2015 Championship division simulated rankings

Jeremy Germita · #1 18-04-2015, 22:42

Using the preliminary match schedules and teams' best OPRs, I've simulated the rankings using the Monte Carlo method.

With every iteration of the match schedule, matches were simulated by summing each teams' OPR and adding in pseudo-random terms corresponding to the "randomness" in a teams actual performance. I'm terrible at explaining with words, so here it is in pseudocode:

Code:

Total score = (OPR1 + (random1)) + (OPR2 + (random2)) + (OPR3 + (random3)) + (random4)

The random terms are in the range of +-10 points.
Each match schedule is simulated 10,000 times and the ranks are averaged. Also shown here are the minimum and maximum ranks for each team during the entire simulation.

Here are the results:

Archimedes division

Code:

Division: arc
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
1023	1.3978	8.0	1.0
234	3.2774	10.0	1.0
5048	3.4219	10.0	1.0
2338	3.8749	10.0	1.0
3602	5.5863	12.0	1.0
314	5.838	14.0	1.0
1640	6.1363	13.0	1.0
135	7.0366	14.0	1.0
1538	10.1193	26.0	3.0
1310	10.6298	26.0	3.0
2342	11.0901	28.0	4.0
68	12.8936	36.0	5.0
2974	15.017	39.0	6.0
3322	15.5098	40.0	5.0
188	17.0073	46.0	7.0
2383	17.359	41.0	8.0
5692	19.7484	51.0	8.0
5505	20.4726	51.0	8.0
4451	20.597	48.0	9.0
4334	22.3571	50.0	8.0
3996	22.3708	53.0	9.0
217	22.7253	53.0	9.0
4201	23.7182	57.0	9.0
857	24.2749	54.0	9.0
280	27.5464	56.0	9.0
5403	28.2321	58.0	10.0
2363	29.204	64.0	9.0
503	29.5875	65.0	10.0
2605	30.1541	62.0	11.0
3103	31.0615	64.0	9.0
836	31.261	65.0	11.0
1648	32.3423	65.0	11.0
2619	33.4638	66.0	12.0
3357	35.6073	66.0	12.0
3238	35.6572	67.0	12.0
1322	35.9092	67.0	12.0
2907	36.4762	68.0	12.0
1706	37.1455	67.0	12.0
1089	37.2545	67.0	13.0
51	43.9209	70.0	15.0
360	44.1808	71.0	16.0
3284	44.6796	73.0	16.0
1572	44.9483	73.0	17.0
2914	45.7168	73.0	17.0
2848	46.9173	73.0	17.0
5687	48.2902	76.0	16.0
2013	48.4849	73.0	18.0
4364	48.8246	74.0	16.0
115	49.5901	75.0	18.0
5162	49.6051	73.0	20.0
2220	49.7157	76.0	16.0
1714	50.227	75.0	20.0
378	51.4943	76.0	17.0
5571	52.4161	75.0	20.0
5667	52.4228	75.0	21.0
691	52.8187	76.0	21.0
4977	52.8632	75.0	18.0
207	55.2896	75.0	20.0
2655	55.8479	76.0	22.0
623	56.2741	76.0	19.0
5536	58.3966	76.0	24.0
1701	59.7677	76.0	23.0
1785	59.9578	76.0	22.0
201	61.9062	76.0	29.0
4213	62.6137	76.0	29.0
41	65.8071	76.0	35.0
5581	66.1306	76.0	36.0
122	67.0141	76.0	39.0
931	68.0114	76.0	39.0
5464	69.4854	76.0	42.0
108	70.3585	76.0	43.0
1700	70.7667	76.0	45.0
4010	71.1342	76.0	42.0
4207	71.9367	76.0	41.0
3278	72.1303	76.0	43.0
5212	72.693	76.0	50.0

Curie division:

Code:

Division: cur
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
1114	1.0089	3.0	1.0
148	2.2884	8.0	1.0
3309	3.4845	12.0	1.0
303	4.6597	15.0	2.0
701	5.0363	17.0	2.0
948	7.3999	26.0	2.0
379	7.5916	26.0	2.0
3959	9.5306	29.0	3.0
4143	10.0	30.0	2.0
1574	10.3795	34.0	2.0
107	12.4993	34.0	3.0
1506	13.8446	37.0	4.0
1156	14.7032	37.0	3.0
56	15.9575	39.0	4.0
3663	17.7725	44.0	4.0
1305	17.7855	45.0	4.0
230	18.2176	42.0	4.0
1816	18.475	44.0	3.0
70	21.5197	44.0	5.0
57	21.862	43.0	6.0
4450	21.9049	46.0	5.0
610	22.8467	49.0	5.0
5046	24.1467	48.0	6.0
120	24.4828	50.0	7.0
5603	24.5584	49.0	7.0
1318	26.0858	54.0	6.0
123	26.3189	49.0	6.0
176	26.4033	48.0	7.0
4061	27.1489	48.0	7.0
88	29.4096	53.0	7.0
5407	29.4362	56.0	8.0
4048	31.3101	55.0	8.0
4613	32.4036	57.0	8.0
5735	35.4293	65.0	11.0
3452	35.9888	60.0	8.0
1086	37.1413	61.0	10.0
2996	37.2362	69.0	13.0
2557	37.3111	63.0	13.0
3974	37.3914	65.0	14.0
2457	40.039	71.0	14.0
341	40.2421	65.0	14.0
1923	40.8736	67.0	16.0
3937	41.2006	66.0	14.0
271	44.3985	69.0	18.0
1319	44.4124	72.0	20.0
3008	44.6476	69.0	17.0
708	48.7769	74.0	20.0
4498	49.2479	74.0	22.0
4653	49.7691	73.0	24.0
2046	51.4662	74.0	26.0
4909	54.1636	75.0	25.0
5572	54.4503	75.0	28.0
4468	54.9184	74.0	27.0
649	56.0985	75.0	33.0
4146	56.1484	75.0	32.0
1622	56.1858	75.0	31.0
4073	57.9905	75.0	33.0
5472	58.1176	75.0	31.0
3495	58.9864	75.0	31.0
228	59.3296	75.0	31.0
2994	59.4883	75.0	34.0
842	59.557	75.0	33.0
900	61.4895	76.0	34.0
5585	62.6177	76.0	35.0
369	63.4445	76.0	38.0
5737	64.2227	76.0	37.0
339	64.8988	76.0	37.0
702	65.3298	76.0	40.0
3193	67.2007	76.0	41.0
4595	67.9674	76.0	38.0
4355	68.1887	76.0	43.0
5586	68.5742	76.0	43.0
2594	70.1853	76.0	46.0
4593	70.617	76.0	44.0
4080	73.9475	76.0	53.0
5654	75.8376	76.0	68.0

Galileo division:

Code:

Division: gal
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
2056	1.0141	3.0	1.0
1690	2.4628	10.0	1.0
1619	4.5228	19.0	1.0
330	4.5569	17.0	1.0
2502	6.3439	28.0	1.0
525	6.5243	27.0	1.0
3618	6.5887	27.0	1.0
2067	7.0049	25.0	2.0
2451	12.0282	35.0	2.0
494	12.1065	36.0	2.0
2836	13.6508	39.0	3.0
27	14.1012	41.0	3.0
365	14.3777	38.0	3.0
3146	16.6604	46.0	3.0
4719	16.9256	40.0	3.0
1189	18.2104	43.0	3.0
4373	20.0732	45.0	3.0
3674	21.0991	45.0	5.0
862	21.1596	48.0	4.0
492	21.5059	44.0	4.0
4961	21.6935	48.0	6.0
245	22.4827	45.0	5.0
1649	22.6178	49.0	5.0
3288	22.8511	48.0	5.0
1	23.442	48.0	6.0
876	23.4893	47.0	4.0
744	23.9551	50.0	5.0
5114	26.4369	51.0	6.0
5460	30.2612	53.0	9.0
3787	30.3468	55.0	8.0
2990	31.5868	61.0	8.0
3668	32.4142	56.0	9.0
219	32.6143	58.0	9.0
45	34.0551	61.0	10.0
1595	35.4828	62.0	12.0
384	35.63	62.0	10.0
2168	37.0177	62.0	9.0
1477	37.1256	63.0	12.0
1726	37.1268	66.0	11.0
5216	37.5237	66.0	12.0
2052	38.2241	65.0	11.0
3562	41.5632	66.0	14.0
1002	44.8684	70.0	19.0
1011	45.3243	68.0	18.0
1902	46.8596	70.0	19.0
5554	48.1529	72.0	23.0
191	48.7881	71.0	20.0
568	49.1348	73.0	20.0
3410	49.7448	70.0	25.0
604	50.2253	73.0	24.0
3142	51.2479	72.0	25.0
967	53.33	75.0	29.0
3944	53.4273	73.0	27.0
111	53.7225	73.0	27.0
5584	53.9458	73.0	29.0
1540	54.4917	72.0	25.0
3026	57.0137	75.0	27.0
1777	58.4356	74.0	26.0
2626	58.9074	76.0	31.0
102	59.0543	76.0	33.0
597	59.3459	76.0	34.0
5429	60.4745	75.0	34.0
4198	60.6687	76.0	36.0
237	61.0003	75.0	37.0
3770	63.4788	76.0	36.0
2375	63.8993	76.0	33.0
1547	64.8409	76.0	36.0
5541	65.075	76.0	42.0
3337	67.6656	76.0	43.0
5498	68.0382	76.0	42.0
5725	70.9994	76.0	47.0
3492	71.4055	76.0	49.0
3397	72.4184	76.0	50.0
3175	72.8355	76.0	51.0
5421	73.8469	76.0	57.0
4920	74.475	76.0	59.0

Newton Division:

Code:

Division: new
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
118	1.0002	2.0	1.0
1671	2.2887	6.0	1.0
1678	3.0969	9.0	2.0
195	3.9759	12.0	2.0
2607	6.5944	21.0	2.0
2522	7.017	22.0	2.0
1756	7.5121	24.0	2.0
955	9.8099	29.0	2.0
1720	10.229	29.0	3.0
3130	11.1025	31.0	3.0
1983	11.2217	30.0	3.0
175	13.2906	32.0	4.0
4678	13.5587	33.0	3.0
3641	13.8471	34.0	4.0
4188	16.2905	38.0	4.0
1918	17.1349	40.0	5.0
2877	17.3426	38.0	5.0
2468	18.9988	42.0	5.0
4522	20.5068	43.0	5.0
3039	21.3506	43.0	5.0
3171	22.6064	43.0	6.0
5188	23.9412	47.0	7.0
1741	24.8436	48.0	6.0
4118	24.8772	50.0	7.0
1466	25.6193	51.0	8.0
3464	25.9994	51.0	7.0
190	26.3793	50.0	6.0
133	27.5246	51.0	8.0
3310	27.7253	50.0	8.0
3838	28.1259	53.0	8.0
74	29.0305	51.0	9.0
155	29.0684	51.0	8.0
25	33.8653	62.0	13.0
3467	34.5156	60.0	13.0
4471	36.2468	64.0	12.0
5495	37.0419	65.0	17.0
5489	37.5476	62.0	15.0
3015	38.0859	62.0	15.0
932	38.7887	63.0	15.0
321	39.1206	62.0	16.0
4954	39.6102	66.0	14.0
4501	43.2024	72.0	19.0
1094	44.5054	69.0	19.0
3314	46.6523	70.0	22.0
3574	47.7115	71.0	22.0
3940	48.1701	70.0	24.0
533	49.4281	70.0	24.0
4575	49.6092	73.0	27.0
2339	49.8405	73.0	27.0
587	50.0355	72.0	25.0
3539	50.5745	73.0	28.0
4841	52.4045	76.0	28.0
5710	53.0343	74.0	29.0
1111	53.7917	75.0	30.0
4013	54.3728	73.0	27.0
269	54.9872	75.0	30.0
2158	55.2492	74.0	31.0
537	57.7536	76.0	33.0
100	57.9475	76.0	33.0
5511	58.3821	76.0	35.0
295	59.4048	76.0	34.0
4903	59.5471	76.0	33.0
2039	61.9978	76.0	31.0
3785	62.8353	76.0	33.0
5529	63.2629	76.0	33.0
2761	64.0839	76.0	36.0
5526	64.7932	76.0	39.0
3137	66.5917	76.0	41.0
5479	68.4802	76.0	39.0
4842	69.3066	76.0	43.0
5012	69.8314	76.0	46.0
4322	71.0456	76.0	45.0
5418	71.1678	76.0	47.0
4541	72.518	76.0	51.0
540	73.0616	76.0	50.0
5027	73.6871	76.0	53.0

