FanPost

Bradley-Terry rankings applied to college basketball

[Bumped.  SpartanDan clearly getting a leg up for when everyone eventually concedes the BCS model is clearly superior to the NCAA Tournament and the NCAA goes out looking for non-margin-of-victory-acknowledging computer rankings to determine the basketball championship game match-up.

More seriously: This system seems to have some utility as basically the antithesis of the Pomeroy ratings.  Answers the question "Who have you beat?", as opposed to "How likely are you to beat future opponents?"  At least I hope so--otherwise we only have a 1/7 chance of beating Texas. -KJ]

For those of you who are hockey fans, you may have heard of KRACH (Ken's Ratings for American College Hockey). The basic idea behind the ratings is as follows:

1) If two teams play a long series, (Team A wins) / (Team B wins) should be equal to (Team A rating) / (Team B rating). Put another way, a team with a rating twice as high as their opponent should win 2/3 of the time.

2) Given the definition above of expected winning percentage in a given matchup, each team's expected winning percentage against their schedule to date should match their actual winning percentage. This is impossible with winless or unbeaten teams (their ratings would have to be 0 or infinite, respectively); as a fix, a fictional tie (half-win, half-loss) against a perfectly average team is added to each team's record. Non-D1 games are ignored.

A more detailed explanation can be seen here (the main differences are that I have used an average rating of 1 instead of 100, which merely scales everything by a factor of 100, and the only tie games are the fictional ones added to avoid zero or infinite ratings and guarantee some degree of connectedness between teams). Also HT: quakk at mgoblog, who has done the same thing for college football, and Ken Pomeroy who provides the list of games in an easy-to-parse format.

Like the RPI, and unlike Pomeroy's rankings, this system cares only about wins and losses (and who those wins and losses came against). The big advantage of this system relative to RPI is that a win can never hurt you. Playing against a terrible team can hurt your SOS badly enough to overcome the gain in record with the RPI, but here it adds slightly less than one win to your projected record - hence your rating must go up slightly (far less than if you beat a good team, however).

Top 10 + MSU are listed here (through games of Saturday); after the jump, a full table (top 100 + all BCS conference teams and MSU non-conference opponents)

  1. Syracuse 110.44 (9-0, SOS = 5.812)
  2. Villanova 98.299 (9-0, 5.173)
  3. Kentucky 73.479 (10-0, 3.499)
  4. New Mexico 58.276 (10-0, 2.775)
  5. Texas 57.524 (8-0, 3.384)
  6. Purdue 54.108 (9-0, 2.848)
  7. Georgetown 53.720 (8-0, 3.160)
  8. West Virginia 42.984 (7-0, 2.866)
  9. Kansas 36.192 (9-0, 1.905)
  10. Missouri St. 36.119 (9-0, 1.901)
  11. Michigan St. 8.867 (8-2, 2.608)

The full rankings:

