Bradley-Terry rankings applied to college basketball

by SpartanDan on Dec 13, 2009 4:00 PM CST

[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)

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

The full rankings:

Rank	Team	Record	SOS	Rating
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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Comments

Sample size is an issue this early

Once there are more games among the teams at the top and nobody is unbeaten, the gaps should come down a bit. (Ignoring the effect on SOS, adding the first loss cuts a team’s rating by a factor of 3; the second one just drops it by 40%, then 29%, 22%, and on down.) I just ran this program on the ‘09 season and the ratings seem to be a bit more compressed: even with UNC’s dominance, three teams had 3:2 odds or better against them, two more 2:1, and four others 3:1. You had to go as far down as 46th (Siena) to see UNC with a 90% chance of winning, compared to 24th based on the current rankings for this year for Syracuse. (Also, our schedule strength last year was absurd – 10.94, with only UConn joining us above 9.)

by SpartanDan on Dec 14, 2009 3:13 AM CST reply actions

KenPom projected game probabilties are up

Actually gives us worse odds of beating Texas: 6%. So much for that theory.

http://kenpom.com/team.php?team=Michigan%20St.

Fight for The Only Colors: Green and White!

by KJ@theonlycolors on Dec 14, 2009 8:39 AM CST reply actions

I was just about to post the same thing

Pomeroy also just posted individual player stats. Lucas is making a better percentage of his twos so far this year and is shooting very well from beyond the arc. He gets my offensive MVP for the season so far, but Draymond Green is right behind him. The Dancing Bear is leading all front court players (at least those playing substantial minutes) in offensive rating, has the highest eFG rate on the team, leads the front court for assist rate, and is the leading rebounder. His turnover rate is a little high but he’s definitely got my vote for most improved player and front court player of the year so far.

by TheCrestedHelm on Dec 14, 2009 10:40 AM CST up reply actions

"Significant Contributors" vs. "Role Players"

I’m guessing that Nix counts as the former and Lucious, Roe and Allen as the latter because of the % of possessions they use when they’re in there. Doesn’t make much sense though, if that’s true. Seems like it should be factored by the % of available minutes played. I’m probably out to lunch here as I’m not very familiar with some of these stats, but I’d appreciate some enlightenment.

by Con-T on Dec 14, 2009 5:53 PM CST up reply actions

Yeah

It’s based on how involved a player is on offense when he’s in the game, not on how many minutes he plays (which is relatively easy to gauge). Within each category, the players are sorted by minutes played, though. (See the final section on this page.)

Planning to take a closer look at the team’s tempo-free numbers through 10 games in the next day or two.

Fight for The Only Colors: Green and White!

by KJ@theonlycolors on Dec 14, 2009 9:05 PM CST up reply actions

Thanks

Looking at Nix’s numbers, there are definitely some things to like. Unfortunately, given that he’s less likely to shoot than any of the regulars save Roe, he doesn’t turn the ball over, and his free throw rate and fouls drawn rate are crazy high it looks like his “involvement” in the offense is pretty much confined to getting fouled and ending possessions on missed free throws. Wow, there’s a stunning revelation.

by Con-T on Dec 14, 2009 10:34 PM CST up reply actions