Sunday, December 6, 2009

Rankings through December 5th

Every time you changed the channel yesterday, there was another wild game on. Alabama rolled Florida. Texas survived last-second confusion and won on a last-second FG. Cincy came back from 21 down and won by the difference of Pitt's botched extra point attempt following a perhaps too-early TD. GT won a back-and-forth match with Clemson. And Fresno State beat Illinois on a stretch into the endzone in the last seconds, followed by a fluke tip drill two-point conversion. Okay, so that last one has zero implication for the BCS bowls, and most of us probably only saw it on SportsCenter; but it was crazy.

Cincy and TCU fans are probably steaming this morning that Texas got that second back. And Texas will probably lose a few votes in the BCS Standings, but the conventional wisdom seems to be that their lead over TCU last week was so large that it won't matter: Texas will play Alabama for the championship.

TCU will get the non-AQ group automatic qualification. The three remaining BCS at-large bids are up to the bowls themselves, but it seems certain that Florida will get one, and it seems likely that Boise State and either Iowa or Penn State will get the other. That is, unless a bowl game chooses to go to a three-loss team, it's just a matter of which team goes where; Brad Edwards at ESPN concisely breaks the process down and makes predictions.

Finally, on to our own rankings. Note the figure below the rank ordering of the 120 teams, because it says something interesting this week. Specifically, it plots the order of the top teams under varying the single "p value" bias parameter in our ranking system, which is a highly imperfect proxy for exploring other ranking systems that work under the same limiting assumptions (notably no margin of victory and no information about dates of games). While Alabama remains the undisputed #1 as the bias varies between its allowed values, Cincy, Florida, and Texas each make appearances at #2.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday December 5th:
1. Alabama (13-0) [1.6882]
2. Florida (12-1) [1.2422]
3. Cincinnati (12-0) [1.2000]
4. Texas (13-0) [1.1248]
5. TCU (12-0) [1.0198]
6. Oregon (10-2) [1.0023]
7. Georgia Tech (11-2) [0.9651]
8. Boise St (13-0) [0.9495]
9. Virginia Tech (9-3) [0.8073]
10. Ohio State (10-2) [0.7910]
11. LSU (9-3) [0.7865]
12. Iowa (10-2) [0.7746]
13. Miami FL (9-3) [0.7666]
14. West Virginia (9-3) [0.6841]
15. Arizona (8-4) [0.6710]
16. Southern Cal (8-4) [0.6678]
17. Stanford (8-4) [0.6546]
18. North Carolina (8-4) [0.6454]
19. Penn State (10-2) [0.6447]
20. Pittsburgh (9-3) [0.6344]
21. Oregon St (8-4) [0.6244]
22. Brigham Young (10-2) [0.6235]
23. Georgia (7-5) [0.6216]
24. Oklahoma St (9-3) [0.6175]
25. California (8-4) [0.6021]
26. Mississippi (8-4) [0.5896]
27. South Carolina (7-5) [0.5764]
28. Clemson (8-5) [0.5750]
29. Arkansas (7-5) [0.5734]
30. Auburn (7-5) [0.5696]
31. Tennessee (7-5) [0.5425]
32. Wisconsin (9-3) [0.5406]
33. Houston (10-3) [0.5280]
34. East Carolina (9-4) [0.5162]
35. Kentucky (7-5) [0.4978]
36. Utah (9-3) [0.4977]
37. Nebraska (9-4) [0.4903]
38. Boston College (8-4) [0.4878]
39. Florida St (6-6) [0.4825]
40. Texas Tech (8-4) [0.4599]
41. Missouri (8-4) [0.4591]
42. Central Michigan (11-2) [0.4558]
43. Northwestern (8-4) [0.4454]
44. Connecticut (7-5) [0.4429]
45. Oklahoma (7-5) [0.4380]
46. Washington (5-7) [0.4369]
47. South Florida (7-5) [0.4368]
48. Mississippi St (5-7) [0.4327]
49. Troy (9-3) [0.4211]
50. Central Florida (8-4) [0.4205]
51. Fresno St (8-4) [0.4197]
52. UCLA (6-6) [0.4193]
53. Rutgers (8-4) [0.4184]
54. Navy (8-4) [0.4175]
55. Nevada (8-4) [0.4011]
56. Notre Dame (6-6) [0.3973]
57. Minnesota (6-6) [0.3862]
58. Temple (9-3) [0.3607]
59. SMU (7-5) [0.3477]
60. Middle Tennessee St (9-3) [0.3437]
61. Wake Forest (5-7) [0.3422]
62. Michigan St (6-6) [0.3296]
63. Texas A&M (6-6) [0.3279]
64. Ohio U. (9-4) [0.3254]
65. Air Force (7-5) [0.3141]
66. North Carolina St (5-7) [0.3131]
67. Purdue (5-7) [0.3102]
68. Marshall (6-6) [0.3034]
69. Wyoming (6-6) [0.3017]
70. Idaho (7-5) [0.3011]
71. Southern Miss (7-5) [0.2985]
72. Bowling Green (7-5) [0.2968]
73. Arizona St (4-8) [0.2795]
74. Iowa St (6-6) [0.2771]
75. Virginia (3-9) [0.2765]
76. Syracuse (4-8) [0.2763]
77. Kansas St (6-6) [0.2736]
78. Duke (5-7) [0.2680]
79. Kansas (5-7) [0.2590]
80. UNLV (5-7) [0.2453]
81. Hawai`i (6-7) [0.2430]
82. Baylor (4-8) [0.2417]
83. Louisville (4-8) [0.2379]
84. Michigan (5-7) [0.2319]
85. Alabama-Birmingham (5-7) [0.2182]
86. Illinois (3-9) [0.2168]
87. Louisiana-Monroe (6-6) [0.2137]
88. Colorado (3-9) [0.2120]
89. Northern Illinois (7-5) [0.2065]
90. Louisiana-Lafayette (6-6) [0.2039]
91. Utah St (4-8) [0.1998]
92. Louisiana Tech (4-8) [0.1984]
93. UTEP (4-8) [0.1947]
94. Indiana (4-8) [0.1935]
95. Vanderbilt (2-10) [0.1921]
96. Tulsa (5-7) [0.1912]
97. San Diego St (4-8) [0.1860]
98. Washington St (1-11) [0.1816]
99. Colorado St (3-9) [0.1813]
100. Maryland (2-10) [0.1808]
101. Buffalo (5-7) [0.1735]
102. Florida Atlantic (5-7) [0.1715]
103. Toledo (5-7) [0.1697]
104. Florida Int'l (3-9) [0.1677]
105. Tulane (3-9) [0.1555]
106. Kent St (5-7) [0.1471]
107. San Jose St (2-10) [0.1420]
108. New Mexico St (3-10) [0.1388]
109. Army (5-6) [0.1341]
110. Rice (2-10) [0.1262]
111. Western Michigan (5-7) [0.1256]
112. Memphis (2-10) [0.1172]
113. Arkansas St (4-8) [0.1162]
114. Miami OH (1-11) [0.1088]
115. New Mexico (1-11) [0.1048]
116. Akron (3-9) [0.1004]
117. North Texas (2-10) [0.0838]
118. Ball St (2-10) [0.0634]
119. Eastern Michigan (0-12) [-0.0003]
120. Western Kentucky (0-12) [-0.0032]
Conference Rankings (Average Per Team):
SEC 0.6927
Pac10 0.5540
BigEast 0.5414
ACC 0.5092
Big10 0.4422
Big12 0.4317
MWC 0.3860
WAC 0.3326
FBSInd 0.3163
CUSA 0.2848
MAC 0.1949
SunBelt 0.1909
Non-FBS -0.0829

Labels:

Sunday, November 29, 2009

Rankings through November 28th

With only one week left before the bowl bids, the teams at the very top just keep on winning. Meanwhile, losses among BCS bid hopefuls Oklahoma State and Pitt have helped to slightly clarify the at-large possibilities.

First, the obvious: the winner of the SEC Championship game next weekend between Florida and Alabama will appear in the National Championship game. The loser will get one of the three BCS at-large bids. Texas will be the other half of the National Championship game if they beat Nebraska for the Big 12 Championship. TCU will get a non-AQ-group automatic bid to a BCS bowl, leaving only two at-large bids left up for grabs.

If Texas loses next weekend, they will certainly get an at-large bid, and we're going to hear lots of controversy about who should play in the National Championship game: Texas, TCU, Cincinnati (if they beat Pitt in the de facto Big East title game), or Boise State (if they win their final regular season game).

Will Boise State get an at-large bid? Let's break it down very quickly by assuming for the present argument that no three-loss team is going to get a BCS bowl bid this year (though that assumption might not be safe). This way, we take Oregon, GT, and Pitt out of at-large contention: if they win, they win the automatic bids from their respective conferences. The remaining variables then are Texas, Cincinnati, the Big Ten at-large hopefuls, and of course, Boise State has to win their regular season finale (otherwise this discussion is moot).

Assuming Boise State wins next weekend and no three-loss team gets an at-large bid, the remaining scenarios are:

If Texas and Cincy both lose next weekend, they very likely take the two remaining at-large bids, though Boise State, Iowa & Penn State fans might not be too pleased with the Cincinnati selection. More importantly, the bowl games (who ultimately make the selections) might decide a different selection is more lucrative. In any case, this scenario is bad for Boise State.

If Cincy wins and Texas loses, Texas certainly takes an at-large bid, leaving one left to go to either Boise State, Iowa, or Penn State. If the split goes the other way (Texas wins and Cincy loses), then perhaps the Cincy selection isn't quite so certain, leaving two at-large bids to split among these teams. Does Boise State get one under this scenario? I have no idea. Note this might also end up depending on the other conference championship games, in that it might be hard to rationalize an Iowa/PennSt selection over a Boise State squad ranked, say, five spots higher in the BCS Standings; but if other teams fall, the rank-order gap might narrow significantly.

