Archimedes 2012!

[Joe Ross]

Similar to what I did in previous years, I ran through 200 simulated qualification match schedules (with 9 matches per team, using the FIRST match generator).

I used each team's highest adjusted opr at any event to choose that team's "best event". Then, for that event, I used their unadjusted OPR for their contribution to a match. I also used the hybrid OPR, bridge OPR, teleop OPR to help calculate the standings. For the co-op bridge, I summed the co-op OPR for all 6 robots in the match and compared that to a threshold. When back-testing against regionals, if the threshold was chosen to be close to the number of actual co-ops at the regional, it had a relatively high correlation to the actual results on the co-op bridge. Almost all regionals had a correlation co-efficient of between 0.6 and 0.85. However, at the Michigan State Championship, the correlation coefficient was only 0.3. I believe this is because almost all of the robots there were able to balance so the balances that didn't happen weren't be cause of the robots, but because of luck. I used this method for calculating the co-ops, trying to get a co-op percent of around 60% (higher then most regionals, but lower then MSC). Overall, this isn't a very good way to do it, as it punishes teams at early regionals and regionals where teams did not co-op that much. However, it's included to help simulate the randomness of the rankings this year. All OPR data is from Ed Law's spreadsheet.

I calculated the results for each of the 200 simulated qualification schedules, and then looked at some statistics from the aggregate results.

Since the standings are much more complicated this year, and the co-op bridge is so important, and there isn't a very good way to simulate it, I looked at both the ranks, the number of qualification points, and the number of wins.

Everyone should attend Karthik's presentation at the championships where he covers "Why 'OPR' is a flawed indicator in Rebound Rumble".

