On Crowds and Contrarian Picks

If you are choosing NCAA tournament picks in a LARGE group (like ESPN), then, if possible, you need to account for what the masses have chosen in making your own selections.  Fortunately, ESPN publicly shows what everyone has picked–and that lets us account for them.

As the number of people approaches infinity, the formula for “Pick Value” is equal to Val=(Stat%*2-Mass%).

If you have very few people in the pool, use Stat% for selecting.  In other words, your best judgment of the odds, as informed by statistics, is the best choice.  And that gradually slides towards the Pick Value equation as the number of people increases.  I haven’t yet figured out how to calculate the actual equation based on the number of people.

I’ve updated the Bayesian Tourney ratings with a few manual tweaks to adjust for teams that have players coming back from injury (or missing from injury, like BYU, who I tweaked down 5 points), and also from games last night.

The updated ratings and odds (GmErr = sqrt(TmStdev^2/2)):

O	Sd	Re	Team	Power	GmErr	32	16	Elite 8	Final 4	Final	Champ
1	1	E	Ohio St.	33.24	10.50	99.70	85.96	60.040	44.997	28.0758	19.7785
8	4	E	Kentucky	27.84	10.14	93.28	60.95	25.212	15.944	7.6292	4.3798
9	3	E	Syracuse	25.19	12.32	88.20	53.29	31.746	12.205	5.0851	2.5636
16	2	E	North Carolina	23.41	11.29	90.47	57.05	29.284	9.887	3.6368	1.6716
12	6	E	Xavier	21.77	12.22	55.28	26.03	13.443	4.146	1.3924	0.5879
6	12	E	Clemson	22.75	9.23	52.64	20.57	5.913	2.989	1.0053	0.4398
13	7	E	Washington	20.00	11.21	62.89	28.78	12.422	3.267	0.9399	0.3530
5	5	E	West Virginia	21.85	9.97	47.36	17.62	4.834	2.331	0.7450	0.3099
11	11	E	Marquette	19.68	9.88	44.72	18.72	8.684	2.118	0.5667	0.2041
3	9	E	Villanova	17.76	10.96	56.95	8.89	2.692	1.033	0.2454	0.0789
14	10	E	Georgia	14.94	10.52	37.11	12.54	3.909	0.640	0.1151	0.0294
4	8	E	George Mason	15.03	11.10	43.05	5.12	1.251	0.403	0.0757	0.0199
10	14	E	Indiana St.	5.26	11.44	11.80	1.95	0.327	0.020	0.0014	0.0002
7	13	E	Princeton	6.74	9.79	6.72	0.86	0.054	0.008	0.0005	0.0001
15	15	E	Long Island	4.33	9.23	9.53	1.63	0.185	0.007	0.0003	0.0000
2	16	E	Texas San Antonio	-2.20	7.49	0.30	0.02	0.000	0.000	0.0000	0.0000
19	1	W	Duke	32.27	8.63	98.75	84.84	58.036	42.875	25.8835	18.0317
26	4	W	Texas	28.38	10.19	90.95	77.85	34.478	21.683	10.8306	6.3678
34	2	W	San Diego St.	26.64	9.95	97.94	70.39	45.682	18.575	8.4489	4.5882
27	3	W	Connecticut	23.38	9.42	89.73	57.13	27.202	8.608	3.1903	1.4517
31	7	W	Temple	19.14	9.46	55.74	17.04	7.594	1.660	0.4517	0.1552
30	6	W	Cincinnati	18.06	12.46	49.15	20.11	7.142	1.650	0.4544	0.1540
29	11	W	Missouri	18.40	10.20	50.85	20.66	7.193	1.527	0.4013	0.1327
21	9	W	Tennessee	18.81	9.67	53.14	8.42	2.866	1.063	0.2835	0.0955