Carson division:

Code:

Division: cars
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
254	1.0	1.0	1.0
2085	3.0159	11.0	2.0
4488	3.2319	11.0	2.0
1730	4.2967	11.0	2.0
1519	5.538	14.0	2.0
225	6.0806	15.0	2.0
1325	6.8824	16.0	2.0
5254	7.0279	17.0	2.0
1501	9.4919	23.0	2.0
3604	10.898	23.0	2.0
85	12.0917	28.0	3.0
5406	13.7255	31.0	5.0
67	13.9754	33.0	5.0
4587	15.6008	34.0	4.0
1711	15.6787	36.0	6.0
1296	15.932	37.0	5.0
999	17.1722	37.0	7.0
3547	18.2348	38.0	8.0
16	19.1887	40.0	8.0
973	20.3772	42.0	6.0
4499	23.4288	43.0	9.0
203	23.6491	46.0	10.0
246	24.698	48.0	9.0
1058	25.5109	48.0	9.0
5053	25.5549	50.0	10.0
5659	27.14	49.0	10.0
1510	27.4675	49.0	10.0
236	28.349	49.0	10.0
399	28.7179	52.0	13.0
3481	28.8591	52.0	11.0
60	28.9231	50.0	12.0
4980	30.0982	54.0	12.0
1885	33.8115	56.0	15.0
2471	34.0111	57.0	16.0
5122	35.6281	57.0	12.0
3478	35.6839	59.0	14.0
375	36.6215	59.0	17.0
93	39.2895	62.0	18.0
3339	40.4344	62.0	20.0
2521	40.6691	63.0	20.0
5549	41.1308	62.0	21.0
2377	42.6155	63.0	18.0
558	44.3918	65.0	22.0
2601	45.015	65.0	24.0
173	45.295	65.0	21.0
5416	46.5475	65.0	25.0
3506	47.486	65.0	23.0
5338	47.5041	68.0	24.0
418	48.5945	68.0	23.0
1241	50.0157	67.0	23.0
4028	50.1212	71.0	26.0
3946	51.3996	70.0	32.0
3256	51.9784	69.0	27.0
20	53.5146	70.0	31.0
1511	53.668	72.0	28.0
5625	54.7989	72.0	28.0
4574	54.9483	72.0	33.0
2534	56.1552	72.0	31.0
2075	57.533	73.0	33.0
4215	58.7857	73.0	34.0
1458	59.1456	74.0	35.0
3880	62.0953	75.0	41.0
467	62.2004	74.0	41.0
5719	65.6953	76.0	42.0
5696	66.5185	76.0	43.0
2905	67.3771	76.0	48.0
5655	67.5709	76.0	48.0
2283	67.6511	76.0	49.0
1306	68.2891	76.0	50.0
4818	68.5804	76.0	54.0
1629	69.2999	76.0	50.0
1710	69.5047	76.0	52.0
5059	70.9297	76.0	52.0
5510	70.9612	76.0	56.0
3728	75.1205	76.0	66.0
4953	75.5756	76.0	67.0

Carver division:

Code:

Division: carv
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
3419	2.2102	14.0	1.0
1986	3.5245	17.0	1.0
193	3.9434	18.0	1.0
4967	5.7247	26.0	1.0
368	5.9792	23.0	1.0
126	6.1636	23.0	1.0
4001	6.7524	26.0	1.0
329	7.3863	26.0	1.0
1024	10.7946	34.0	1.0
359	11.1298	36.0	1.0
3140	11.5817	35.0	1.0
2852	12.7099	35.0	1.0
1768	12.8963	41.0	1.0
829	14.0028	37.0	1.0
971	16.0882	42.0	1.0
3512	17.4827	42.0	2.0
66	18.713	43.0	3.0
5402	19.1513	43.0	2.0
1208	19.3593	43.0	4.0
2834	22.7598	48.0	5.0
4039	23.5241	53.0	4.0
3536	24.9202	56.0	6.0
71	25.215	56.0	6.0
172	25.5367	54.0	7.0
4911	26.1874	52.0	8.0
1717	27.0564	54.0	6.0
1592	27.3843	56.0	5.0
75	28.1822	59.0	6.0
1425	28.9182	56.0	8.0
5260	29.0438	56.0	6.0
4381	32.3542	60.0	10.0
1625	32.6885	59.0	10.0
3566	34.4215	62.0	11.0
4915	35.2377	67.0	11.0
2130	35.3071	61.0	10.0
2630	36.2086	65.0	13.0
4384	36.2847	66.0	13.0
2337	36.4334	64.0	11.0
4183	37.0672	65.0	13.0
2876	37.1205	68.0	11.0
4253	37.6184	65.0	13.0
2767	38.4558	67.0	14.0
233	41.5708	68.0	17.0
337	45.8658	72.0	16.0
216	47.7942	72.0	20.0
1868	47.9405	74.0	21.0
3504	48.1056	75.0	21.0
5437	48.15	72.0	18.0
1718	50.4801	74.0	20.0
1369	50.8188	72.0	20.0
5442	51.883	74.0	22.0
144	53.6802	75.0	24.0
585	53.7805	76.0	23.0
1884	55.1439	75.0	21.0
3352	55.1627	76.0	25.0
5431	55.1742	76.0	28.0
2648	55.9759	76.0	27.0
2491	57.796	76.0	27.0
3721	58.2749	76.0	31.0
5689	58.7006	76.0	32.0
3802	59.0146	76.0	30.0
4536	59.4786	76.0	25.0
3653	59.569	76.0	32.0
5465	60.8736	76.0	30.0
3507	63.9498	76.0	29.0
5291	65.1566	76.0	41.0
3324	66.6272	76.0	37.0
5515	67.2695	76.0	40.0
3844	67.6613	76.0	42.0
4721	67.8311	76.0	41.0
771	69.1796	76.0	41.0
4945	69.8923	76.0	44.0
128	71.5299	76.0	49.0
3881	71.9869	76.0	48.0
5458	72.3954	76.0	45.0
5546	73.7673	76.0	50.0

Hopper division:

Code:

Division: hop
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
2826	1.0503	5.0	1.0
987	3.2193	13.0	1.0
3683	3.8896	15.0	1.0
4362	4.8436	16.0	1.0
548	4.9257	18.0	1.0
33	6.1369	19.0	1.0
573	7.7273	24.0	1.0
1218	9.13	24.0	1.0
3620	10.4871	28.0	2.0
2590	10.6372	30.0	2.0
263	10.8048	33.0	1.0
469	10.9088	28.0	2.0
2614	13.7624	34.0	3.0
1676	15.3548	40.0	4.0
2512	15.8955	46.0	4.0
3735	16.6804	41.0	3.0
166	18.2162	44.0	4.0
5576	19.1331	49.0	3.0
125	19.4122	52.0	5.0
2016	21.844	57.0	6.0
2169	23.5506	52.0	6.0
343	23.9499	53.0	6.0
1124	24.4614	59.0	7.0
4391	25.6651	58.0	8.0
1723	27.473	60.0	9.0
2228	27.7726	57.0	8.0
5562	27.9529	59.0	8.0
3688	30.5388	63.0	9.0
2344	31.4592	66.0	11.0
3098	31.6559	62.0	10.0
11	33.2331	62.0	12.0
1533	33.6665	66.0	11.0
5015	33.9089	65.0	12.0
3255	33.9698	65.0	11.0
4130	34.6789	67.0	9.0
5509	36.0843	67.0	12.0
5413	36.1381	66.0	13.0
4918	37.3935	68.0	13.0
2783	37.6939	66.0	10.0
2064	40.596	68.0	14.0
78	43.7441	70.0	14.0
1746	44.453	70.0	15.0
4550	44.9409	71.0	16.0
2830	44.9785	70.0	19.0
3950	45.3123	72.0	17.0
3501	46.6799	71.0	18.0
4265	46.7277	74.0	16.0
3042	46.8192	73.0	17.0
2609	48.7305	74.0	19.0
223	49.1074	72.0	16.0
5771	50.25	73.0	19.0
103	50.7697	73.0	19.0
4405	51.5727	73.0	17.0
811	52.0624	74.0	21.0
1817	53.442	74.0	22.0
2531	54.8484	76.0	21.0
5454	56.025	75.0	23.0
4486	56.3927	75.0	25.0
1391	56.7782	76.0	25.0
5024	58.5537	76.0	26.0
5318	59.0149	76.0	27.0
2183	59.5647	76.0	23.0
781	59.9533	76.0	25.0
3266	62.2842	76.0	31.0
1796	62.3743	76.0	34.0
5428	64.2639	76.0	34.0
3939	65.0668	76.0	35.0
5118	68.0041	76.0	37.0
2500	68.5521	76.0	42.0
4329	68.6246	76.0	39.0
4930	69.3458	76.0	43.0
4731	70.1509	76.0	36.0
5493	70.8666	76.0	44.0
2530	70.9739	76.0	39.0
4799	73.8649	76.0	51.0
4589	75.0051	76.0	57.0