Finally, the good news for Boise State: if Texas and Cincy both win next weekend, they take their respective conferences' automatic bids, leaving two at-large bids remaining. In this scenario, an undefeated Boise State is all but certain to grab a BCS bid, since the Big Ten can only take one at-large bid (to either Iowa or Penn State). The only way to deny Boise State in this scenario is to give an at-large bid to a three-loss team. So the Broncos will be cheering for the Longhorns and Bearcats, and if all three win, it looks like we'll see two non-AQ group schools in the BCS games for the first time.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 28th:
1. Alabama (12-0) [1.4900]
2. Florida (12-0) [1.4155]
3. Cincinnati (11-0) [1.1452]
4. Texas (12-0) [1.0918]
5. TCU (12-0) [1.0246]
6. Boise St (12-0) [0.9648]
7. Oregon (9-2) [0.9501]
8. Georgia Tech (10-2) [0.9121]
9. Ohio State (10-2) [0.7874]
10. Virginia Tech (9-3) [0.7827]
11. LSU (9-3) [0.7669]
12. Miami FL (9-3) [0.7656]
13. Southern Cal (8-3) [0.7645]
14. Iowa (10-2) [0.7552]
15. Pittsburgh (9-2) [0.6931]
16. Oregon St (8-3) [0.6788]
17. California (8-3) [0.6785]
18. Stanford (8-4) [0.6565]
19. Penn State (10-2) [0.6446]
20. West Virginia (8-3) [0.6358]
21. Brigham Young (10-2) [0.6218]
22. North Carolina (8-4) [0.6187]
23. Oklahoma St (9-3) [0.6181]
24. Georgia (7-5) [0.6170]
25. Clemson (8-4) [0.6148]
26. Houston (10-2) [0.5983]
27. Arizona (7-4) [0.5967]
28. South Carolina (7-5) [0.5749]
29. Mississippi (8-4) [0.5728]
30. Arkansas (7-5) [0.5678]
31. Auburn (7-5) [0.5456]
32. Tennessee (7-5) [0.5430]
33. Wisconsin (8-3) [0.5170]
34. Nebraska (9-3) [0.5057]
35. Utah (9-3) [0.4952]
36. Kentucky (7-5) [0.4924]
37. Florida St (6-6) [0.4890]
38. South Florida (7-4) [0.4845]
39. Boston College (8-4) [0.4844]
40. Texas Tech (8-4) [0.4635]
41. Rutgers (8-3) [0.4605]
42. Missouri (8-4) [0.4569]
43. East Carolina (8-4) [0.4418]
44. Northwestern (8-4) [0.4401]
45. Oklahoma (7-5) [0.4367]
46. Troy (9-3) [0.4295]
47. Mississippi St (5-7) [0.4284]
48. Central Florida (8-4) [0.4237]
49. Navy (8-4) [0.4199]
50. UCLA (6-6) [0.4165]
51. Central Michigan (10-2) [0.4135]
52. Connecticut (6-5) [0.4011]
53. Fresno St (7-4) [0.3965]
54. Nevada (8-4) [0.3957]
55. Notre Dame (6-6) [0.3933]
56. Minnesota (6-6) [0.3872]
57. Washington (4-7) [0.3808]
58. Temple (9-3) [0.3637]
59. Ohio U. (9-3) [0.3557]
60. Middle Tennessee St (9-3) [0.3467]
61. SMU (7-5) [0.3434]
62. Wake Forest (5-7) [0.3420]
63. Texas A&M (6-6) [0.3256]
64. Michigan St (6-6) [0.3248]
65. North Carolina St (5-7) [0.3189]
66. Air Force (7-5) [0.3135]
67. Purdue (5-7) [0.3067]
68. Marshall (6-6) [0.3017]
69. Bowling Green (7-5) [0.2987]
70. Southern Miss (7-5) [0.2975]
71. Wyoming (6-6) [0.2968]
72. Idaho (7-5) [0.2954]
73. Syracuse (4-8) [0.2801]
74. Iowa St (6-6) [0.2788]
75. Arizona St (4-8) [0.2766]
76. Kansas St (6-6) [0.2754]
77. Virginia (3-9) [0.2729]
78. Duke (5-7) [0.2676]
79. Kansas (5-7) [0.2584]
80. Hawai`i (6-6) [0.2518]
81. UNLV (5-7) [0.2469]
82. Baylor (4-8) [0.2397]
83. Louisville (4-8) [0.2378]
84. Michigan (5-7) [0.2292]
85. Illinois (3-8) [0.2262]
86. Alabama-Birmingham (5-7) [0.2129]
87. Louisiana-Monroe (6-6) [0.2109]
88. Colorado (3-9) [0.2088]
89. Louisiana-Lafayette (6-6) [0.2051]
90. Northern Illinois (7-5) [0.2041]
91. UTEP (4-8) [0.1987]
92. Utah St (4-8) [0.1975]
93. Vanderbilt (2-10) [0.1936]
94. Indiana (4-8) [0.1921]
95. Tulsa (5-7) [0.1916]
96. Maryland (2-10) [0.1891]
97. Florida Int'l (3-8) [0.1875]
98. San Diego St (4-8) [0.1832]
99. Washington St (1-11) [0.1824]
100. Louisiana Tech (3-8) [0.1811]
101. Colorado St (3-9) [0.1793]
102. Buffalo (5-7) [0.1768]
103. Toledo (5-7) [0.1691]
104. San Jose St (2-9) [0.1567]
105. Tulane (3-9) [0.1565]
106. Florida Atlantic (4-7) [0.1515]
107. Kent St (5-7) [0.1509]
108. Army (5-6) [0.1361]
109. Rice (2-10) [0.1264]
110. Western Michigan (5-7) [0.1248]
111. New Mexico St (3-9) [0.1220]
112. Memphis (2-10) [0.1167]
113. Arkansas St (3-8) [0.1092]
114. Miami OH (1-11) [0.1084]
115. New Mexico (1-11) [0.1035]
116. Akron (3-9) [0.1004]
117. North Texas (2-10) [0.0790]
118. Ball St (2-10) [0.0631]
119. Western Kentucky (0-11) [0.0062]
120. Eastern Michigan (0-12) [-0.0022]
Conference Rankings (Average Per Team):
SEC 0.6840
Pac10 0.5581
BigEast 0.5423
ACC 0.5048
Big10 0.4373
Big12 0.4300
MWC 0.3850
WAC 0.3290
FBSInd 0.3164
CUSA 0.2841
MAC 0.1944
SunBelt 0.1917
Non-FBS -0.0825

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Sunday, November 22, 2009

Rankings through November 21st

Another week of wins at the top of last week's BCS Standings. The most prominent loss near the top of the Standings was LSU's confused clock management thriller at Ole Miss. Of course, other losses by Notre Dame, Kansas and Michigan make big news because coaching jobs might be on the line, but we're now most interested in the BCS Bowl bids here.

All signs continue to point to a probable Alabama/Florida v. Texas National Championship Game, though of course that might depend on teams continuing to win. That said, it's becoming conceivable that Texas could lose a game down the stretch and still appear in the National Championship (the earliest compelling argument I heard for this was on Slate's Hang Up and Listen podcast). So I continue to be most interested right now in whether Boise State will get a BCS at-large bid this year.