32	10	W	Penn St.	16.93	12.05	44.26	12.38	4.943	1.018	0.2547	0.0793
22	8	W	Michigan	17.73	9.69	46.86	6.57	2.075	0.712	0.1741	0.0541
23	5	W	Arizona	14.64	9.91	62.69	13.09	1.792	0.485	0.0916	0.0223
24	12	W	Memphis	9.93	10.65	37.31	5.24	0.455	0.084	0.0106	0.0017
25	13	W	Oakland	10.22	8.96	9.05	3.82	0.282	0.048	0.0055	0.0008
28	14	W	Bucknell	5.56	10.45	10.27	2.11	0.232	0.012	0.0009	0.0001
20	16	W	Hampton	4.03	9.18	1.25	0.18	0.016	0.001	0.0001	0.0000
33	15	W	Northern Colorado	-0.20	8.59	2.06	0.19	0.012	0.000	0.0000	0.0000
36	1	SW	Kansas	29.35	10.84	97.99	73.25	51.612	33.055	21.8938	10.8096
44	3	SW	Purdue	25.65	10.24	94.59	66.24	38.327	19.245	11.0369	4.3671
51	2	SW	Notre Dame	25.58	11.49	94.47	68.29	38.353	19.181	10.8944	4.3571
43	4	SW	Louisville	24.42	10.37	83.21	58.15	25.633	13.263	7.1766	2.6195
38	9	SW	Illinois	20.55	9.15	56.04	15.76	7.677	3.164	1.3813	0.3622
47	6	SW	Georgetown	19.58	10.64	61.79	22.85	9.634	3.377	1.4063	0.3594
40	5	SW	Vanderbilt	18.35	9.54	60.69	24.15	6.933	2.468	0.9380	0.2054
39	8	SW	Nevada Las Vegas	18.46	10.30	43.96	10.85	4.702	1.707	0.6605	0.1513
49	10	SW	Florida St.	17.62	7.10	52.49	16.42	5.545	1.537	0.5317	0.0951
48	7	SW	Texas A&M	16.90	9.02	47.51	14.71	4.885	1.346	0.4575	0.0848
46	11	SW	Virginia Commonwealth	15.16	10.21	38.21	10.15	3.149	0.781	0.2396	0.0402
41	12	SW	Richmond	14.49	10.61	39.31	12.29	2.656	0.724	0.2136	0.0345
42	13	SW	Morehead St.	10.10	10.66	16.79	5.42	0.777	0.145	0.0300	0.0031
45	14	SW	St. Peter's	1.09	11.34	5.41	0.76	0.065	0.004	0.0004	0.0000
50	15	SW	Akron	0.01	11.16	5.53	0.58	0.042	0.002	0.0002	0.0000
37	16	SW	Boston University	-0.99	10.05	2.01	0.14	0.010	0.000	0.0000	0.0000
53	1	SE	Pittsburgh	25.94	8.56	96.74	70.15	41.056	27.370	13.9741	5.5168
60	4	SE	Wisconsin	26.11	11.94	72.73	45.36	25.407	16.500	8.4654	3.5119
68	2	SE	Florida	23.22	11.58	87.01	55.38	35.122	16.882	7.4605	2.5685
61	3	SE	Brigham Young	19.68	11.12	78.11	44.65	21.519	8.403	2.9789	0.7815
58	12	SE	Utah St.	21.64	10.91	53.26	24.43	10.838	5.947	2.3840	0.7224
57	5	SE	Kansas St.	20.41	10.43	46.74	20.01	8.187	4.245	1.5620	0.4237
56	8	SE	Butler	19.26	12.54	62.09	21.60	9.038	4.430	1.5664	0.4188
64	6	SE	St. John's	17.44	12.59	53.25	27.06	11.682	4.056	1.2767	0.2981
65	7	SE	UCLA	17.83	10.36	50.82	21.38	10.833	3.687	1.1287	0.2455
66	10	SE	Michigan St.	17.52	11.32	49.18	20.49	10.223	3.474	1.0652	0.2361
63	11	SE	Gonzaga	16.11	10.37	46.75	22.22	8.713	2.610	0.6990	0.1299
59	13	SE	Belmont	15.93	11.87	27.27	10.21	3.171	1.304	0.3618	0.0720
55	9	SE	Old Dominion	14.39	9.60	37.91	7.82	2.270	0.826	0.1852	0.0275
62	14	SE	Wofford	6.95	12.06	21.89	6.08	1.292	0.192	0.0247	0.0021
67	15	SE	UC Santa Barbara	5.60	10.50	12.99	2.75	0.617	0.070	0.0068	0.0004
54	16	SE	NC Asheville	-1.40	12.11	3.26	0.43	0.033	0.003	0.0002	0.0000