RankTeamRecordSOSRating
1 Syracuse 9 - 0 5.813 110.44
2 Villanova 9 - 0 5.174 98.299
3 Kentucky 10 - 0 3.499 73.479
4 New Mexico 10 - 0 2.775 58.276
5 Texas 8 - 0 3.384 57.524
6 Purdue 9 - 0 2.848 54.108
7 Georgetown 8 - 0 3.16 53.72
8 West Virginia 7 - 0 2.866 42.984
9 Kansas 9 - 0 1.905 36.192
10 Missouri St. 9 - 0 1.901 36.119
11 Mississippi 8 - 1 6.054 34.307
12 Kansas St. 8 - 1 5.83 33.034
13 Duke 7 - 1 6.389 31.943
14 Texas Tech 9 - 0 1.504 28.574
15 Florida 8 - 1 4.198 23.786
16 Seton Hall 8 - 0 1.284 21.82
17 Western Carolina 8 - 1 3.384 19.173
18 Connecticut 6 - 2 7.074 18.393
19 North Carolina 8 - 2 5.381 18.297
20 St. John's 7 - 1 3.512 17.558
21 Texas A&M 7 - 2 4.665 13.995
22 Tennessee 7 - 1 2.634 13.168
23 Tulsa 6 - 1 2.879 12.474
24 Northwestern 6 - 1 2.787 12.075
25 Dayton 7 - 2 3.997 11.991
26 Nevada Las Vegas 6 - 1 2.693 11.669
27 Charlotte 8 - 1 1.964 11.131
28 Temple 7 - 2 3.646 10.938
29 North Carolina St. 7 - 1 2.071 10.353
30 Wisconsin 7 - 2 3.424 10.273
31 Washington 6 - 2 3.91 10.167
32 Cornell 7 - 2 3.223 9.6687
33 California 6 - 3 5.015 9.3136
34 Gonzaga 7 - 2 3.09 9.2698
35 William & Mary 6 - 2 3.498 9.0958
36 Northern Iowa 7 - 1 1.819 9.0939
37 Michigan St. 8 - 2 2.608 8.8668
38 Oklahoma St. 7 - 1 1.739 8.6974
39 Ohio St. 7 - 2 2.862 8.5856
40 Virginia Tech 8 - 1 1.447 8.2008
41 Cincinnati 6 - 1 1.888 8.1833
42 Miami FL 8 - 1 1.429 8.0998
43 Clemson 7 - 2 2.576 7.7272
44 Memphis 7 - 1 1.533 7.6646
45 Pittsburgh 8 - 2 2.204 7.4924
46 Georgia Tech 6 - 1 1.672 7.2466
47 Illinois St. 7 - 0 0.4657 6.9858
48 Butler 7 - 3 3.191 6.8381
49 Florida St. 7 - 2 2.262 6.7872
50 Wake Forest 5 - 2 3.021 6.6464
51 Harvard 7 - 2 2.177 6.5325
52 St. Mary's 6 - 1 1.499 6.4939
53 South Carolina 6 - 2 2.479 6.4464
54 Baylor 6 - 1 1.431 6.199
55 Virginia Commonwealth 6 - 2 2.38 6.1888
56 UAB 8 - 1 1.053 5.9698
57 Richmond 7 - 2 1.935 5.8053
58 Brigham Young 8 - 1 1.022 5.794
59 Rhode Island 7 - 1 1.096 5.4788
60 South Florida 7 - 1 1.076 5.3797
61 Southern Mississippi 3 - 1 2.304 5.3772
62 Notre Dame 9 - 2 1.398 5.3142
63 Wisconsin Green Bay 7 - 2 1.762 5.2874
64 Texas El Paso 5 - 0 0.469 5.1588
65 Washington St. 7 - 2 1.622 4.8674
66 Alabama 6 - 3 2.548 4.7313
67 Mississippi St. 7 - 2 1.546 4.6392
68 Minnesota 7 - 3 2.149 4.6047
69 San Diego St. 7 - 2 1.521 4.5621
70 Pacific 7 - 2 1.501 4.5037
71 Maryland 5 - 3 2.84 4.4634
72 Murray St. 6 - 1 1.01 4.3778
73 Vanderbilt 5 - 3 2.695 4.2353
74 Illinois 7 - 2 1.406 4.219
75 Louisiana St. 5 - 2 1.902 4.185
76 Wichita St. 8 - 1 0.7176 4.0665
77 Hofstra 6 - 3 2.113 3.9243
78 Loyola Chicago 5 - 2 1.776 3.9081
79 DePaul 5 - 3 2.422 3.8054
80 La Salle 6 - 3 2.049 3.8046
81 Marquette 7 - 3 1.653 3.5412
82 Coastal Carolina 5 - 2 1.542 3.3924
83 Louisiana Tech 8 - 2 0.967 3.2879
84 Louisville 5 - 3 2.066 3.2468
85 Bradley 5 - 3 2.047 3.2164
86 Arizona St. 7 - 3 1.482 3.1761
87 Duquesne 6 - 3 1.698 3.1542
88 Boston College 6 - 3 1.664 3.0899
89 Portland 6 - 3 1.66 3.0831
90 Iowa St. 7 - 3 1.409 3.0185
91 Xavier 5 - 3 1.898 2.9819
92 Western Kentucky 5 - 3 1.872 2.9421
93 IUPUI 6 - 3 1.541 2.8625
94 Central Florida 6 - 2 1.049 2.7287
95 Marshall 6 - 1 0.6219 2.6947
96 Wright St. 6 - 2 1.013 2.6348
97 Belmont 7 - 2 0.8688 2.6063
98 Long Beach St. 3 - 4 3.236 2.5166
99 George Washington 7 - 2 0.8217 2.465
100 Siena 6 - 4 1.699 2.4534
102 Rutgers 6 - 2 0.9021 2.3454
106 Auburn 5 - 4 1.801 2.2007
114 Providence 7 - 4 1.157 1.9277
115 Oklahoma 7 - 3 0.8855 1.8974
116 Arizona 4 - 5 2.279 1.865
120 Nebraska 7 - 2 0.6117 1.8352
128 Missouri 6 - 3 0.9166 1.7023
132 Georgia 4 - 4 1.613 1.6129
140 Saint Joseph's 3 - 6 2.686 1.4461
146 Stanford 4 - 3 1.02 1.3116
147 Indiana 4 - 5 1.589 1.3001
152 Penn St. 6 - 4 0.8359 1.2074
154 Southern California 4 - 4 1.175 1.1745
156 Oregon 4 - 4 1.16 1.1596
160 Oakland 3 - 5 1.753 1.1154
161 Wofford 4 - 6 1.608 1.1135
164 Virginia 4 - 4 1.06 1.0597
177 Massachusetts 4 - 5 1.142 0.9343
179 Oregon St. 4 - 4 0.9254 0.92543
183 The Citadel 4 - 5 1.09 0.89168
188 Colorado 4 - 4 0.8273 0.82732
203 Iowa 3 - 7 1.46 0.68116
207 Michigan 3 - 4 0.8481 0.65962
227 Arkansas 4 - 5 0.5764 0.4716
240 Valparaiso 2 - 6 1.104 0.42463
248 UCLA 2 - 6 1.032 0.39675
281 IUPU Fort Wayne 2 - 5 0.5369 0.24407
294 Toledo 2 - 8 0.6806 0.20018
307 Texas Arlington 2 - 3 0.2087 0.1491
327 Florida Gulf Coast 1 - 6 0.2988 0.068949

This is a FanPost, written by a member of the TOC community. It does not represent the official positions of The Only Colors, Inc.--largely because we have no official positions.

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