Random Walker Rankings

Rankings through November 21st

2009-11-22T08:08:00.002-05:00

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

Breaking Down the BCS Bowl Bids

2009-11-20T16:41:00.005-05:00

Last year in this space, we watched anxiously throughout November as Boise State tried to make its case for a BCS Bowl bid on the field, and in the Standings, only to have the last at-large bowl bid go to a lesser-ranked Ohio State team. Anyone else getting a sense of deja vu here?

Wait, you say, Boise State is currently #6 in the BCS Standings, and there are 10 BCS Bowl bids (Fiesta, Orange, Rose, Sugar, and the National Championship Game). Ah, but how do teams qualify for BCS games? In the rules, Boise State is what the latest politically correct college football language deems a "non-AQ group" school (that is, they are not from a conference with an Automatic Qualifier). A non-AQ group school can earn an automatic BCS berth if they do well enough in the Standings; but the rules are also very explicit that "No more than one such team from the non-AQ group shall earn an automatic berth in any year." Last year, that berth went to Utah. This year, if both TCU and Boise State win out, it will almost certainly go to TCU.

So does Boise State have any shot at getting an at-large selection this year? First, it obviously depends on their winning out; if they lose, their BCS bid is finished. Second, it depends on who wins the AQ conferences, because those winners take 6 of the 10 spots. If TCU wins out, they'll almost certainly take a 7th automatic qualification (and if they don't, then the discussion simplifies because an undefeated Boise State would get it instead). So who will get the other three at-large spots? The SEC runner-up, definitely a given. If Texas doesn't win the Big 12, they would almost certainly still be in the running for a bid. So there may be either one or two more slots for Boise State to try to take.

Remembering that BCS at-large bids do not need to follow the BCS Standings beyond a top-14 requirement (as when Ohio State was selected over Boise State last year), it's perhaps still reasonable to look at the top teams in the Standings to see who else might legitimately get selected over a non-automatic Boise State. In the Big East, Cincinnati is currently #5 and Pitt is #9, and obviously only one of them will win that conference. At #7, Georgia Tech might be a candidate for an at-large bid if they fail to win the ACC. Luckily for Boise State, #8 LSU is not a worry right now because each conference can only get two bids, and we already counted two to the SEC. Meanwhile, #10 Ohio State has already wrapped up the Big Ten, which is also good for Boise State. In contrast, #11 Oregon is still fighting in the Pac-10, and #12 Oklahoma State won last night to increase their chances. And the financial incentives for the bowl games built into the at-large selections might cause one to look at a second Big Ten school, with Iowa at #13 and Penn State at #14.

That's a lot of teams fighting for at most two spots. While some of the confusion might clarify this weekend or next, much might remain unresolved until the conference championships.

----

Unsurprisingly, we aren't the only ones who have been talking about Boise State's BCS at-large chances. See also:

PR firm hired to make push for Boise St.

Boise State still in line for at-large

Boise State fans need to pull for Texas, root against Oklahoma State

A backlog of Trent McCotter's columns

2009-11-18T03:47:00.002-05:00

Apparently Trent McCotter's brief stint writing thought-provoking articles about stats and sports for the News & Observer has come to an end. I'm disappointed by this, because I enjoyed each of his columns (not just the two we previously linked to from here). Indeed, I've been asking him every week for the past month whether a new one was coming or not. His columns were concise, and I know Trent well enough to know that he could have found a lot more to write about each topic. I'm certain it can't be an easy task to condense such thoughts into the strictly allotted newspaper space.

Trent's stories that appeared are still online:

How to fix the 'perfect game'

Zimmerman best in state at hitting streaks

'Tiger-proofing' golf courses yields surprises

Time to monkey around with BCS?

Ichiro a version of Wee Willie Keeler

The 'hot hand' in basketball: Does it exist?

Statistics gaffes highlight sports history

When is a conversion worth the risk?