Without repeating yesterday's post, the LSU loss possibly hurts Boise State a little, simply because LSU wasn't going to get a BCS Bowl bid anyway (assuming Florida and Alabama get them, with only two allowed per conference). So LSU will fall from their current BCS#8 spot, and someone else who might be in the running for an at-large bid will be able to make a stronger case. Maybe I'm splitting hairs here worrying on Boise State's behalf about one loss by LSU. But there could be a lot of teams making a respectable case for an at-large bid if they don't win their conference championships: Texas plays Nebraska, GT faces Clemson, Cincy gets Pitt, and Oregon hosts Oregon State in the now de facto Pac-10 championship game. Again, we take it as a given that the loser of Florida/Alabama will get an at-large bid, and we assume that TCU will get the non-AQ-group automatic berth if they beat New Mexico next week. That leaves two at-large bids remaining, some of which could disappear to losers of the conference championship games, or even to the Big Ten.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 21st:
1. Alabama (11-0) [1.3873]
2. Florida (11-0) [1.2604]
3. Cincinnati (10-0) [1.2062]
4. Georgia Tech (10-1) [1.1521]
5. TCU (11-0) [1.1169]
6. Texas (11-0) [1.0729]
7. Oregon (9-2) [0.9538]
8. Boise St (11-0) [0.9062]
9. Pittsburgh (9-1) [0.8839]
10. Ohio State (10-2) [0.8350]
11. Virginia Tech (8-3) [0.7996]
12. Miami FL (8-3) [0.7874]
13. Iowa (10-2) [0.7809]
14. North Carolina (8-3) [0.7454]
15. Southern Cal (7-3) [0.7449]
16. Clemson (8-3) [0.7240]
17. Penn State (10-2) [0.6923]
18. California (8-3) [0.6850]
19. Oklahoma St (9-2) [0.6742]
20. Oregon St (8-3) [0.6731]
21. LSU (8-3) [0.6490]
22. Stanford (7-4) [0.6206]
23. Mississippi (8-3) [0.6025]
24. Houston (9-2) [0.5948]
25. Arizona (6-4) [0.5763]
26. Arkansas (7-4) [0.5670]
27. West Virginia (7-3) [0.5627]
28. Utah (9-2) [0.5575]
29. South Florida (7-3) [0.5547]
30. Brigham Young (9-2) [0.5481]
31. Wisconsin (8-3) [0.5401]
32. Florida St (6-5) [0.5242]
33. Auburn (7-4) [0.5063]
34. Navy (8-3) [0.5059]
35. Kentucky (7-4) [0.5029]
36. Boston College (7-4) [0.4981]
37. South Carolina (6-5) [0.4919]
38. Georgia (6-5) [0.4811]
39. Nebraska (8-3) [0.4753]
40. Rutgers (7-3) [0.4727]
41. Northwestern (8-4) [0.4598]
42. Temple (9-2) [0.4448]
43. Tennessee (6-5) [0.4446]
44. Notre Dame (6-5) [0.4387]
45. Missouri (7-4) [0.4333]
46. UCLA (6-5) [0.4262]
47. Texas Tech (7-4) [0.4256]
48. East Carolina (7-4) [0.4150]
49. Central Florida (7-4) [0.4123]
50. Minnesota (6-6) [0.4084]
51. Central Michigan (9-2) [0.4007]
52. Troy (8-3) [0.3985]
53. Connecticut (5-5) [0.3958]
54. Nevada (8-3) [0.3955]
55. Fresno St (7-4) [0.3857]
56. Washington (3-7) [0.3645]
57. Mississippi St (4-7) [0.3637]
58. Oklahoma (6-5) [0.3586]
59. Michigan St (6-6) [0.3419]
60. Wake Forest (4-7) [0.3372]
61. Southern Miss (7-4) [0.3362]
62. Marshall (6-5) [0.3341]
63. Idaho (7-4) [0.3291]
64. SMU (6-5) [0.3276]
65. Middle Tennessee St (8-3) [0.3266]
66. Purdue (5-7) [0.3241]
67. Air Force (7-5) [0.3215]
68. Syracuse (4-7) [0.3196]
69. Virginia (3-8) [0.3158]
70. Duke (5-6) [0.3154]
71. Texas A&M (6-5) [0.3116]
72. Ohio U. (8-3) [0.3014]
73. North Carolina St (4-7) [0.2844]
74. Wyoming (5-6) [0.2841]
75. Iowa St (6-6) [0.2825]
76. Arizona St (4-7) [0.2815]
77. Kansas (5-6) [0.2761]
78. Bowling Green (6-5) [0.2736]
79. Louisville (4-7) [0.2728]
80. Kansas St (6-6) [0.2699]
81. Baylor (4-7) [0.2485]
82. Michigan (5-7) [0.2481]
83. Northern Illinois (7-4) [0.2280]
84. UNLV (4-7) [0.2276]
85. Alabama-Birmingham (5-6) [0.2244]
86. Louisiana-Monroe (6-5) [0.2230]
87. Illinois (3-7) [0.2219]
88. Colorado (3-8) [0.2155]
89. Louisiana-Lafayette (6-5) [0.2121]
90. Maryland (2-9) [0.2100]
91. San Diego St (4-7) [0.2051]
92. Indiana (4-8) [0.2047]
93. Colorado St (3-8) [0.1993]
94. Hawai`i (5-6) [0.1967]
95. Toledo (5-6) [0.1940]
96. Washington St (1-10) [0.1870]
97. Vanderbilt (2-10) [0.1809]
98. Florida Int'l (3-8) [0.1781]
99. Kent St (5-6) [0.1717]
100. Louisiana Tech (3-8) [0.1702]
101. Tulsa (4-7) [0.1675]
102. Buffalo (4-7) [0.1650]
103. UTEP (3-8) [0.1637]
104. Tulane (3-8) [0.1588]
105. Utah St (3-8) [0.1586]
106. Western Michigan (5-6) [0.1557]
107. Army (5-6) [0.1415]
108. Florida Atlantic (3-7) [0.1384]
109. San Jose St (1-9) [0.1352]
110. New Mexico St (3-8) [0.1303]
111. Memphis (2-9) [0.1249]
112. Rice (2-9) [0.1204]
113. Miami OH (1-11) [0.1152]
114. Akron (2-9) [0.0997]
115. Arkansas St (2-8) [0.0908]
116. North Texas (2-9) [0.0851]
117. New Mexico (1-10) [0.0814]
118. Ball St (1-10) [0.0415]
119. Western Kentucky (0-10) [0.0134]
120. Eastern Michigan (0-11) [0.0131]
Conference Rankings (Average Per Team):
SEC 0.6198
BigEast 0.5836
ACC 0.5578
Pac10 0.5513
Big10 0.4597
Big12 0.4203
MWC 0.3935
FBSInd 0.3620
WAC 0.3119
CUSA 0.2816
MAC 0.2003
SunBelt 0.1851
Non-FBS -0.0831

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Sunday, November 15, 2009

Rankings through November 14th

No big changes at the top of the RWFL rankings this week.

TCU solidified their position across various p bias values---if you look at the plot below the list of ranks, their win against Utah definitely helps in general, but still leaves them in fourth-place at the selected p=0.75 value posted here. This might help solidify TCU's narrowly-held #4 position in the BCS Standings, since they were already ahead of Cincinnati in both polls and should now do better than before in the computer component. But of course TCU will still be behind Texas in the BCS Standings, since they were already ahead of Texas in the composite of the computers and were still well behind Texas in the Standings.

That is, unless someone loses, we seem to be on course for a championship game between Texas and the winner of the Florida-Alabama "semifinal" SEC Championship game. TCU is on course for an automatic BCS bowl game berth; in contrast, Boise State's relatively weaker strength of schedule continues to leave them later in the discussion. Because of the wrinkles in the rules that only give one automatic BCS bid to the "non-AQ group", Boise State will possibly be hoping for one of the at-large bids, and those at-large bids do not have to follow the BCS Standings, as Boise State learned all too well last year when they watched a lower-rated Ohio State team take the last BCS bid.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 14th:
1. Alabama (10-0) [1.4580]
2. Florida (10-0) [1.3715]
3. Cincinnati (10-0) [1.1665]
4. TCU (10-0) [1.1513]
5. Georgia Tech (10-1) [1.1157]
6. Texas (10-0) [1.0832]
7. Boise St (10-0) [0.9626]
8. Oregon (8-2) [0.9185]
9. Pittsburgh (9-1) [0.8749]
10. Ohio State (9-2) [0.8747]
11. Iowa (9-2) [0.8048]
12. LSU (8-2) [0.7904]
13. Southern Cal (7-3) [0.7818]
14. Virginia Tech (7-3) [0.7656]
15. Miami FL (7-3) [0.7521]
16. Stanford (7-3) [0.7219]
17. Clemson (7-3) [0.7040]
18. Oregon St (7-3) [0.6998]
19. Oklahoma St (8-2) [0.6666]
20. Penn State (9-2) [0.6635]
21. Arizona (6-3) [0.6618]
22. Wisconsin (8-2) [0.6567]
23. North Carolina (7-3) [0.6480]
24. California (7-3) [0.6326]
25. Houston (8-2) [0.6094]
26. Utah (8-2) [0.5507]
27. Boston College (7-3) [0.5498]
28. Georgia (6-4) [0.5491]
29. Arkansas (6-4) [0.5351]
30. Navy (8-3) [0.5326]
31. Rutgers (7-2) [0.5299]
32. Brigham Young (8-2) [0.5200]
33. Mississippi (7-3) [0.5192]
34. Notre Dame (6-4) [0.5182]
35. West Virginia (7-3) [0.5174]
36. South Florida (6-3) [0.5016]
37. Auburn (7-4) [0.4948]
38. Florida St (5-5) [0.4892]
39. South Carolina (6-5) [0.4885]
40. Kentucky (6-4) [0.4662]
41. Nebraska (7-3) [0.4464]
42. Tennessee (5-5) [0.4407]
43. Temple (8-2) [0.4321]
44. Minnesota (6-5) [0.4253]
45. UCLA (5-5) [0.4175]
46. Central Michigan (8-2) [0.4161]
47. Northwestern (7-4) [0.4023]
48. Nevada (7-3) [0.4020]
49. Missouri (6-4) [0.4008]
50. Mississippi St (4-6) [0.4004]
51. Troy (7-3) [0.3978]
52. Washington (3-7) [0.3974]
53. Oklahoma (6-4) [0.3954]
54. Fresno St (6-4) [0.3905]
55. Central Florida (6-4) [0.3814]
56. Texas Tech (6-4) [0.3731]
57. SMU (6-4) [0.3699]
58. Michigan St (6-5) [0.3674]
59. Idaho (7-4) [0.3505]
60. East Carolina (5-4) [0.3505]
61. Air Force (7-4) [0.3443]
62. Wake Forest (4-7) [0.3439]
63. Connecticut (4-5) [0.3345]
64. Purdue (4-7) [0.3231]
65. Virginia (3-7) [0.3212]
66. Arizona St (4-6) [0.3201]
67. Middle Tennessee St (7-3) [0.3143]
68. Duke (5-5) [0.3137]
69. Southern Miss (6-4) [0.3070]
70. Iowa St (6-5) [0.3040]
71. North Carolina St (4-6) [0.2888]
72. Marshall (5-5) [0.2861]
73. Kansas St (6-5) [0.2809]
74. Texas A&M (5-5) [0.2760]
75. Baylor (4-6) [0.2692]
76. Ohio U. (7-3) [0.2686]
77. Northern Illinois (7-3) [0.2680]
78. Louisville (4-6) [0.2678]
79. Kansas (5-5) [0.2672]
80. Wyoming (5-5) [0.2672]
81. Michigan (5-6) [0.2657]
82. Bowling Green (5-5) [0.2629]
83. Syracuse (3-7) [0.2547]
84. Louisiana-Monroe (6-4) [0.2545]
85. Alabama-Birmingham (5-5) [0.2298]
86. Colorado St (3-7) [0.2291]
87. Indiana (4-7) [0.2266]
88. UNLV (4-7) [0.2246]
89. Illinois (3-7) [0.2220]
90. Maryland (2-8) [0.2139]
91. San Diego St (4-6) [0.2120]
92. Colorado (3-7) [0.2109]
93. Washington St (1-9) [0.1993]
94. Tulsa (4-5) [0.1976]
95. UTEP (3-7) [0.1941]
96. Toledo (4-6) [0.1931]
97. Vanderbilt (2-9) [0.1914]
98. Louisiana-Lafayette (5-5) [0.1894]
99. Hawai`i (4-6) [0.1863]
100. Louisiana Tech (3-7) [0.1856]
101. Kent St (5-5) [0.1831]
102. Tulane (3-7) [0.1678]
103. San Jose St (1-8) [0.1599]
104. Western Michigan (5-6) [0.1574]
105. Florida Int'l (3-7) [0.1571]
106. Buffalo (3-7) [0.1481]
107. Utah St (3-7) [0.1453]
108. Florida Atlantic (3-6) [0.1425]
109. New Mexico St (3-7) [0.1328]
110. Army (4-6) [0.1321]
111. Miami OH (1-10) [0.1248]
112. Memphis (2-8) [0.1102]
113. Akron (2-8) [0.1020]
114. North Texas (2-8) [0.0981]
115. Rice (1-9) [0.0951]
116. Arkansas St (2-7) [0.0923]
117. New Mexico (0-10) [0.0460]
118. Ball St (1-9) [0.0344]
119. Eastern Michigan (0-10) [0.0140]
120. Western Kentucky (0-10) [0.0125]
Conference Rankings (Average Per Team):
SEC 0.6421
Pac10 0.5751
BigEast 0.5559
ACC 0.5422
Big10 0.4756
Big12 0.4145
FBSInd 0.3943
MWC 0.3939
WAC 0.3239
CUSA 0.2749
MAC 0.2004
SunBelt 0.1843
Non-FBS -0.0836

