Margin-Aware Bradley-Terry Ratings for College Football 2023

Updated through games of January 8

Parameters

Home field: Multiply home rating by 1.311
Victory point formula: `V_A=1/(1+e^(-M_A/6.5))`
Win probability for a matchup: `W_(A,B)=R_A^2.09/(R_A^2.09+R_B^2.09)`
Expected margin for a matchup: `M_(A,B)=13.3*ln(R_A/R_B)`
Home field equivalent to 3.6 points in expected margin

Ratings

Rank	Team	Record	SOS	Rating	Win % vs Average	Margin vs Average
1	Michigan	15-0	1.519	8.8324	0.9896	29.0
2	Georgia	13-1	1.311	5.8703	0.9759	23.5
3	Oregon	12-2	1.298	5.3688	0.9710	22.4
4	Ohio State	11-2	1.517	4.6361	0.9611	20.4
5	Texas	12-2	1.459	4.2435	0.9535	19.2
6	Florida State	13-1	1.214	3.9033	0.9451	18.1
7	Alabama	12-2	1.595	3.8599	0.9439	18.0
8	Washington	14-1	1.683	3.8544	0.9437	17.9
9	Penn State	10-3	1.332	3.6065	0.9359	17.1
10	Notre Dame	10-3	1.192	3.4393	0.9297	16.4
11	Missouri	11-2	1.339	3.0332	0.9104	14.8
12	Kansas State	9-4	1.346	2.9553	0.9059	14.4
13	Liberty	13-1	0.8323	2.905	0.9028	14.2
14	Mississippi	11-2	1.305	2.8867	0.9016	14.1
15	Oklahoma	10-3	1.285	2.8852	0.9016	14.1
16	LSU	10-3	1.306	2.6983	0.8884	13.2
17	Troy	11-3	0.9964	2.5264	0.8740	12.3
18	Arizona	10-3	1.113	2.4141	0.8632	11.7
19	Oregon State	8-5	1.311	2.1892	0.8372	10.4
20	James Madison	11-2	0.9239	2.1054	0.8258	9.9
21	Tennessee	9-4	1.173	1.9878	0.8078	9.1
22	Kansas	9-4	1.1	1.9486	0.8013	8.9
23	Clemson	9-4	1.16	1.8699	0.7872	8.3
24	Southern Methodist	11-3	0.7977	1.854	0.7842	8.2
25	Louisville	10-4	1.14	1.8264	0.7788	8.0
26	Duke	8-5	1.165	1.8153	0.7766	7.9
27	Maryland	8-5	1.098	1.7536	0.7638	7.5
28	Miami OH	11-3	0.7757	1.7383	0.7605	7.4
29	North Carolina State	9-4	1.123	1.7005	0.7521	7.1
30	Oklahoma State	10-4	1.156	1.6274	0.7346	6.5
31	USC	8-5	1.261	1.6256	0.7341	6.5
32	Texas A&M	7-6	1.088	1.6057	0.7290	6.3
33	Memphis	10-3	0.8374	1.5727	0.7204	6.0
34	Toledo	11-3	0.7595	1.5667	0.7188	6.0
35	Iowa State	7-6	1.235	1.5501	0.7142	5.8
36	West Virginia	9-4	1.011	1.5407	0.7116	5.7
37	Boise State	8-6	0.9851	1.4858	0.6958	5.3
38	Iowa	10-4	1.135	1.4817	0.6946	5.2
39	Miami FL	7-6	1.095	1.4796	0.6940	5.2
40	UCLA	8-5	1.004	1.4609	0.6883	5.0
41	Air Force	9-4	0.7925	1.4347	0.6801	4.8
42	Kentucky	7-6	1.093	1.4265	0.6775	4.7
43	UTSA	9-4	0.7604	1.4097	0.6721	4.6
44	Appalachian State	9-5	0.9193	1.4015	0.6694	4.5
45	Utah	8-5	1.155	1.3923	0.6663	4.4
46	North Carolina	8-5	0.9809	1.372	0.6595	4.2
47	Tulane	11-3	0.8182	1.3651	0.6571	4.1
48	Virginia Tech	7-6	1.013	1.3347	0.6464	3.8
49	Texas Tech	7-6	1.184	1.3037	0.6351	3.5
50	TCU	5-7	1.129	1.2673	0.6213	3.2
51	Wisconsin	7-6	1.023	1.2399	0.6105	2.9
52	Ohio	10-3	0.6554	1.2272	0.6054	2.7
53	Rutgers	7-6	1.149	1.1545	0.5745	1.9
54	Georgia Tech	7-6	1.102	1.1499	0.5725	1.9
55	Western Kentucky	8-5	0.8537	1.1474	0.5714	1.8
56	San Jose State	7-6	0.9254	1.1278	0.5625	1.6
57	Jacksonville State	9-4	0.7383	1.1248	0.5611	1.6
58	South Alabama	7-6	0.8345	1.123	0.5603	1.5
59	Coastal Carolina	8-5	0.9342	1.1193	0.5586	1.5
60	UNLV	9-5	0.8128	1.1136	0.5560	1.4
61	Washington State	5-7	1.094	1.1061	0.5525	1.3
62	Nebraska	5-7	1.008	1.0904	0.5451	1.2
63	New Mexico State	10-5	0.7637	1.0825	0.5413	1.1
64	Wyoming	9-4	0.8766	1.0591	0.5299	0.8
65	Northwestern	8-5	1.014	1.0516	0.5263	0.7