The following were the values that were used in the simulation

Team 	OPR	Teleop	Hybrid	Bridge	Coop
67	36.70	19.41	11.17	6.12	1.06
2056	36.61	23.24	11.81	1.63	0.30
1114	35.10	18.64	15.19	0.91	0.78
359	30.79	19.15	9.14	2.79	1.27
1218	30.55	21.75	7.82	1.88	1.13
973	28.16	13.06	4.97	3.05	0.23
2590	26.84	13.99	6.09	6.76	0.16
1676	25.02	14.09	8.96	1.86	0.89
2826	24.35	12.57	8.34	3.44	0.92
1796	23.67	11.61	9.58	2.57	0.50
2415	23.42	14.01	4.60	5.53	0.27
1311	23.15	11.10	10.38	1.48	0.18
716	22.90	10.60	5.06	7.19	0.03
2996	22.70	9.88	7.82	5.09	0.56
245	22.58	8.63	7.30	6.65	0.44
195	21.68	12.79	4.65	4.05	1.06
2614	21.39	8.63	6.61	6.16	0.28
2046	21.27	12.87	5.02	3.49	0.42
75	20.94	8.12	9.43	3.40	0.53
3968	20.92	10.65	6.60	3.54	0.69
1592	20.85	13.16	6.06	1.52	0.02
1816	19.58	4.76	10.48	4.26	-0.35
2557	19.35	5.98	3.75	9.63	0.87
272	18.51	7.25	7.45	3.81	0.46
126	17.73	9.56	5.47	3.31	0.78
3015	17.69	4.48	7.57	5.53	0.08
1868	17.64	9.20	5.40	3.90	0.47
1403	17.09	7.24	8.30	1.73	0.96
2603	16.54	4.59	7.68	4.27	-0.16
3476	16.42	8.29	5.68	2.44	-0.06
1902	15.93	3.58	4.77	7.38	0.60
1756	15.50	7.75	3.88	3.87	0.49
234	15.05	7.80	3.29	4.12	-0.08
2898	14.36	4.61	7.87	2.18	0.51
1987	14.35	4.26	8.05	1.99	0.07
2512	14.33	9.60	1.28	3.67	-0.14
781	14.13	6.09	0.13	7.71	0.19
247	13.80	2.77	6.85	3.74	0.26
3008	13.67	6.53	5.90	1.33	-0.16
4334	13.50	4.46	4.99	4.05	0.78
369	13.23	2.75	7.60	2.84	0.69
3997	13.20	6.02	4.42	2.58	0.28
1261	12.81	5.75	3.77	3.06	0.23
4256	12.77	3.54	5.38	3.92	0.25
1736	12.50	4.00	3.60	4.90	0.17
1647	12.45	4.72	4.60	3.12	-0.14
839	12.25	5.67	0.99	5.30	0.30
3747	11.50	3.70	3.31	4.49	0.26