Tesla division:

Code:

Division: tes
Teams found: 76
Iterations: 10000
Number	AvgRank	Max	Min
624	2.753	12.0	1.0
2122	2.9871	13.0	1.0
3824	3.0106	15.0	1.0
1403	3.3736	13.0	1.0
2481	4.5837	17.0	1.0
3132	7.2504	23.0	1.0
1806	9.009	24.0	1.0
48	9.7063	25.0	1.0
2170	9.8833	25.0	1.0
2054	10.2985	27.0	1.0
1658	11.8384	28.0	1.0
2137	11.8583	26.0	1.0
2883	12.7878	28.0	1.0
1025	14.0846	30.0	2.0
2959	15.216	32.0	4.0
58	16.7812	36.0	3.0
4256	18.0007	33.0	5.0
2930	18.229	37.0	5.0
226	19.3793	39.0	5.0
1647	19.4475	41.0	5.0
3360	19.5211	39.0	6.0
2062	22.6393	42.0	6.0
3476	22.6652	46.0	5.0
1523	24.3665	45.0	9.0
1225	25.3981	46.0	7.0
3656	25.8282	48.0	8.0
358	29.2479	55.0	12.0
2960	29.8476	53.0	13.0
706	30.2083	54.0	11.0
319	31.2138	56.0	11.0
2587	31.2417	53.0	13.0
1502	31.3946	55.0	14.0
340	32.3953	58.0	13.0
4003	34.6363	61.0	17.0
2635	34.9996	60.0	15.0
1836	35.3965	61.0	15.0
4481	35.7096	63.0	14.0
292	40.6967	72.0	18.0
2415	41.4196	69.0	21.0
2191	41.7812	70.0	15.0
5415	41.9394	67.0	21.0
5072	43.6243	72.0	20.0
3250	43.6917	72.0	20.0
244	44.7466	70.0	25.0
2526	46.1086	73.0	24.0
171	46.6736	73.0	25.0
3847	47.2878	72.0	22.0
612	48.8585	72.0	26.0
141	49.7407	73.0	27.0
5006	50.8794	73.0	27.0
3941	52.4459	73.0	27.0
5627	52.5065	75.0	27.0
2658	53.3862	73.0	28.0
2613	53.6837	75.0	28.0
5314	54.1221	74.0	31.0
2399	54.8055	76.0	30.0
1311	56.4736	75.0	30.0
2059	58.2863	76.0	29.0
1255	58.6604	75.0	31.0
4050	58.774	75.0	34.0
2875	60.0987	76.0	33.0
2486	60.9733	76.0	35.0
668	61.4742	76.0	36.0
2950	62.7291	76.0	38.0
4571	63.224	76.0	38.0
5712	65.0133	76.0	35.0
5422	65.1275	76.0	36.0
3184	65.2496	76.0	39.0
2992	65.8024	76.0	36.0
5678	66.7551	76.0	39.0
1515	68.8687	76.0	44.0
1323	70.5948	76.0	42.0
1610	70.9683	76.0	44.0
5528	72.379	76.0	46.0
5730	73.6153	76.0	52.0
5582	75.3465	76.0	61.0

Once I clean up the code, I'll post the source here.