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Sunday, November 8, 2009

Rankings through November 7th

Two key losses this week effectively eliminate the title hopes of both Iowa and Oregon. Whatever our own rankings say below, it seems clear that the BCS is on a likely trajectory to a championship game between Texas and the winner of the Florida-Alabama "national semi-final" SEC Championship Game. Of course, if someone stumbles, Cincinnati, TCU & Boise State are all there waiting and hoping...

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday November 7th:
1. Alabama (9-0) [1.4886]
2. Florida (9-0) [1.3796]
3. Cincinnati (9-0) [1.1104]
4. TCU (9-0) [1.0754]
5. Georgia Tech (9-1) [1.0749]
6. Texas (9-0) [1.0623]
7. Iowa (9-1) [0.9969]
8. Boise St (9-0) [0.9968]
9. Oregon (7-2) [0.9503]
10. Southern Cal (7-2) [0.8936]
11. Miami FL (7-2) [0.8435]
12. LSU (7-2) [0.8376]
13. Ohio State (8-2) [0.7920]
14. Pittsburgh (8-1) [0.7876]
15. Arizona (6-2) [0.7793]
16. Virginia Tech (6-3) [0.7577]
17. Houston (8-1) [0.7383]
18. Penn State (8-2) [0.6932]
19. Wisconsin (7-2) [0.6782]
20. Clemson (6-3) [0.6766]
21. Stanford (6-3) [0.6530]
22. Oregon St (6-3) [0.6506]
23. Oklahoma St (7-2) [0.5992]
24. South Florida (6-2) [0.5860]
25. Utah (8-1) [0.5841]
26. Notre Dame (6-3) [0.5727]
27. West Virginia (7-2) [0.5629]
28. Auburn (7-3) [0.5611]
29. California (6-3) [0.5426]
30. Brigham Young (7-2) [0.5242]
31. North Carolina (6-3) [0.5139]
32. Arkansas (5-4) [0.5073]
33. Navy (7-3) [0.5064]
34. Boston College (6-3) [0.5047]
35. Georgia (5-4) [0.4917]
36. Tennessee (5-4) [0.4911]
37. South Carolina (6-4) [0.4844]
38. Kentucky (5-4) [0.4713]
39. Mississippi (6-3) [0.4702]
40. Washington (3-6) [0.4643]
41. Troy (7-2) [0.4590]
42. Fresno St (6-3) [0.4577]
43. Temple (7-2) [0.4420]
44. Florida St (4-5) [0.4358]
45. UCLA (4-5) [0.4302]
46. Northwestern (6-4) [0.4300]
47. Texas Tech (6-3) [0.4225]
48. Rutgers (6-2) [0.4216]
49. Minnesota (5-5) [0.4131]
50. Nebraska (6-3) [0.4129]
51. Central Michigan (7-2) [0.4061]
52. Mississippi St (4-5) [0.4012]
53. Oklahoma (5-4) [0.3762]
54. Idaho (7-3) [0.3761]
55. Purdue (4-6) [0.3604]
56. Wake Forest (4-6) [0.3598]
57. Michigan St (5-5) [0.3564]
58. Missouri (5-4) [0.3527]
59. SMU (5-4) [0.3354]
60. Kansas St (6-4) [0.3331]
61. Nevada (5-3) [0.3309]
62. Arizona St (4-5) [0.3285]
63. Marshall (5-4) [0.3240]
64. Virginia (3-6) [0.3201]
65. East Carolina (5-4) [0.3191]
66. Air Force (6-4) [0.3105]
67. Connecticut (4-5) [0.3095]
68. Michigan (5-5) [0.3061]
69. Texas A&M (5-4) [0.3045]
70. Duke (5-4) [0.2961]
71. Middle Tennessee St (6-3) [0.2948]
72. Kansas (5-4) [0.2913]
73. Syracuse (3-6) [0.2911]
74. Central Florida (5-4) [0.2905]
75. Iowa St (5-5) [0.2848]
76. North Carolina St (4-5) [0.2840]
77. Northern Illinois (6-3) [0.2838]
78. Ohio U. (6-3) [0.2678]
79. Southern Miss (5-4) [0.2672]
80. Louisiana-Monroe (5-4) [0.2636]
81. Bowling Green (4-5) [0.2630]
82. Indiana (4-6) [0.2499]
83. Baylor (4-5) [0.2470]
84. Illinois (3-6) [0.2449]
85. Wyoming (4-5) [0.2381]
86. Colorado (3-6) [0.2381]
87. UTEP (3-6) [0.2364]
88. San Diego St (4-5) [0.2363]
89. Louisville (3-6) [0.2342]
90. UNLV (4-6) [0.2334]
91. Louisiana-Lafayette (5-4) [0.2290]
92. Colorado St (3-7) [0.2200]
93. San Jose St (1-6) [0.2162]
94. Toledo (4-5) [0.2149]
95. Alabama-Birmingham (4-5) [0.2137]
96. Washington St (1-8) [0.2132]
97. Tulane (3-6) [0.2061]
98. Tulsa (4-5) [0.2033]
99. Maryland (2-7) [0.1981]
100. Vanderbilt (2-8) [0.1888]
101. Kent St (5-5) [0.1836]
102. Louisiana Tech (3-6) [0.1767]
103. Hawai`i (3-6) [0.1746]
104. Western Michigan (4-6) [0.1652]
105. Buffalo (3-6) [0.1614]
106. New Mexico St (3-6) [0.1511]
107. Florida Int'l (2-7) [0.1494]
108. Miami OH (1-9) [0.1402]
109. Florida Atlantic (2-6) [0.1293]
110. Utah St (2-7) [0.1288]
111. Army (3-6) [0.1255]
112. North Texas (2-7) [0.1241]
113. Arkansas St (2-6) [0.1226]
114. Memphis (2-7) [0.1217]
115. Akron (2-7) [0.1106]
116. Rice (0-9) [0.0540]
117. Ball St (1-8) [0.0483]
118. New Mexico (0-9) [0.0421]
119. Western Kentucky (0-9) [0.0270]
120. Eastern Michigan (0-9) [0.0251]
Conference Rankings (Average Per Team):
SEC 0.6477
Pac10 0.5906
BigEast 0.5379
ACC 0.5221
Big10 0.5019
Big12 0.4104
FBSInd 0.4016
MWC 0.3849
WAC 0.3343
CUSA 0.2758
MAC 0.2086
SunBelt 0.1999
Non-FBS -0.0842

Labels:

Sunday, November 1, 2009

Rankings through October 31st

The undefeated teams all won again, with Iowa adding to their catalog of close calls. That said, you have to give the Hawkeyes credit: wins are wins. We have a lot of football left to play this season, so virtually anything can happen. Certainly Iowa has some big games left on their schedule. However, if Iowa continues to win and there's any BCS controversy down the stretch, I'd expect the off-season BCS discussions to include reconsideration of the rules which prevent computer rankings from including margin of victory.

In the meantime, I'd be surprised if Iowa falls much in this week's official BCS Standings, if at all, since they were already only #8 in both polls last week. Oregon, after their impressive victory over USC, is the obvious candidate to potentially pass Iowa. TCU, Boise State, and Cincinnati were each already ahead of Iowa in the polls, but behind Iowa in the total standings because of the computer ranking component, and it's hard for me to see how that will change.