2949	10.85	1.00	6.97	3.15	0.93
1504	10.78	6.32	5.75	-1.28	0.45
3947	10.64	5.63	2.94	2.07	0.66
587	10.52	2.11	3.88	4.84	0.45
100	10.00	2.69	4.46	0.73	0.01
2851	9.99	4.22	1.28	4.49	0.88
2974	8.57	3.22	4.93	0.15	0.11
1458	8.56	1.41	4.64	2.99	-0.03
2022	8.48	4.07	1.39	2.93	0.61
3481	8.48	5.29	0.86	2.44	0.05
4143	8.04	0.63	4.91	2.50	0.06
20	7.93	3.95	0.79	2.96	0.01
3335	7.91	0.60	4.87	2.64	-0.10
128	7.85	1.78	3.97	2.11	0.46
4356	7.55	0.05	0.40	6.88	-0.09
2395	7.50	6.48	1.23	-0.21	-0.32
2638	7.37	5.69	1.95	-1.30	0.50
1	7.36	2.70	1.45	3.20	-0.04
4001	7.12	1.95	0.73	4.66	0.51
1306	7.02	2.23	6.18	-1.39	0.25
3456	6.85	1.98	0.39	4.63	0.20
190	6.62	1.99	5.48	-1.09	-0.04
1875	6.40	4.25	1.20	1.16	-0.16
1014	6.22	0.28	5.60	0.68	0.27
1642	6.15	0.39	0.15	5.30	0.48
144	5.98	3.99	3.94	-2.06	-0.26
1710	5.60	1.20	4.92	-0.56	-0.17
2403	5.59	2.84	0.98	2.57	0.14
236	4.94	3.61	4.49	-2.85	0.25
2410	4.84	0.70	3.26	0.89	-0.09
2815	4.54	4.93	1.65	-2.03	0.21
3410	4.49	0.63	1.00	2.42	-0.07
246	4.47	1.12	0.12	3.24	0.37
4300	4.15	3.80	1.51	-0.84	0.02
2648	4.07	4.21	-2.41	2.27	0.50
1058	3.91	-0.23	0.46	0.86	0.05
3081	3.91	-0.93	2.48	2.18	-0.22
3158	3.88	0.91	1.58	1.85	0.05
1018	3.79	1.09	4.06	-1.36	-0.08
2809	3.68	4.38	-0.21	-1.53	0.13
692	2.70	2.60	-0.82	0.62	0.43
2085	2.70	1.82	0.23	0.41	0.37
4403	1.92	1.16	0.52	0.39	0.50
956	1.76	2.06	1.81	-2.10	0.05
3999	1.44	-0.82	2.77	-2.06	0.16
4218	1.35	-0.11	0.24	1.30	0.31
4206	0.44	1.16	-1.98	1.56	0.21
4082	0.22	0.61	0.46	-0.26	0.03
3585	0.07	-0.25	-0.65	1.04	-0.12
3128	-0.78	-1.40	0.03	0.17	-0.13
3927	-1.75	-0.85	0.11	-1.16	0.19
3634	-5.53	0.03	-3.29	-2.67	0.31