Rankings through November 14th

2009-11-15T08:16:00.003-05:00

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

Rankings through November 7th

2009-11-08T05:08:00.002-05:00

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

Rankings through October 31st

2009-11-01T08:51:00.003-05:00

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

Concise Definition of RWFL Rankings

2009-11-01T08:18:00.002-05:00

The general mathematical description of the random walker (RW) ranking methodology is presented as a sidebar on p.889 of ''The Bowl Championship Series: A Mathematical Review,'' T. Callaghan, P. J. Mucha and M. A. Porter, Notices of the American Mathematical Society 51, 887-893 (2004). These RW rankings, which amount to an amalgamation of first-place votes, depend on a bias value p setting the extent to which random walkers respect each individual game outcome.

The RWFL rankings at bias value p are calculated by the difference between first-place votes (following game winners) and last-place votes (following game losers). This is equivalent to subtracting RW at bias value (1-p) from RW at bias value p.

Starting in November 2009, all of our rankings are calculated on the full connected network of teams connected by games played, of which the FBS teams are a relatively small subset (even when we only report the FBS results). Prior to November 2009, our weekly rankings treated all non-FBS teams as a single catch-all "team" (who played a lot of games). However, our bowl predictions have used the full connected network in previous seasons.

Got Math? Part Two: The Consequences

2009-10-31T17:10:00.003-04:00

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

Rankings through October 24th

2009-10-25T08:49:00.003-04:00

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

Got Math?

2009-10-24T20:12:00.006-04:00

On a day full of exciting action, including a last-second blocked FG attempt that may turn out to have serious BCS implications, it may seem rather pedestrian to ask a math question. Then again, that's essentially what we do here. So while we're watching the rest of the games, I have a question, brought to my attention by another football ranking fan, Martien Maas.

Martien Maas' Rating System also appears on Kenneth Massey's College Football Ranking Comparison page. Perhaps in part because we ended up very close to each other in the comparisons this week, Martien noted that the RWFL rank order this week is precisely the same as that from Eugene Potemkin's E-Rating System (see also his more detailed discussion). Indeed, the two are nearly the same every week (except for some examples from last year, including here, here, and here). And there are clearly some philosophical similarities between the two rankings. But I haven't sat down to try to work out whether we're mathematically equivalent, so I'd be happy if someone could tell me if they have an expert opinion here. My gut instinct is that our p=0.75 bias value choice happens to set our rankings to the same linear algebra problem, with perhaps the small differences in the past due to details about how non-FBS teams are handled. But, like I said, I haven't looked at it sufficiently yet. Nevertheless, I thought it was worth mentioning...

----

Addition (October 25): Of course, while I tried to leave this puzzle for others, I couldn't let it go myself. I can never resist a good puzzle. It's probably a good thing that I get to solve puzzles for a living. Plus I received an email from Eugene Potemkin responding to a query I sent him directly.

Eugene and I had a wonderfully pleasant exchange of emails back and forth today, wherein he shared some of the details of his E-Rating implementation for college football, adding further mathematical details, including: (1) Where he uses ratios of "ratings" and "anti-ratings" to obtain scores in other sports, he uses a difference for American college football (this is the same as the "First-minus-Last" part in RWFL). (2) Like us, he usually treats the collection of all non-FBS teams as effectively one team. (3) To get around the singular nature of random walks on the fully directed graph---sorry for the lingo here but be thankful I'm not using it to launch into an entire discussion of how this relates to the original PageRank algorithm!---he doesn't treat a win as a full win; rather he equates a win as effectively 3 wins and 1 loss. This is perfectly identical to the "bias value" p=0.75 choice that we've espoused here, which is nice for a variety of reasons. So it appears that the minor differences must be small round-off or tie-breaking differences, and the RWFL(p=0.75) and E-Ratings are completely identical.

Again, a huge thanks to both Martien and Eugene. It's been nice emailing with both of them.

Going forward, we still have value to add, don't worry. For instance, we should spend a lot more time in future posts looking at the plots I post every week that show the top rankings across different choices of this infamous "bias value" p, because those plots hold a lot of utility in being a proxy for various kinds of ranking choices.