Speaking of the remaining BCS busters, we have double intrigue waiting for the official BCS Standings this week. First, I'm interested to see whether BCS#6 TCU stays ahead of BCS#7 Boise State in this week's Standings. Boise State, already ahead of TCU in both polls last week, is likely to get a small boost in the computer rankings from the follow-on effect of Oregon's victory over USC, given Boise State's season-opening win over Oregon. Will it be enough to pass TCU in the official Standings? Second, we eagerly wait to see the relative rankings between Oregon and Boise State. The Ducks will undoubtedly get a big boost across all the BCS components this week, but will it be enough to pass the Broncos, the only team to beat them on the field this season?

Using the random walker rankings across various p values as an imperfect proxy for other rankings, the closeness of these questions regarding Boise State are evident in the figure presented here below the p=0.75 rankings. Boise State is ranked higher than TCU for p > 0.7 (approximately) and higher than Oregon for p > 0.8. In other words, very slight changes in the methodology (e.g., changing the p value) can reasonably have big effects in the rank ordering in this situation.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 31st:
1. Florida (8-0) [1.5226]
2. Iowa (9-0) [1.3781]
3. Alabama (8-0) [1.3288]
4. Oregon (7-1) [1.2656]
5. Boise St (8-0) [1.1549]
6. Texas (8-0) [1.1480]
7. TCU (8-0) [1.0819]
8. Cincinnati (8-0) [1.0588]
9. Georgia Tech (8-1) [1.0200]
10. LSU (7-1) [0.9699]
11. Southern Cal (6-2) [0.9276]
12. Penn State (8-1) [0.8159]
13. Miami FL (6-2) [0.7950]
14. Arizona (5-2) [0.7487]
15. Houston (7-1) [0.7412]
16. Pittsburgh (7-1) [0.7346]
17. Virginia Tech (5-3) [0.7173]
18. Notre Dame (6-2) [0.7120]
19. Wisconsin (6-2) [0.6726]
20. Utah (7-1) [0.6687]
21. California (6-2) [0.6666]
22. Ohio State (7-2) [0.6604]
23. Oklahoma St (6-2) [0.6069]
24. Clemson (5-3) [0.5981]
25. South Florida (6-2) [0.5667]
26. Auburn (6-3) [0.5600]
27. Washington (3-5) [0.5577]
28. West Virginia (6-2) [0.5328]
29. Oregon St (5-3) [0.5319]
30. South Carolina (6-3) [0.5292]
31. Brigham Young (6-2) [0.5189]
32. Georgia (4-4) [0.5091]
33. Boston College (6-3) [0.5045]
34. Stanford (5-3) [0.5002]
35. Tennessee (4-4) [0.4980]
36. Troy (6-2) [0.4887]
37. Kentucky (4-4) [0.4732]
38. North Carolina (5-3) [0.4711]
39. Florida St (4-4) [0.4556]
40. Arkansas (4-4) [0.4500]
41. Minnesota (5-4) [0.4463]
42. Idaho (7-2) [0.4406]
43. Oklahoma (5-3) [0.4341]
44. Texas Tech (6-3) [0.4313]
45. Mississippi (5-3) [0.4245]
46. Fresno St (5-3) [0.4179]
47. Central Michigan (7-2) [0.4109]
48. Missouri (5-3) [0.4108]
49. Rutgers (6-2) [0.4092]
50. Temple (6-2) [0.4047]
51. Mississippi St (4-5) [0.4026]
52. Michigan (5-4) [0.4012]
53. Navy (6-3) [0.3883]
54. UCLA (3-5) [0.3765]
55. Nebraska (5-3) [0.3680]
56. Kansas (5-3) [0.3633]
57. Texas A&M (5-3) [0.3633]
58. Michigan St (4-5) [0.3583]
59. Marshall (5-3) [0.3572]
60. Nevada (5-3) [0.3554]
61. Arizona St (4-4) [0.3493]
62. Duke (5-3) [0.3388]
63. SMU (4-4) [0.3271]
64. Virginia (3-5) [0.3258]
65. Iowa St (5-4) [0.3229]
66. Wake Forest (4-5) [0.3193]
67. Purdue (3-6) [0.3192]
68. East Carolina (5-3) [0.3141]
69. Kansas St (5-4) [0.3081]
70. Air Force (5-4) [0.3060]
71. Connecticut (4-4) [0.2868]
72. UTEP (3-5) [0.2821]
73. Northern Illinois (5-3) [0.2799]
74. Syracuse (3-5) [0.2797]
75. Northwestern (5-4) [0.2788]
76. Ohio U. (6-3) [0.2776]
77. Middle Tennessee St (5-3) [0.2723]
78. Bowling Green (3-5) [0.2686]
79. Louisiana-Monroe (4-4) [0.2655]
80. Indiana (4-5) [0.2628]
81. Wyoming (4-4) [0.2608]
82. Colorado St (3-6) [0.2544]
83. North Carolina St (3-5) [0.2542]
84. Southern Miss (5-4) [0.2541]
85. Louisville (3-5) [0.2489]
86. San Jose St (1-6) [0.2317]
87. Washington St (1-7) [0.2299]
88. San Diego St (4-4) [0.2258]
89. Kent St (5-4) [0.2189]
90. Colorado (2-6) [0.2176]
91. Maryland (2-6) [0.2113]
92. Central Florida (4-3) [0.2107]
93. Tulsa (4-4) [0.2093]
94. Louisiana-Lafayette (4-4) [0.2077]
95. UNLV (3-6) [0.2069]
96. Illinois (2-6) [0.2042]
97. Alabama-Birmingham (3-5) [0.2037]
98. Toledo (4-5) [0.2018]
99. Baylor (3-5) [0.1968]
100. Western Michigan (4-5) [0.1901]
101. Buffalo (3-5) [0.1798]
102. Tulane (2-6) [0.1780]
103. Hawai`i (2-6) [0.1666]
104. Arkansas St (2-5) [0.1647]
105. Vanderbilt (2-7) [0.1580]
106. Utah St (2-6) [0.1555]
107. Louisiana Tech (3-5) [0.1539]
108. Florida Int'l (2-6) [0.1537]
109. New Mexico St (3-6) [0.1476]
110. Miami OH (1-8) [0.1444]
111. Florida Atlantic (2-5) [0.1443]
112. Army (3-5) [0.1292]
113. North Texas (2-6) [0.1264]
114. Memphis (2-6) [0.1161]
115. Akron (1-7) [0.0875]
116. Ball St (1-8) [0.0440]
117. Rice (0-8) [0.0391]
118. New Mexico (0-8) [0.0277]
119. Eastern Michigan (0-8) [0.0183]
120. Western Kentucky (0-8) [0.0063]
Conference Rankings (Average Per Team):
SEC 0.6522
Pac10 0.6154
Big10 0.5271
BigEast 0.5147
ACC 0.5009
Big12 0.4309
FBSInd 0.4098
MWC 0.3946
WAC 0.3582
CUSA 0.2694
MAC 0.2097
SunBelt 0.2033
Non-FBS -0.0854

Labels:

Saturday, October 31, 2009

Got Math? Part Two: The Consequences

In an earlier post, we explored the remarkable similarities between our RWFL rankings posted on Kenneth Massey's comparisons page, using our selected p=0.75 bias value, and Eugene Potemkin's E-Ratings. Through completely independent rationalizations, we ended up at equivalent linear algebra problems that we each solved to reach our rankings.

Well, this didn't seem to be adding much value to the comparisons, so Kenneth nicely asked me if we would do something to make sure ours were unique. So we're going to tweak our algorithm used to bring you weekly rankings, though we're going to do so in a logically consistent way. From now on, we're going to bring you the RWFL rankings as obtained by running the algorithm on the full set of 716 connected college football teams that include the FBS (that is, including all the FCS and DivII schools that play against the FBS, and all the schools who play them, etc.), and we'll report the ordered results from the FBS. This isn't actually "new" per se for us, as these are the rankings we've been using for our bowl predictions the past two years, because we think in principle they should be better. We just didn't want to spring a change without a compelling reason; needing to do something distinct from the E-Ratings is certainly a good enough reason.

If you decide you liked the old RWFL run on the FBS plus a single made-up catch-all non-FBS team, don't worry: you can still see those as the E-Ratings in Massey's comparisons. Indeed, comparing and contrasting the two should be interesting, in that the difference is all because of the treatment of the non-FBS teams, emphasizing the follow-on indirect effects present in the rankings.

An interesting part about this switch has to do with the only other change we've ever made in our rankings. Back in the original days of the Random Walker rankings, when all of us involved were all still at Georgia Tech, our "RW" rankings were just the linear algebra problem described in our manuscripts (which you can reach quickly from the sidebar), describing walkers with first-place votes. As noted at the end of our American Mathematical Monthly paper, there were a lot of reasons to expect improvement using this along with a second set of walkers, with last-place votes. For years, we've simply subtracted these second vote counts from the first to give the RWFL rankings ("Random Walkers First-Last").

But on the whole connected network of 716 teams, very little total weight of those last-place votes ends up in the FBS at all, so the rankings of the FBS teams are only very slightly modified by the last-place piece. One might argue that it would be more interesting to look at ratios instead of differences between the first-place and last-place votes, but that's not something we're going to do without some mathematical and computational investigation first.