Seeds:

	avg	med	mode	min	max	stdev	top8	#1
67	3.25	3	1	1	15	2.61	191	64
2056	12.67	11	8	1	60	8.81	73	5
1114	5.65	4	1	1	38	5.57	159	39
359	4.35	3	2	1	32	4.04	179	36
1218	5.11	4	3	1	45	4.86	173	28
973	25.77	22.5	19	4	69	14.09	9	0
2590	26.79	24	17	5	87	13.85	7	0
1676	10.63	9	6	1	43	7.86	94	2
2826	10.01	8	4	1	41	7.83	111	7
1796	18.33	16	9	1	84	13.37	48	2
2415	29.29	27.5	25	5	77	15.24	7	0
1311	31.77	29	21	3	80	15.84	6	0
716	39.48	36	35	7	89	17.80	2	0
2996	19.09	17	13	1	66	12.57	40	3
245	23.45	21	11	1	70	14.37	26	1
195	12.09	10	7	1	40	8.21	87	5
2614	31.06	28	25	3	88	17.06	13	0
2046	27.68	25	16	4	78	15.83	16	0
75	22.23	19.5	15	2	79	13.28	28	0
3968	17.81	14.5	8	1	70	12.74	53	1
1592	43.59	40	40	8	99	20.17	1	0
1816	57.86	59	52	16	99	18.62	0	0
2557	19.00	15.5	11	1	68	12.74	37	1
272	26.66	24	18	2	74	14.76	15	0
126	19.67	17	17	1	56	12.21	40	2
3015	42.26	39	23	7	92	19.11	1	0
1868	30.48	28	17	1	81	16.74	16	1
1403	16.92	14	8	1	54	11.78	58	2
2603	54.75	53	53	12	97	20.00	0	0
3476	55.01	52.5	40	8	100	20.64	1	0
1902	29.31	27	32	1	83	15.67	8	1
1756	32.89	29	26	2	93	18.67	7	0
234	58.91	57.5	45	15	99	20.01	0	0
2898	30.49	29	32	2	99	17.53	12	0
1987	49.67	47	43	13	99	21.47	0	0
2512	66.46	67	78	16	100	18.89	0	0
781	53.27	52	60	8	100	21.76	1	0
247	46.12	45	42	4	90	20.38	3	0
3008	61.56	62	67	16	99	20.62	0	0
4334	26.15	25	21	2	92	13.55	11	0
369	27.55	24	12	2	75	15.92	12	0
3997	45.82	45	34	7	92	19.16	2	0
1261	49.97	49	49	11	98	18.81	0	0
4256	45.73	44	43	8	96	18.44	1	0
1736	53.71	54.5	47	5	98	20.70	1	0
1647	69.82	75	75	15	100	19.45	0	0
839	51.87	51	49	12	99	19.69	0	0
3747	51.74	52	52	13	93	19.77	0	0
2949	24.19	20	19	2	80	15.23	23	0
1504	43.87	41	47	10	93	19.67	0	0
3947	38.57	36	26	2	88	18.14	6	0
587	43.49	43	58	6	90	18.80	3	0
100	61.46	64	73	23	99	20.39	0	0
2851	30.72	28	23	4	90	17.51	12	0
2974	57.21	56	56	12	100	21.18	0	0
1458	70.04	72	87	21	100	18.86	0	0
2022	45.32	44	51	6	95	20.44	4	0
3481	69.72	72.5	88	10	100	19.31	0	0
4143	68.10	69.5	96	17	100	19.44	0	0
20	70.76	71.5	65	25	100	18.84	0	0
3335	68.97	68	68	20	100	19.37	0	0
128	50.23	50	60	8	95	20.32	1	0
4356	77.40	79	91	22	100	16.35	0	0
2395	84.44	89	96	32	100	14.46	0	0
2638	49.05	50	54	9	94	19.54	0	0
1	72.86	77	91	20	100	18.66	0	0
4001	49.13	46	36	12	94	19.64	0	0
1306	58.21	60	69	11	95	19.78	0	0
3456	61.68	61	48	11	99	20.42	0	0
190	70.82	74.5	90	18	100	20.86	0	0
1875	80.12	85	92	14	100	16.58	0	0
1014	58.26	57	54	12	98	20.60	0	0
1642	57.33	59	73	13	96	19.62	0	0
144	80.70	85	95	18	100	17.48	0	0
1710	77.36	81.5	94	30	100	17.43	0	0
2403	68.09	70	60	9	100	18.46	0	0
236	63.07	64	88	14	100	20.12	0	0
2410	77.15	80.5	90	7	100	17.83	1	0
2815	65.93	67	85	9	100	19.91	0	0
3410	80.54	83	99	31	100	15.26	0	0
246	62.25	62	62	15	98	19.33	0	0
4300	75.45	79	91	9	100	18.51	0	0
2648	59.16	60	53	16	99	21.54	0	0
1058	79.60	84	83	28	100	16.46	0	0
3081	82.69	86	100	23	100	15.06	0	0
3158	74.78	78.5	84	21	100	18.77	0	0
1018	77.94	79.5	78	25	100	15.24	0	0
2809	71.96	74	98	13	100	19.62	0	0
692	60.30	62.5	49	6	100	21.63	1	0
2085	62.93	63	63	17	98	20.44	0	0
4403	61.50	62	82	13	99	19.08	0	0
956	75.00	80	81	15	100	17.89	0	0
3999	74.19	77	88	17	100	17.67	0	0
4218	68.16	70	76	9	98	18.69	0	0
4206	75.18	77	69	38	100	16.48	0	0
4082	84.92	90	99	37	100	14.01	0	0
3585	87.01	92	100	26	100	14.52	0	0
3128	87.76	93	100	42	100	12.39	0	0
3927	80.52	84	97	20	100	16.19	0	0
3634	80.42	83.5	94	23	100	15.48	0	0