Rankings through October 17th

2009-10-18T08:42:00.004-04:00

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

Rankings through October 10th

2009-10-11T06:45:00.002-04:00

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

Comparing Conferences: So much movement, so little reason

2009-10-07T08:14:00.001-04:00

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.

Rankings through October 3rd

2009-10-04T08:15:00.003-04:00

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]

Virginia Tech, Really?

2009-10-02T07:42:00.004-04:00

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.

Return of the Random Walkers!

2009-09-27T10:29:00.003-04:00

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]

Trent McCotter talks about the monkeys

2009-09-13T10:20:00.005-04:00

A quick but big thank you to Trent McCotter for mentioning our random walker "monkey" rankings in his latest column! See "Time to monkey around with the BCS?"

Quarterback ratings

2009-08-23T09:43:00.006-04:00

Trent McCotter is back again as one of the targets of links in today's post, courtesy of his first column in the The News & Observer, which he will write in his copious spare time as a UNC law student. Yesterday, I sang the praises of Steve Strogatz, so now it's Trent's turn. One of the outwardly most mellow people I know, Trent's outward calm conceals a strong passion for sports statistics. A four time winner of the Jack Kavanagh Memorial Youth Baseball Research Award from SABR (three times in the college division, once in the high school division), Trent distinguishes himself by frequently taking a different tack in his work while also delving into the detailed numbers when needed.

In "How to fix the 'perfect game'," Trent avoids the details of the quarterback ratings definition and gets right to the interesting issue of the recent prevalence of perfect passer rating performances, wondering along the way quite how perfect they are.

While we're talking about quarterback ratings and looking forward to the upcoming season, check out "Vick as a Quarterback? He’s Underrated" by Brian Burke of Advanced NFL Stats in The Fifth Down (both sites are full of interesting items). Without getting into recalculations of possible quarterback ratings, Burke's discussion about more conventional statistics makes clear that neither they nor quarterback ratings tell the whole story.

The Mathematics of Hitting Streaks

2009-08-22T16:39:00.007-04:00

With the hope that there's actually someone other than my coauthors reading these posts once the college football season arrives (when the hits to the old page understandably ramped up in past years), one of the upsides to transitioning to a blog is to provide easy pointers to other interesting work in the mathematics and statistics of sports.

There are a pair of papers about hitting streaks that have appeared on arXiv.org in the past year. Making things particularly interesting, these two papers take completely different methodological approaches. Sam Arbesman and Steve Strogatz "examine Joe DiMaggio’s 56-game hitting streak and look at its likelihood, using a number of simple models. And it turns out that, contrary to many people’s expectations, an extreme streak, while unlikely in any given year, is not unlikely to have occurred about once within the history of baseball." Meanwhile, Trent McCotter uses permutation tests to find that there appear to have been a significantly larger number of 20-25 game streaks in real life than one would obtain in an independent-games model. You can hear Steve talk more about both studies in a Radiolab podcast from earlier this summer.

Finally, for perhaps the only timely element of this post, Steve has a new book just out this past week, The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math. If it's like everything else Steve does, it will be amazing.

----
Addition (29Aug): For more discussion about hitting streaks, other streaks, and the way that people tend to overinterpret streaks, check out Leonard Mlodinow's interesting WSJ essay, "The Triumph of the Random."

----
Another addition (31Aug): Trent McCotter's second N&O column is about hitting streaks, with a decidedly local-to-NC flavor ("Zimmerman best in state at hitting streaks").

Random walking through baseball

2009-08-11T09:30:00.000-04:00

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.

Rebuilding the old site into a blog

2009-08-09T20:40:00.000-04:00

With the new college football season almost upon us, I wanted to finally start to clean this site up and see if we can't give it a more uniform look and feel, now that we've switched to a blog format. The blog will have its benefits, including automatically archiving everything and allowing for comments. But converting the old, existing pages is a pain; in particular, there are already figures and tables in those pages that would have to be reformatted for the blog. I would rather use that time to start adding some new content here. So we're going to keep most of the old site as is, at http://rankings.amath.unc.edu/old.