Without further ado, as a means of comparison, let's back up to the beginning of the week (not just so we can relive the Carolina victory over Virginia Tech). The rankings listed below with the full connected set of teams definitely differs in some places from the old, simpler setting.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 24th:
1. Iowa (8-0) [1.5817]
2. Florida (7-0) [1.5259]
3. Alabama (8-0) [1.5150]
4. Boise St (7-0) [1.1477]
5. TCU (7-0) [1.1042]
6. Southern Cal (6-1) [1.0839]
7. Oregon (6-1) [1.0780]
8. Texas (7-0) [1.0615]
9. LSU (6-1) [1.0351]
10. Georgia Tech (7-1) [1.0196]
11. Cincinnati (7-0) [0.9606]
12. Virginia Tech (5-2) [0.8658]
13. Arizona (5-2) [0.8354]
14. Penn State (7-1) [0.7979]
15. Miami FL (5-2) [0.7636]
16. Notre Dame (5-2) [0.7396]
17. South Carolina (6-2) [0.7216]
18. Pittsburgh (7-1) [0.7082]
19. Houston (6-1) [0.7080]
20. Oklahoma St (6-1) [0.6849]
21. Ohio State (6-2) [0.6686]
22. West Virginia (6-1) [0.6671]
23. Wisconsin (5-2) [0.6599]
24. California (5-2) [0.6102]
25. Utah (6-1) [0.5987]
26. Clemson (4-3) [0.5983]
27. Washington (3-5) [0.5971]
28. Georgia (4-3) [0.5816]
29. Kentucky (4-3) [0.5785]
30. Central Michigan (7-1) [0.5483]
31. Stanford (5-3) [0.5317]
32. Auburn (5-3) [0.5246]
33. Mississippi (5-2) [0.5227]
34. Michigan (5-3) [0.5090]
35. Oregon St (4-3) [0.5085]
36. Brigham Young (6-2) [0.4973]
37. Arkansas (3-4) [0.4728]
38. Kansas (5-2) [0.4617]
39. Navy (6-2) [0.4476]
40. Tennessee (3-4) [0.4473]
41. Boston College (5-3) [0.4472]
42. Troy (5-2) [0.4423]
43. Idaho (6-2) [0.4359]
44. Michigan St (4-4) [0.4309]
45. South Florida (5-2) [0.4255]
46. Oklahoma (4-3) [0.4157]
47. UCLA (3-4) [0.4119]
48. Arizona St (4-3) [0.4097]
49. Fresno St (4-3) [0.4068]
50. Iowa St (5-3) [0.3971]
51. Minnesota (4-4) [0.3863]
52. Nebraska (4-3) [0.3834]
53. Florida St (3-4) [0.3770]
54. Texas Tech (5-3) [0.3711]
55. Kansas St (5-3) [0.3708]
56. Marshall (5-3) [0.3688]
57. Missouri (4-3) [0.3631]
58. Virginia (3-4) [0.3422]
59. Wake Forest (4-4) [0.3391]
60. Rutgers (5-2) [0.3358]
61. Temple (5-2) [0.3357]
62. Mississippi St (3-5) [0.3356]
63. UTEP (3-4) [0.3356]
64. Nevada (4-3) [0.3286]
65. North Carolina (4-3) [0.3278]
66. Connecticut (4-3) [0.3232]
67. Purdue (3-5) [0.3231]
68. Louisiana-Monroe (4-3) [0.3146]
69. Duke (4-3) [0.3062]
70. SMU (3-4) [0.2991]
71. Texas A&M (4-3) [0.2976]
72. East Carolina (4-3) [0.2973]
73. North Carolina St (3-4) [0.2907]
74. Louisiana-Lafayette (4-3) [0.2842]
75. Colorado St (3-5) [0.2837]
76. Northern Illinois (4-3) [0.2814]
77. Southern Miss (5-3) [0.2748]
78. Wyoming (4-3) [0.2716]
79. Ohio U. (5-3) [0.2709]
80. Colorado (2-5) [0.2703]
81. Northwestern (5-3) [0.2684]
82. Air Force (4-4) [0.2677]
83. Bowling Green (3-5) [0.2592]
84. Syracuse (3-4) [0.2571]
85. Middle Tennessee St (4-3) [0.2457]
86. Toledo (4-4) [0.2452]
87. Western Michigan (4-4) [0.2379]
88. Indiana (4-4) [0.2353]
89. Tulsa (4-3) [0.2344]
90. Washington St (1-6) [0.2296]
91. Baylor (3-4) [0.2288]
92. Louisville (2-5) [0.2238]
93. Central Florida (4-3) [0.2203]
94. San Jose St (1-5) [0.2175]
95. San Diego St (3-4) [0.2165]
96. Arkansas St (2-4) [0.2080]
97. Buffalo (3-5) [0.2024]
98. Florida Atlantic (2-4) [0.2010]
99. Maryland (2-6) [0.1958]
100. Hawai`i (2-5) [0.1819]
101. Kent St (4-4) [0.1814]
102. UNLV (3-5) [0.1725]
103. Louisiana Tech (3-4) [0.1615]
104. Alabama-Birmingham (2-5) [0.1571]
105. Tulane (2-5) [0.1545]
106. Vanderbilt (2-6) [0.1516]
107. Utah St (2-5) [0.1453]
108. New Mexico St (3-5) [0.1423]
109. Memphis (2-5) [0.1413]
110. Illinois (1-6) [0.1366]
111. North Texas (1-6) [0.1264]
112. Florida Int'l (1-6) [0.1256]
113. Army (3-5) [0.1185]
114. Miami OH (0-8) [0.1078]
115. Akron (1-6) [0.1038]
116. Ball St (1-7) [0.0379]
117. Rice (0-8) [0.0368]
118. New Mexico (0-7) [0.0185]
119. Western Kentucky (0-7) [0.0139]
120. Eastern Michigan (0-7) [0.0083]
Conference Rankings (Average Per Team):
SEC 0.7010
Pac10 0.6296
Big10 0.5452
ACC 0.4894
BigEast 0.4877
Big12 0.4422
FBSInd 0.4353
MWC 0.3812
WAC 0.3519
CUSA 0.2690
SunBelt 0.2180
MAC 0.2169
Non-FBS -0.0867

Labels: ,

Sunday, October 25, 2009

Rankings through October 24th

Many of the top teams won easily yesterday, while both Iowa and Alabama maintained their undefeated records through end-of-game heroics. But to these rankings, a win is a win, period.

Comparing with last week's RWFL ranking, there has been significant shakeup in the ordering of the teams immediately following the top 4. GT and VT both fall a few spots because of Miami's loss to Clemson (the intertwined nature of these three teams was discussed last week). In contrast, USC jumped a number of spots, presumably due to similar secondary effects from victories obtained by teams they previously beat (e.g., Ohio State and Notre Dame). We note the very close net vote percentages in square brackets, from #5 USC [1.6882] down to #9 Boise State [1.6228], with the difference between #5 and #7 in the fourth digit after the decimal point (under rounding). That's really close, so future secondary effects could continue to shake up these rankings, while we await more losses among the top 10 to hopefully decide things.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 24th:
1. Florida (7-0) [2.5831]
2. Iowa (8-0) [2.5206]
3. Alabama (8-0) [2.4836]
4. Texas (7-0) [1.8001]
5. Southern Cal (6-1) [1.6882]
6. TCU (7-0) [1.6881]
7. Oregon (6-1) [1.6879]
8. LSU (6-1) [1.6597]
9. Boise St (7-0) [1.6228]
10. Cincinnati (7-0) [1.5428]
11. Georgia Tech (7-1) [1.5167]
12. Virginia Tech (5-2) [1.2926]
13. Arizona (5-2) [1.0958]
14. Notre Dame (5-2) [1.0319]
15. Miami FL (5-2) [0.9884]
16. Penn State (7-1) [0.9727]
17. Pittsburgh (7-1) [0.9532]
18. Houston (6-1) [0.9350]
19. South Carolina (6-2) [0.8567]
20. Oklahoma St (6-1) [0.8559]
21. Wisconsin (5-2) [0.8480]
22. Ohio State (6-2) [0.8447]
23. Utah (6-1) [0.8052]
24. West Virginia (6-1) [0.7966]
25. California (5-2) [0.6695]
26. Kentucky (4-3) [0.6415]
27. Washington (3-5) [0.6179]
28. Georgia (4-3) [0.6150]
29. Clemson (4-3) [0.5506]
30. Brigham Young (6-2) [0.5400]
31. Oregon St (4-3) [0.5221]
32. Stanford (5-3) [0.5134]
33. Mississippi (5-2) [0.4995]
34. Central Michigan (7-1) [0.4918]
35. Auburn (5-3) [0.4483]
36. Kansas (5-2) [0.3811]
37. Idaho (6-2) [0.3730]
38. Boston College (5-3) [0.3716]
39. Oklahoma (4-3) [0.3697]
40. Michigan (5-3) [0.3167]
41. Arkansas (3-4) [0.2987]
42. Navy (6-2) [0.2916]
43. Troy (5-2) [0.2619]
44. Arizona St (4-3) [0.2591]
45. UCLA (3-4) [0.2513]
46. Minnesota (4-4) [0.2418]
47. Iowa St (5-3) [0.2333]
48. Nebraska (4-3) [0.2251]
49. Michigan St (4-4) [0.2172]
50. South Florida (5-2) [0.2126]
51. Missouri (4-3) [0.1572]
52. Tennessee (3-4) [0.1469]
53. Fresno St (4-3) [0.1418]
54. Rutgers (5-2) [0.1200]
55. Nevada (4-3) [0.0854]
56. Connecticut (4-3) [0.0675]
57. Texas Tech (5-3) [0.0539]
58. Florida St (3-4) [0.0486]
59. Louisiana-Monroe (4-3) [0.0448]
60. Marshall (5-3) [0.0350]
61. Mississippi St (3-5) [0.0117]
62. Kansas St (5-3) [0.0113]
63. North Carolina (4-3) [-0.0818]
64. Wake Forest (4-4) [-0.0973]
65. Texas A&M (4-3) [-0.1199]
66. Air Force (4-4) [-0.1264]
67. Purdue (3-5) [-0.1306]
68. Northern Illinois (4-3) [-0.1443]
69. Colorado St (3-5) [-0.1773]
70. Southern Miss (5-3) [-0.1884]
71. East Carolina (4-3) [-0.2288]
72. UTEP (3-4) [-0.2325]
73. Baylor (3-4) [-0.2581]
74. Wyoming (4-3) [-0.2635]
75. Louisiana-Lafayette (4-3) [-0.2675]
76. Northwestern (5-3) [-0.2768]
77. Syracuse (3-4) [-0.2855]
78. North Carolina St (3-4) [-0.3074]
79. Louisville (2-5) [-0.3100]
80. SMU (3-4) [-0.3102]
81. San Diego St (3-4) [-0.3315]
82. Duke (4-3) [-0.3404]
83. Central Florida (4-3) [-0.3514]
84. Middle Tennessee St (4-3) [-0.3598]
85. Ohio U. (5-3) [-0.3613]
86. Virginia (3-4) [-0.3724]
87. Colorado (2-5) [-0.3881]
88. Tulsa (4-3) [-0.3909]
89. Temple (5-2) [-0.4241]
90. Western Michigan (4-4) [-0.4333]
91. Indiana (4-4) [-0.4431]
92. Bowling Green (3-5) [-0.4488]
93. Arkansas St (2-4) [-0.4608]
94. Toledo (4-4) [-0.4756]
95. Florida Atlantic (2-4) [-0.5493]
96. UNLV (3-5) [-0.5680]
97. Louisiana Tech (3-4) [-0.5888]
98. San Jose St (1-5) [-0.6078]
99. Kent St (4-4) [-0.6440]
100. Washington St (1-6) [-0.6731]
101. Buffalo (3-5) [-0.6979]
102. Hawai`i (2-5) [-0.7916]
103. Utah St (2-5) [-0.7968]
104. Tulane (2-5) [-0.8196]
105. Alabama-Birmingham (2-5) [-0.8352]
106. Memphis (2-5) [-0.8717]
107. New Mexico St (3-5) [-0.8827]
108. Maryland (2-6) [-0.9288]
109. Vanderbilt (2-6) [-0.9366]
110. Illinois (1-6) [-1.0920]
111. Army (3-5) [-1.1913]
112. Florida Int'l (1-6) [-1.3427]
113. North Texas (1-6) [-1.4819]
114. Akron (1-6) [-1.4836]
115. FCS teams (XXX-XXX) [-1.6343]
116. Miami OH (0-8) [-1.7733]
117. Rice (0-8) [-2.3124]
118. New Mexico (0-7) [-2.3608]
119. Ball St (1-7) [-2.7930]
120. Western Kentucky (0-7) [-2.8963]
121. Eastern Michigan (0-7) [-3.4677]
Conference Rankings (Average Per Team):
SEC 0.7757
Pac10 0.6632
BigEast 0.3871
Big10 0.3654
Big12 0.2768
ACC 0.2200
FBSInd 0.0441
MWC -0.0882
WAC -0.1605
CUSA -0.4643
SunBelt -0.7835
MAC -0.9735
Non-FBS -1.6343