66	Central Florida	6-7	0.9857	1.0512	0.5260	0.7
67	Bowling Green	7-6	0.8807	1.0419	0.5214	0.5
68	Auburn	6-8	1.069	1.0381	0.5195	0.5
69	Florida	5-7	1.149	1.0379	0.5194	0.5
70	Texas State	8-5	0.7599	1.0346	0.5178	0.5
71	Fresno State	9-4	0.7	1.0252	0.5130	0.3
72	California	6-7	1.094	0.96954	0.4838	-0.4
73	Georgia State	7-6	0.8869	0.91457	0.4535	-1.2
74	Minnesota	6-7	1.087	0.88413	0.4360	-1.6
75	South Carolina	5-7	1.072	0.87861	0.4328	-1.7
76	Louisiana	6-7	0.7554	0.87127	0.4285	-1.8
77	Arkansas	4-7	0.9683	0.8346	0.4066	-2.4
78	Boston College	7-6	0.9128	0.83208	0.4051	-2.4
79	Arkansas State	6-7	0.8431	0.8315	0.4048	-2.5
80	Brigham Young	5-7	1.082	0.82863	0.4030	-2.5
81	Colorado	4-8	1.18	0.82587	0.4014	-2.5
82	Georgia Southern	6-7	0.8118	0.77522	0.3700	-3.4
83	Mississippi State	5-7	1.034	0.75966	0.3602	-3.7
84	Army	6-6	0.7568	0.75004	0.3541	-3.8
85	Illinois	5-7	1.079	0.74371	0.3500	-3.9
86	Northern Illinois	7-6	0.609	0.74204	0.3490	-4.0
87	Old Dominion	6-7	0.9085	0.74154	0.3487	-4.0
88	Syracuse	6-7	0.8526	0.73234	0.3428	-4.1
89	Purdue	4-8	1.111	0.72044	0.3351	-4.4
90	Virginia	3-9	1.175	0.69351	0.3176	-4.9
91	South Florida	7-6	0.7167	0.69106	0.3160	-4.9
92	Marshall	6-7	0.926	0.67177	0.3033	-5.3
93	Rice	6-7	0.7276	0.65623	0.2931	-5.6
94	Wake Forest	4-8	0.995	0.65127	0.2898	-5.7
95	Michigan State	4-8	1.145	0.64278	0.2842	-5.9
96	Utah State	5-7	0.7857	0.6261	0.2732	-6.2
97	Middle Tennessee	4-8	0.7908	0.60647	0.2601	-6.7
98	North Texas	5-7	0.6928	0.58941	0.2488	-7.0
99	Pittsburgh	3-9	1.007	0.57362	0.2384	-7.4
100	Navy	5-7	0.691	0.57143	0.2369	-7.4
101	Houston	4-8	1.024	0.57016	0.2361	-7.5
102	Indiana	3-9	0.9851	0.56931	0.2355	-7.5
103	Colorado State	5-7	0.7193	0.56179	0.2306	-7.7
104	Arizona State	3-9	1.095	0.55408	0.2255	-7.9
105	Florida Atlantic	4-8	0.7068	0.54789	0.2214	-8.0
106	San Diego State	4-8	0.7712	0.54424	0.2190	-8.1
107	Cincinnati	3-9	0.9159	0.53459	0.2127	-8.3
108	Stanford	3-9	1.141	0.51701	0.2012	-8.8
109	Western Michigan	4-8	0.7909	0.51623	0.2007	-8.8
110	Ball State	4-8	0.7382	0.50458	0.1932	-9.1
111	Tulsa	4-8	0.7259	0.50383	0.1927	-9.1
112	Connecticut	3-8	0.8147	0.48606	0.1813	-9.6
113	Baylor	3-9	0.9415	0.48097	0.1780	-9.7
114	Alabama-Birmingham	4-8	0.762	0.46107	0.1655	-10.3
115	New Mexico	4-8	0.72	0.4563	0.1625	-10.4
116	Southern Miss	3-9	0.8759	0.44717	0.1568	-10.7
117	Eastern Michigan	6-7	0.5587	0.42998	0.1463	-11.2
118	East Carolina	2-10	0.7686	0.42524	0.1434	-11.4
119	Louisiana Tech	3-9	0.7204	0.42459	0.1430	-11.4
120	Massachusetts	3-9	0.8248	0.42242	0.1417	-11.5
121	Sam Houston	3-9	0.7088	0.42077	0.1407	-11.5
122	UTEP	3-9	0.7727	0.41171	0.1353	-11.8
123	Hawaii	5-8	0.674	0.40977	0.1342	-11.9
124	Central Michigan	5-7	0.6782	0.39669	0.1265	-12.3
125	Buffalo	3-9	0.6825	0.38089	0.1174	-12.8
126	Vanderbilt	2-10	0.972	0.36038	0.1059	-13.6
127	Louisiana-Monroe	2-10	0.8724	0.35552	0.1033	-13.8
128	Florida International	4-8	0.6695	0.33124	0.0904	-14.7
129	Temple	3-9	0.6795	0.31033	0.0798	-15.6
130	Charlotte	3-9	0.7059	0.30958	0.0794	-15.6
131	Akron	2-10	0.5715	0.27152	0.0615	-17.3
132	Nevada	2-10	0.6924	0.24755	0.0513	-18.6
133	Kent State	1-11	0.6305	0.1775	0.0263	-23.0
134	1-AA	4-114	1.047	0.11425	0.0106	-28.9