Apologies to those who click through and find themselves on the old site. The old sidebar now includes a link back to the "RWR Blog" on most pages. If you end up somewhere without this link, please make use of your friendly browser's back button.

Press coverage (college football edition)

2009-08-09T20:35:00.000-04:00

We're grateful for the positive attention about the random walker rankings as a means of ranking college football teams. We have particularly enjoyed the diversity of outlets interested in this project, including

ESPN the Magazine (issue dated Nov. 10, 2003),
Nature Science Update (Nov. 14, 2003),
Georgia Tech news releases [long and short] (Nov. 18, 2003),
The Chronicle of Higher Education (issue dated Nov. 28, 2003; subscription required),
CNN Headline News (Dec. 30, 2003),
La Recherche (Jan. 2004, subscription required),
Atlanta Business Chronicle (Jan. 16, 2004),
WGST AM640 (May 20, 2004),
The Atlanta Journal-Constitution (May 24, 2004; registration required),
WKY AM930 (May 28, 2004),
American Mathematical Society press release (Aug. 11, 2004),
Science News (week of Sept. 4, 2004),
The Washington Post (Sports columnist Sally Jenkins, Dec. 10, 2005), and
The Mathematical Tourist at MAA Online (Nov. 15, 2007).

Our manuscripts about college football

2009-08-09T20:32:00.001-04:00

In addition to the rants on this collection of web pages, we have written a pair of scholarly, academic articles about ranking with random walkers. The now somewhat amusingly misnamed "Division I-A Football" article (it was properly named when it was submitted; and the Michigan Wolverines hadn't famously lost to Appalachian State Mountaineers, an FCS née I-AA program) discusses a number of issues in greater depth than covered on this website, including the community structure of the football matchups network and its influence on rankings, ideas about choosing a good p value, and the improved properties of the RWFL ranking system.

''Random Walker Ranking for NCAA Division I-A Football,''
T. Callaghan, P. J. Mucha and M. A. Porter,
American Mathematical Monthly, 114, 761-777 (2007)
[originally made available as arxiv.org/physics/0310148].
Abstract: Each December, college football fans and pundits across America debate which two teams should meet in the NCAA Division I-A National Championship game. The Bowl Championship Series (BCS) standings employed to select the teams invited to this game are intended to provide an unequivocal #1 v. #2 game for the championship; however, this selection process has itself been highly controversial in four of the past six years. The computer algorithms that constitute one part of the BCS standings often act as lightning rods for the controversy, in part because they are inadequately explained to the public. We present an alternative algorithm that is simply explained yet remains effective at ranking the best teams. We define a ranking in terms of biased random walkers on the graph formed by the schedule of games played, with two teams (vertices) connected by an edge if they played each other. Each random walker moves from team to team by selecting a game and "voting" for its winner with probability p, tracing out a never-ending path motivated by the "my team beat your team" argument. We study the statistical properties of a collection of such walkers, relate the rankings to the community structure of the underlying network, and compare these rankings for recent NCAA Division I-A seasons. We also discuss the algorithm's asymptotic behavior, illustrated with some analytically tractable cases for round-robin tournaments, and discuss possible generalizations.

''The Bowl Championship Series: A Mathematical Review,''
T. Callaghan, P. J. Mucha and M. A. Porter,
Notices of the American Mathematical Society 51, 887-893 (2004).
Abstract: We discuss individual components of the college football Bowl Championship Series. Comparing with a simple algorithm defined by random walks on a biased graph, we attempt to predict whether the proposed changes will truly lead to increased BCS bowl access for non-BCS schools. We conclude by arguing that the true problem with the BCS Standings lies not in the computer rankings, but rather in misguided addition.

2008 Random Walker Rankings [link]

2009-08-09T20:31:00.001-04:00

http://rankings.amath.unc.edu/old/2008.htm

2007 Random Walker Rankings [link]

2009-08-09T20:30:00.001-04:00

http://rankings.amath.unc.edu/old/2007.htm