Labels:

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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Sunday, October 11, 2009

Rankings through October 10th

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 10th:
1. Alabama (6-0) [2.8485]
2. Florida (5-0) [2.6827]
3. Virginia Tech (5-1) [2.2702]
4. Iowa (6-0) [2.0390]
5. Boise St (5-0) [1.6920]
6. LSU (5-1) [1.6258]
7. Cincinnati (5-0) [1.5538]
8. Texas (5-0) [1.3964]
9. Miami FL (4-1) [1.3367]
10. Oregon (5-1) [1.3116]
11. Kansas (5-0) [1.2830]
12. TCU (5-0) [1.2791]
13. Southern Cal (4-1) [1.2467]
14. Nebraska (4-1) [1.1471]
15. Ohio State (5-1) [1.1221]
16. Notre Dame (4-1) [1.0609]
17. Wisconsin (5-1) [1.0124]
18. Washington (3-3) [0.9582]
19. Georgia Tech (5-1) [0.9528]
20. South Carolina (5-1) [0.8006]
21. Idaho (5-1) [0.7461]
22. Auburn (5-1) [0.7218]
23. Stanford (4-2) [0.7102]
24. Arizona (3-2) [0.6976]
25. Arkansas (3-2) [0.6553]
26. Utah (4-1) [0.6315]
27. Houston (4-1) [0.6219]
28. Georgia (3-3) [0.5921]
29. Oregon St (4-2) [0.5826]
30. Brigham Young (5-1) [0.5434]
31. Pittsburgh (5-1) [0.5422]
32. Michigan (4-2) [0.5398]
33. South Florida (5-0) [0.5376]
34. Missouri (4-1) [0.5340]
35. Oklahoma St (4-1) [0.5112]
36. UCLA (3-2) [0.5055]
37. Penn State (5-1) [0.5033]
38. Boston College (4-2) [0.4687]
39. West Virginia (4-1) [0.4296]
40. Troy (3-2) [0.3954]
41. California (3-2) [0.3941]
42. Wake Forest (4-2) [0.3808]
43. Minnesota (4-2) [0.3324]
44. Rutgers (4-1) [0.3309]
45. Oklahoma (3-2) [0.3057]
46. Central Michigan (5-1) [0.2853]
47. Marshall (4-2) [0.2571]
48. Tennessee (3-3) [0.2478]
49. Mississippi (3-2) [0.2379]
50. Louisiana-Lafayette (3-2) [0.2371]
51. Kentucky (2-3) [0.2229]
52. Michigan St (3-3) [0.1393]
53. Northern Illinois (3-2) [0.1218]
54. Connecticut (3-2) [0.1204]
55. Arizona St (3-2) [0.0818]
56. Clemson (2-3) [0.0669]
57. Baylor (3-2) [0.0500]
58. North Carolina (4-2) [0.0485]
59. Ohio U. (4-2) [-0.0222]
60. Middle Tennessee St (3-2) [-0.0295]
61. Colorado St (3-3) [-0.0413]
62. Fresno St (2-3) [-0.0631]
63. Navy (4-2) [-0.0905]
64. SMU (3-2) [-0.0962]
65. Texas Tech (4-2) [-0.0999]
66. Louisiana-Monroe (3-2) [-0.1121]
67. Iowa St (3-3) [-0.1201]
68. Florida St (2-4) [-0.1366]
69. Tulsa (4-1) [-0.1541]
70. East Carolina (3-3) [-0.1733]
71. Bowling Green (2-4) [-0.1905]
72. Texas A&M (3-2) [-0.1974]
73. Nevada (2-3) [-0.2029]
74. North Carolina St (3-3) [-0.2071]
75. Wyoming (4-2) [-0.2754]
76. Duke (3-3) [-0.2805]
77. Mississippi St (2-4) [-0.3006]
78. Kansas St (3-3) [-0.3077]
79. Louisville (2-3) [-0.3211]
80. Arkansas St (1-3) [-0.3220]
81. Air Force (3-3) [-0.3373]
82. Southern Miss (3-3) [-0.3419]
83. Indiana (3-3) [-0.3512]
84. Northwestern (4-2) [-0.3527]
85. Central Florida (3-2) [-0.3544]
86. San Jose St (1-4) [-0.4218]
87. Syracuse (2-4) [-0.4240]
88. San Diego St (2-3) [-0.4299]
89. UTEP (2-4) [-0.4442]
90. Western Michigan (3-3) [-0.4619]
91. Maryland (2-4) [-0.4661]
92. Tulane (2-3) [-0.5388]
93. Louisiana Tech (2-3) [-0.6053]
94. Purdue (1-5) [-0.6489]
95. Illinois (1-4) [-0.6538]
96. Virginia (2-3) [-0.6539]
97. Alabama-Birmingham (2-3) [-0.6564]
98. New Mexico St (3-3) [-0.6630]
99. Toledo (3-3) [-0.6763]
100. UNLV (2-4) [-0.6777]
101. Memphis (2-4) [-0.6936]
102. Washington St (1-5) [-0.7090]
103. Colorado (1-4) [-0.7794]
104. Kent St (2-4) [-0.8684]
105. Buffalo (2-4) [-0.8856]
106. Hawai`i (2-3) [-0.9227]
107. Temple (3-2) [-0.9663]
108. Army (3-3) [-0.9929]
109. Vanderbilt (2-4) [-0.9958]
110. North Texas (1-4) [-1.0296]
111. Utah St (1-4) [-1.0645]
112. Akron (1-4) [-1.0808]
113. Florida Int'l (1-4) [-1.1920]
114. Florida Atlantic (0-4) [-1.4301]
115. FCS teams (XXX-XXX) [-1.6184]
116. Miami OH (0-6) [-1.8676]
117. New Mexico (0-6) [-2.2432]
118. Rice (0-6) [-2.3721]
119. Eastern Michigan (0-5) [-2.5733]
120. Western Kentucky (0-5) [-3.0848]
121. Ball St (0-6) [-3.6768]
Conference Rankings (Average Per Team):
SEC 0.7783
Pac10 0.5779
BigEast 0.3462
Big10 0.3347
ACC 0.3150
Big12 0.3102
FBSInd -0.0075
WAC -0.1672
MWC -0.1723
CUSA -0.4122
SunBelt -0.7297
MAC -0.9894
Non-FBS -1.6184

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Wednesday, October 7, 2009

Comparing Conferences: So much movement, so little reason

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 3rd
Conference Rankings (Average Per Team):
SEC 0.7928
Pac10 0.6051
Big10 0.4282
ACC 0.3528
Big12 0.3359
BigEast 0.3310
WAC -0.1242
FBSInd -0.1543
MWC -0.2016
CUSA -0.4783
SunBelt -0.8022
MAC -1.0214
Non-FBS -1.5533

Only a week ago, the rankings made it look like the ACC was hands down the weakest of the so-called major conferences. Sure, VT and Miami were highly ranked; but on average, the squads in the ACC garnered fewer net RWFL votes per team. But here we are only a week later, and the same methodology puts the ACC very slightly ahead but in essentially a dead heat with the Big 12 and the Big East (varying the bias value p in the plot at the bottom of this post does change things, but not as vigorously as last week).