And here are the pick values, using the ESPN 1-2-4-8-16-32 weighting system and the picks of the ESPN pool.  The value for each round is the cumulative value of having the team reach that round.  Interestingly, there are a lot of teams in the later rounds with similar values, so there are a variety of different choices that could be made without losing much expected value versus the ESPN crowds.

The pick using this method for NCAA champ is Texas–in other words, Texas is greatly undervalued by the ESPN crowd.  Other Final 4 teams would be Wisconsin, Ohio St., and Kansas.  Ohio State and Kansas are so good that even though the crowd may like them, there’s no value in picking against them.

O	Sd	Re	Team	32	16	8	4	2	Champ
1	1	E	Ohio St.	0.999	2.515	4.13	6.43	7.64	11.98
2	16	E	Texas San Antonio	0.001	-0.004	-0.01	-0.02	-0.02	-0.02
3	9	E	Villanova	0.596	0.786	0.93	1.05	1.10	1.12
4	8	E	George Mason	0.404	0.497	0.55	0.59	0.60	0.58
5	5	E	West Virginia	0.155	0.322	0.37	0.57	0.70	0.80
6	12	E	Clemson	0.845	1.620	2.07	2.53	2.84	3.12
7	13	E	Princeton	0.086	0.093	0.09	0.08	0.06	0.06
8	4	E	Kentucky	0.914	1.952	3.22	5.10	6.99	9.41
9	3	E	Syracuse	0.794	1.404	2.62	3.62	4.56	5.62
10	14	E	Indiana St.	0.206	0.266	0.28	0.28	0.28	0.28
11	11	E	Marquette	0.471	1.138	1.79	2.11	2.27	2.40
12	6	E	Xavier	0.529	1.290	2.24	2.86	3.25	3.60
13	7	E	Washington	0.530	1.157	1.83	2.24	2.44	2.60
14	10	E	Georgia	0.470	0.922	1.21	1.30	1.32	1.34
15	15	E	Long Island	0.180	0.235	0.24	0.24	0.24	0.24
16	2	E	North Carolina	0.820	1.368	1.34	1.04	0.36	-0.11
17	1	W	Duke	0.981	2.483	3.99	6.09	8.10	12.12
18	16	W	Hampton	0.019	0.020	0.01	0.01	0.01	0.01
19	9	W	Tennessee	0.525	0.701	0.86	1.00	1.06	1.08
20	8	W	Michigan	0.475	0.614	0.73	0.81	0.85	0.86
21	5	W	Arizona	0.459	0.199	-0.16	-0.54	-0.73	-0.84
22	12	W	Memphis	0.541	0.709	0.73	0.73	0.71	0.71
23	13	W	Oakland	0.066	0.185	0.20	0.19	0.17	0.17
24	4	W	Texas	0.934	3.032	5.14	8.04	11.00	14.78
25	3	W	Connecticut	0.828	1.619	2.54	3.07	3.45	3.80
26	14	W	Bucknell	0.172	0.237	0.24	0.24	0.24	0.24
27	11	W	Missouri	0.590	1.330	1.86	2.08	2.19	2.25
28	6	W	Cincinnati	0.410	0.970	1.43	1.65	1.76	1.83
29	7	W	Temple	0.560	1.067	1.59	1.80	1.92	1.98
30	10	W	Penn St.	0.440	0.823	1.17	1.31	1.38	1.39
31	15	W	Northern Colorado	0.019	0.013	0.01	0.00	0.00	0.00
32	2	W	San Diego St.	0.981	2.166	4.11	5.83	7.78	10.05
33	1	SW	Kansas	0.969	2.069	3.38	4.65	8.88	13.81
34	16	SW	Boston University	0.031	0.027	0.02	0.01	0.01	0.01
35	9	SW	Illinois	0.624	1.124	1.68	2.15	2.58	2.78
36	8	SW	Nevada Las Vegas	0.376	0.668	0.98	1.23	1.40	1.47
37	5	SW	Vanderbilt	0.591	1.237	1.64	1.96	2.21	2.28
38	12	SW	Richmond	0.409	0.841	1.02	1.12	1.17	1.20
39	13	SW	Morehead St.	0.292	0.484	0.53	0.55	0.54	0.55
40	4	SW	Louisville	0.708	1.594	2.58	3.89	5.61	6.87
41	3	SW	Purdue	0.920	1.993	3.42	5.51	8.34	10.56
42	14	SW	St. Peter's	0.080	0.095	0.09	0.08	0.08	0.08
43	11	SW	Virginia Commonwealth	0.605	0.973	1.21	1.32	1.38	1.40
44	6	SW	Georgetown	0.395	0.423	0.55	0.57	0.78	0.85
45	7	SW	Texas A&M	0.410	0.837	1.16	1.34	1.45	1.48
46	10	SW	Florida St.	0.590	1.129	1.52	1.74	1.89	1.92
47	15	SW	Akron	0.096	0.109	0.10	0.10	0.10	0.10
48	2	SW	Notre Dame	0.904	1.936	2.78	4.30	6.27	7.78
49	1	SE	Pittsburgh	0.942	1.862	2.19	2.55	2.96	1.43
50	16	SE	NC Asheville	0.058	0.067	0.06	0.05	0.05	0.05
51	9	SE	Old Dominion	0.353	0.598	0.75	0.86	0.90	0.92
52	8	SE	Butler	0.647	1.199	1.80	2.44	2.90	3.10
53	5	SE	Kansas St.	0.216	0.600	1.03	1.59	2.01	2.22
54	12	SE	Utah St.	0.784	1.705	2.55	3.48	4.23	4.69
55	13	SE	Belmont	0.339	0.700	0.94	1.13	1.23	1.28
56	4	SE	Wisconsin	0.661	1.755	3.33	5.52	8.03	10.18
57	3	SE	Brigham Young	0.616	1.092	2.09	2.79	3.22	3.37
58	14	SE	Wofford	0.384	0.597	0.69	0.70	0.69	0.70
59	11	SE	Gonzaga	0.600	1.431	2.10	2.50	2.71	2.79
60	6	SE	St. John's	0.400	1.106	1.88	2.44	2.79	2.91
61	7	SE	UCLA	0.588	1.347	2.17	2.74	3.08	3.21
62	10	SE	Michigan St.	0.412	1.013	1.72	2.23	2.54	2.66
63	15	SE	UC Santa Barbara	0.244	0.344	0.39	0.39	0.39	0.39
64	2	SE	Florida	0.756	1.314	2.30	3.71	4.94	5.44

And the obligatory cool chart:

Download the updated spreadsheets here:

• Tournament Picks Calculation Sheets, including Masses vs. Stats calcs
• Bayesian Ratings