7) [-3.6397]
Conference Rankings (Average Per Team):
SEC 0.7894
Pac10 0.6103
BigEast 0.4088
Big10 0.3193
Big12 0.3057
ACC 0.2867
FBSInd -0.1029
MWC -0.1219
WAC -0.2012
CUSA -0.4470
SunBelt -0.7381
MAC -0.9710
Non-FBS -1.6214

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Friday, October 2, 2009

Virginia Tech, Really?

The midweek games have already come and gone, and I'm still a little puzzled about our RWFL rankings previously posted. Again, it's far too early in the season to expect good performance out of a computer ranking system that, like ours, ignores margin of victory, dates of games, and the previous season. But Virginia Tech (3-1) edging Iowa (4-0) for 2nd place?!? Now, sure, from a ranking violations standpoint, that's fine, since the loss came at the hands of #1 Alabama. But with so many undefeateds (including three potential BCS busters!), I found this result surprising.

The surprise disappears when we dig just a little further into the rankings. As we've done in this space for previous years, our tabulated results are for the specific bias value p=0.75 for the random walker algorithm. What this means is that each walker, considering a game between two teams, will decide that the winner is the better team 75% of the time. Why 75%? Seriously, essentially because it's halfway between 50% (ignoring the outcome altogether) and 100% (complete certainty that the outcome represents the better team). Okay, there's very slightly more to it than that: we tested the rankings across different p values and found that the middle of the range, around 75%, typically corresponds to the low values of rankings violations and the best values to predict bowl game outcomes in historical comparisons. And if you really press me for some other mathematical reasons, it turns out that RWFL rankings of round-robin tournaments appear (in numerical exploration) to agree perfectly with the resulting standings provided p is less than a value somewhere roughly around 0.75.

So, after all that mumbo jumbo, let's vary p and see what happens. You can see in the figure below that Virginia Tech and Miami both do well on the left (p closer to 0.5), but they fall quickly from these high perches as p increases moving to the right in the figure (VT and Miami are represented by the two curves moving quickly upwards towards worse rankings as p increases from left to right). Loosely speaking, this corresponds to the algorithm assigning an on-average stronger schedule to these teams on the left, while penalizing them for their losses on the right. At this point, the balance happens to be working out one way for them; but this high ranking is clearly tenuous at best.
We close today's post by briefly noting that the upcoming conference play might drastically change the above plot against Virginia Tech and Miami, even if they win, simply because the ACC is, on average, not ranked highly by this algorithm. In the plot below, we plot the average numbers of net RWFL votes (expressed as percentages) per team for each FBS conference (grouping the independents together). The way to read this plot is to look at vertical slices (fixed p values), wherein higher values correspond to greater numbers of net votes per team. So far, the ACC appears to be the weakest of the so-called major conferences at most p values, and indeed, it ranks weaker than some of the so-called mid-majors at higher values of p! No hate mail about this please; I'm just the messenger.

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