How is this big change in one week possible?

First, it would seem easy to go to my favorite rationalization: it's still early in the season. The problem with that argument in this case is that last weekend resulted in very little new information about the ACC's strength relative to the other conferences, with 10 of the 12 teams playing against each other.

Okay, so it must be those two interconference games? Sure, Georgia Tech beat Mississippi State, and of course the big win was Miami over Oklahoma. Those two ACC victories over SEC teams certainly move up the ACC rankings, especially the win over a highly rated Oklahoma team (starting QB or no). Such apparent sensitivity of rankings to a few interconference games only highlights the difficulty in ranking teams from the limited information that the BCS Standings allow.

Did anything else happen to cause this change in the rankings? Very possibly. The ACC was likely also helped this week by intraconference outcomes changing the rankings inside the conferences. For instance, Florida State's intraconference loss to Boston College further suppressed their RWFL rating, thereby decreasing the newly-assessed value of South Florida's interconference win over Florida State the week before. Reshuffled comparisons like this are happening all throughout the season, potentially changing the relative rankings of conferences even in the absence of direct matchups. The potential importance of such indirect effects make attempts to rank teams both interesting and maddening.

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Sunday, October 4, 2009

Rankings through October 3rd

There are obviously still a lot of unknowns this early in the season (there's a reason the official BCS Standings don't come out this early), but rankings do start to make a little more sense with another week of games on the books. Obviously, all eyes are on the upcoming Florida-LSU game. Meanwhile, there are only two potential BCS busters left after Houston's loss.

2009 Random Walker Rankings (RWFL, p=0.75)
Games through Saturday October 3rd:
1. Alabama (5-0) [2.5017]
2. LSU (5-0) [2.4968]
3. Iowa (5-0) [2.0009]
4. Virginia Tech (4-1) [1.8947]
5. Wisconsin (5-0) [1.5998]
6. Miami FL (3-1) [1.5444]
7. Auburn (5-0) [1.5160]
8. Texas (4-0) [1.4734]
9. Florida (4-0) [1.4694]
10. Boise St (5-0) [1.4400]
11. Cincinnati (5-0) [1.3715]
12. TCU (4-0) [1.2569]
13. Stanford (4-1) [1.2250]
14. Kansas (4-0) [1.2161]
15. Southern Cal (4-1) [1.1354]
16. Georgia Tech (4-1) [1.1309]
17. Oregon (4-1) [1.0211]
18. Notre Dame (4-1) [1.0181]
19. Arizona (3-1) [1.0069]
20. Ohio State (4-1) [0.8263]
21. Washington (2-3) [0.8211]
22. Missouri (4-0) [0.8186]
23. Georgia (3-2) [0.8182]
24. UCLA (3-1) [0.7916]
25. Boston College (4-1) [0.7564]
26. Nebraska (3-1) [0.7227]
27. Idaho (4-1) [0.6980]
28. South Florida (5-0) [0.6580]
29. Michigan (4-1) [0.6452]
30. Penn State (4-1) [0.6292]
31. Baylor (3-1) [0.6022]
32. Connecticut (3-1) [0.6013]
33. Wake Forest (3-2) [0.5748]
34. Brigham Young (4-1) [0.5423]
35. South Carolina (4-1) [0.5347]
36. West Virginia (3-1) [0.4952]
37. Central Michigan (4-1) [0.4842]
38. Houston (3-1) [0.4083]
39. California (3-2) [0.3957]
40. Utah (3-1) [0.3867]
41. Oklahoma St (3-1) [0.3446]
42. Rutgers (3-1) [0.3301]
43. Minnesota (3-2) [0.3293]
44. Louisiana-Lafayette (2-2) [0.2786]
45. Middle Tennessee St (3-1) [0.2491]
46. Clemson (2-3) [0.2491]
47. Arkansas (2-2) [0.2421]
48. Pittsburgh (4-1) [0.2379]
49. Oregon St (3-2) [0.2180]
50. Kentucky (2-2) [0.1927]
51. Northern Illinois (3-2) [0.1752]
52. Michigan St (2-3) [0.1551]
53. Mississippi (3-1) [0.1403]
54. Mississippi St (2-3) [0.1342]
55. North Carolina (3-2) [0.0998]
56. Oklahoma (2-2) [0.0922]
57. Florida St (2-3) [0.0567]
58. Colorado St (3-2) [0.0383]
59. North Carolina St (3-2) [0.0314]
60. Indiana (3-2) [0.0182]
61. Marshall (3-2) [0.0152]
62. East Carolina (3-2) [0.0144]
63. Navy (3-2) [0.0051]
64. Kansas St (3-2) [-0.0052]
65. Iowa St (3-2) [-0.0111]
66. Texas A&M (3-1) [-0.0771]
67. Tennessee (2-3) [-0.0811]
68. Arizona St (2-2) [-0.1049]
69. Ohio U. (3-2) [-0.1323]
70. Louisiana Tech (2-2) [-0.1732]
71. Southern Miss (3-2) [-0.1735]
72. Troy (2-2) [-0.1832]
73. Tulsa (4-1) [-0.1996]
74. Louisiana-Monroe (3-2) [-0.2057]
75. Fresno St (1-3) [-0.2100]
76. UTEP (2-3) [-0.2418]
77. Maryland (2-3) [-0.2482]
78. Syracuse (2-3) [-0.2810]
79. Wyoming (3-2) [-0.2888]
80. Air Force (3-2) [-0.3169]
81. San Jose St (1-3) [-0.3252]
82. Texas Tech (3-2) [-0.3597]
83. SMU (2-2) [-0.3628]
84. Nevada (1-3) [-0.3841]
85. Central Florida (3-2) [-0.3879]
86. San Diego St (2-3) [-0.3948]
87. Illinois (1-3) [-0.4138]
88. Vanderbilt (2-3) [-0.4519]
89. Washington St (1-4) [-0.4590]
90. Northwestern (3-2) [-0.4649]
91. Tulane (2-2) [-0.4788]
92. Toledo (3-2) [-0.4989]
93. Kent St (2-3) [-0.5253]
94. Arkansas St (1-3) [-0.5730]
95. Bowling Green (1-4) [-0.5739]
96. Western Michigan (2-3) [-0.5815]
97. Purdue (1-4) [-0.6155]
98. Hawai`i (2-2) [-0.6160]
99. Akron (1-3) [-0.6825]
100. UNLV (2-3) [-0.6936]
101. Utah St (1-3) [-0.6950]
102. Duke (2-3) [-0.7184]
103. Louisville (1-3) [-0.7645]
104. Alabama-Birmingham (2-3) [-0.7741]
105. Colorado (1-3) [-0.7861]
106. New Mexico St (2-3) [-0.8521]
107. North Texas (1-3) [-0.9751]
108. Temple (2-2) [-1.0962]
109. Memphis (1-4) [-1.1092]
110. Virginia (1-3) [-1.1385]
111. Buffalo (1-4) [-1.1989]
112. Army (2-3) [-1.4860]
113. FCS teams (XXX-XXX) [-1.5533]
114. Florida Atlantic (0-4) [-1.6109]
115. Florida Int'l (0-4) [-1.6260]
116. Miami OH (0-5) [-1.6788]
117. New Mexico (0-5) [-2.3440]
118. Rice (0-5) [-2.4494]
119. Western Kentucky (0-4) [-2.5740]
120. Eastern Michigan (0-4) [-3.3076]
121. Ball St (0-5) [-3.6623]

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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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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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Tuesday, August 11, 2009

Random walking through baseball

Now that the new site format appears to be largely up and working, it's time to start digging into a backlog of math-in-sports topics I've wanted to briefly write about. That said, if anyone has a general solution for the seemingly infamous "Publishing your blog is taking longer than expected" problem occasionally afflicting those of us who ftp-publish to other servers, I would love to hear about it, please!

Today's links are all about baseball. No, not the recent Yankees 4-game sweeping of the Red Sox (just typing that hurts). Instead, consistent with the title of this site, today is all about random walker rankings applied to baseball players. Well, sort of. Specifically, some of my collaborators and I recently wrote a paper (submitted for publication) studying the network of baseball players defined by the collection of pitcher-batter matchups across 1954-2008. Our focus so far is the study of this large network, and one of the (many) ways to try to understand a network is to study some process occurring on that network: enter the biased random walkers that can be used to define a ranking. Of course, the result is a very crude ranking. If one wanted to turn this into a more serious ranking of baseball players, numerous effects could and indeed should be included.

Brandon Keim picked up the story about our work for Wired Science, nicely including some thoughts (both ours and his) about the limitations of using this as a ranking. From there it got some nice attention and further helpful comments, some of which we'll use to clarify and acknowledge in an eventual revision. My coauthor, Mason Porter, has already collected most of the resulting links, including an interview he did with 27pitches.com.

A big thanks to Brandon for writing such a nice story about our work.

Don't worry, we'll start discussing and adding links to less narcissistic topics soon. Maybe.

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