QPs:

	avg	med	mode	min	max	stdev	Perfect
67	32.28	32	34	26	36	2.26	21
2056	27.14	28	28	18	36	3.02	1
1114	30.37	30	30	20	36	2.98	9
359	32.00	32	34	23	36	2.48	15
1218	31.61	32	32	20	36	2.61	11
973	24.26	24	26	16	32	3.25	0
2590	23.76	24	24	12	32	3.29	0
1676	28.35	28	28	20	34	3.03	0
2826	28.84	29.5	30	20	36	3.20	3
1796	25.73	26	28	13	36	3.69	1
2415	23.40	24	22	14	32	3.34	0
1311	22.18	22	22	14	32	3.24	0
716	21.28	22	22	12	30	3.47	0
2996	25.67	26	24	16	36	3.75	1
245	24.58	24	24	14	33	3.57	0
195	28.61	28	30	22	36	3.19	3
2614	22.74	23	24	12	31	3.68	0
2046	23.92	24	26	14	32	3.70	0
75	24.59	24	26	14	34	3.33	0
3968	26.19	26	28	16	34	3.53	0
1592	20.15	20	20	7	30	3.94	0
1816	17.29	18	18	8	26	3.31	0
2557	26.38	26	26	16	36	3.39	1
272	23.77	24	26	14	32	3.36	0
126	26.02	26	26	18	34	3.50	0
3015	20.20	20	22	10	28	3.53	0
1868	23.42	24	24	14	34	3.84	0
1403	26.42	26	26	18	34	3.58	0
2603	17.87	18	18	8	26	3.51	0
3476	17.99	18	20	6	30	3.97	0
1902	23.53	24	24	14	34	3.57	0
1756	22.93	24	24	10	34	4.07	0
234	17.77	18	20	6	27	3.74	0
2898	22.68	22	22	6	33	3.94	0
1987	18.84	19.5	20	8	27	3.95	0
2512	16.61	16	16	7	25	3.68	0
781	19.29	19	18	7	30	4.05	0
247	19.63	20	22	11	30	3.90	0
3008	16.71	17	16	6	26	3.92	0
4334	24.15	24	22	12	33	3.15	0
369	23.45	24	24	14	32	3.64	0
3997	20.14	20	18	12	30	3.64	0
1261	19.34	20	18	8	28	3.63	0
4256	19.96	20	18	10	30	3.47	0
1736	18.64	18	18	8	31	4.00	0
1647	15.33	15	14	6	26	3.78	0
839	19.48	20	20	10	28	3.58	0
3747	19.15	20	20	10	28	3.71	0
2949	24.49	24	24	14	34	3.67	0
1504	20.18	20	20	10	28	3.67	0
3947	21.84	22	20	12	34	3.76	0
587	20.65	20	20	11	30	3.66	0
100	17.02	16	16	8	24	3.77	0
2851	23.77	24	24	12	32	3.68	0
2974	17.66	18	18	6	26	4.04	0
1458	15.18	15	14	6	24	3.72	0
2022	20.71	20	22	12	32	3.84	0
3481	16.02	16	16	6	27	3.81	0
4143	15.58	16	16	4	26	3.94	0
20	15.78	16	16	6	24	3.73	0
3335	15.37	16	18	6	24	3.92	0
128	19.37	20	20	10	29	3.84	0
4356	14.48	14	16	4	24	3.68	0
2395	12.57	12	12	2	23	3.64	0
2638	19.85	20	18	10	29	3.64	0
1	15.25	15	14	4	26	3.97	0
4001	19.90	20	22	10	28	3.60	0
1306	17.54	17	16	9	28	3.71	0
3456	17.71	18	18	9	28	3.82	0
190	15.05	14	14	6	26	4.15	0
1875	13.72	14	14	6	25	3.66	0
1014	17.45	18	18	8	28	3.80	0
1642	18.60	18	18	11	28	3.44	0
144	12.87	12.5	14	1	26	4.05	0
1710	13.58	14	12	2	22	3.76	0
2403	16.36	16	16	8	30	3.55	0
236	16.77	16	16	6	26	3.76	0
2410	14.01	14	14	4	30	3.92	0
2815	16.59	16	18	8	27	3.89	0
3410	13.61	14	14	4	24	3.57	0
246	17.64	18	18	10	26	3.62	0
4300	14.50	14	12	5	32	4.04	0
2648	18.43	18	18	8	28	3.84	0
1058	14.11	14	14	6	24	3.50	0
3081	12.79	13	14	1	24	3.76	0
3158	14.64	14	14	6	24	3.93	0
1018	13.78	14	14	5	24	3.40	0
2809	15.53	16	16	6	26	4.10	0
692	18.19	18	16	8	32	4.09	0
2085	17.46	17	16	8	26	3.73	0
4403	17.68	18	18	8	28	3.53	0
956	14.75	14	14	6	26	3.64	0
3999	14.65	14	14	6	26	3.73	0
4218	16.53	16	18	10	29	3.43	0
4206	15.28	16	16	8	22	3.37	0
4082	12.65	12	12	2	23	3.61	0
3585	12.10	12	12	2	24	3.82	0
3128	11.71	12	12	4	22	3.48	0
3927	13.81	14	14	4	26	3.60	0
3634	14.14	14	14	6	24	3.51	0

Wins:

	avg	med	mode	min	max	stdev	Perfect
67	8.03	8	8	5	9	0.89	68
2056	8.09	8	8	5	9	0.94	78
1114	7.85	8	8	4	9	1.04	63
359	7.41	8	8	4	9	1.13	32
1218	7.51	8	8	4	9	1.12	36
973	7.02	7	7	3	9	1.19	20
2590	6.91	7	7	2	9	1.29	21
1676	6.54	6.5	6	3	9	1.29	13
2826	6.48	6.5	6	3	9	1.30	10
1796	6.46	7	7	3	9	1.31	10
2415	6.29	6	6	2	9	1.39	5
1311	6.26	6	6	3	9	1.30	4
716	6.27	6	7	2	9	1.35	6
2996	6.38	6	6	3	9	1.31	7
245	6.33	6	6	3	9	1.35	4
195	6.10	6	7	3	9	1.37	6
2614	5.89	6	6	2	9	1.33	2
2046	5.92	6	6	1	9	1.57	7
75	5.86	6	6	3	9	1.29	2
3968	6.03	6	6	2	9	1.39	4
1592	5.96	6	7	1	9	1.53	4
1816	5.87	6	6	2	9	1.30	4
2557	5.58	6	5	2	9	1.40	3
272	5.68	6	6	2	9	1.41	1
126	5.60	6	6	2	9	1.48	2
3015	5.69	6	6	2	9	1.42	1
1868	5.63	6	6	2	9	1.41	4
1403	5.29	5	6	1	9	1.58	1
2603	5.38	5	5	2	9	1.40	3
3476	5.08	5	5	1	8	1.52	0
1902	5.04	5	5	1	9	1.43	2
1756	5.27	5	6	2	9	1.51	4
234	4.93	5	4	1	8	1.48	0
2898	4.99	5	5	1	9	1.50	2
1987	4.77	5	4	1	9	1.53	1
2512	4.79	5	4	2	8	1.45	0
781	4.69	5	4	1	9	1.49	1
247	4.69	5	5	1	9	1.54	1
3008	4.84	5	5	1	8	1.49	0
4334	4.68	5	5	0	8	1.43	0
369	4.64	5	5	1	8	1.55	0
3997	4.67	5	5	1	8	1.40	0
1261	4.50	4	4	1	9	1.48	1
4256	4.63	5	4	0	8	1.46	0
1736	4.42	4	5	1	9	1.55	1
1647	4.23	4	4	0	9	1.44	2
839	4.40	5	5	1	8	1.43	0
3747	4.19	4	4	0	8	1.50	0
2949	4.34	4	5	0	9	1.56	1
1504	3.98	4	4	1	7	1.45	0
3947	4.10	4	4	1	8	1.51	0
587	4.16	4	4	0	8	1.56	0
100	4.26	4	5	0	8	1.45	0
2851	4.14	4	5	1	8	1.59	0
2974	4.09	4	4	1	8	1.54	0
1458	3.73	4	4	0	7	1.31	0
2022	3.55	3	3	0	8	1.50	0
3481	3.68	4	4	1	8	1.38	0
4143	3.53	4	4	0	8	1.59	0
20	3.76	4	4	0	8	1.63	0
3335	3.81	4	4	0	8	1.54	0
128	3.63	4	4	0	8	1.44	0
4356	3.36	3	3	0	8	1.47	0
2395	3.51	3	3	0	8	1.40	0
2638	3.64	4	4	0	7	1.53	0
1	3.48	4	4	0	7	1.49	0
4001	3.56	4	3	1	7	1.46	0
1306	3.47	3	3	0	8	1.46	0
3456	3.69	4	4	0	7	1.49	0
190	3.35	3	3	0	8	1.48	0
1875	3.39	3	3	0	8	1.49	0
1014	3.29	3	3	0	7	1.44	0
1642	3.18	3	3	0	7	1.37	0
144	3.25	3	3	0	8	1.56	0
1710	3.34	3	3	0	7	1.40	0
2403	3.30	3	3	0	8	1.31	0
236	3.13	3	4	0	8	1.43	0
2410	3.20	3	3	0	8	1.34	0
2815	3.11	3	2	0	7	1.44	0
3410	2.95	3	3	0	7	1.44	0
246	3.07	3	3	0	7	1.34	0
4300	2.95	3	3	0	8	1.38	0
2648	3.02	3	3	0	8	1.50	0
1058	2.73	3	3	0	6	1.38	0
3081	3.13	3	4	0	7	1.39	0
3158	2.97	3	3	0	7	1.51	0
1018	3.05	3	3	0	7	1.33	0
2809	3.06	3	3	0	7	1.35	0
692	3.00	3	2	0	8	1.58	0
2085	2.89	3	2	0	7	1.28	0
4403	2.53	2	2	0	6	1.31	0
956	2.75	3	3	0	7	1.30	0
3999	2.55	2	2	0	6	1.33	0
4218	2.67	3	2	0	6	1.38	0
4206	2.50	2	2	0	6	1.31	0
4082	2.22	2	2	0	6	1.22	0
3585	2.35	2	2	0	6	1.29	0
3128	2.16	2	2	0	5	1.32	0
3927	1.98	2	2	0	5	1.21	0
3634	1.62	2	1	0	4	1.14	0