SM987 · #2 18-04-2015, 23:22

Thanks, this is awesome.

Jack S. · #3 18-04-2015, 23:36

Very interesting. Thanks for the data!

Comparing the top of Tesla to the top of the other divisions is intriguing. It's the only division with no clear frontrunner by this metric. Should be fun!

MaGiC_PiKaChU · #4 18-04-2015, 23:38

Quote:

Originally Posted by Jack S.

Very interesting. Thanks for the data!

Comparing the top of Tesla to the top of the other divisions is intriguing. It's the only division with no clear frontrunner by this metric. Should be fun!

Definitely fun! Can't wait to play with your team!

LittleDries · #5 18-04-2015, 23:40

10000 out of 10000 iterations 254 ranks 1. Thats crazy

Nuttyman54 · #6 19-04-2015, 01:42

Quote:

Originally Posted by LittleDries

10000 out of 10000 iterations 254 ranks 1. Thats crazy

Having an OPR of 158 will do that

MechEng83 · #7 18-04-2015, 23:39

This is awesome!

I do have a suggestion (which also may not convey easily in words) which could be even better, but also requires more input data.

Rather than using a +/- 10 range in OPR, it would be good to use a team's standard deviation of OPR, which I guess would be related to the residuals from the OPR calculation. I don't know if this information is readily available, but it could narrow or expand the range possible, based on a team's consistency.

Just a thought.

Spoam · #8 19-04-2015, 02:51

Quote:

Originally Posted by MechEng83

This is awesome!

I do have a suggestion (which also may not convey easily in words) which could be even better, but also requires more input data.

Rather than using a +/- 10 range in OPR, it would be good to use a team's standard deviation of OPR, which I guess would be related to the residuals from the OPR calculation. I don't know if this information is readily available, but it could narrow or expand the range possible, based on a team's consistency.

Just a thought.

I had the exact same idea actually. The problem with the OPR residual, however, is that it gives you information about the accuracy of the regression with regard to each match, not each robot.

If you took the set of residuals from the matches a robot played in, it makes intuitive sense that that data should contain some level of information about that robot's deviation from their OPR. But is a data set of only 8-12 elements enough for this value to dominate the noise generated by their alliance partners' deviations (and therefore produce a meaningful standard deviation itself)? I dunno.

If some statistics wiz would like to chime in on this, I'd love to hear it.

themccannman · #9 19-04-2015, 05:16

Quote:

Originally Posted by Spoam

I had the exact same idea actually. The problem with the OPR residual, however, is that it gives you information about the accuracy of the regression with regard to each match, not each robot.

If you took the set of residuals from the matches a robot played in, it makes intuitive sense that that data should contain some level of information about that robot's deviation from their OPR. But is a data set of only 8-12 elements enough for this value to dominate the noise generated by their alliance partners' deviations (and therefore produce a meaningful standard deviation itself)? I dunno.

If some statistics wiz would like to chime in on this, I'd love to hear it.

The problem with trying to use variation or standard deviation with OPR is that the number it spits out pretty much just tells you what their match schedule was like. OPR is already a calculation of how much an alliances score tends to change when certain teams are playing, calculating standard deviation for that basically just going backwards. OPR tries to determine how one robot affects an alliances score, where as SD (with unique alliances) would give you how each alliance affected that robots score.

Unfortunately it's not very useful unless you have actual scouted data for each team to use, in which case you can make much more accurate predictions about rankings. Our scouting system had a little less than an 80% success rate guessing the winners of each match in our division the last two years, and those games were very defense heavy. I would bet on this system approaching a 95% success rate guessing match results this year since the game is much more consistent.

Lidor51 · #10 19-04-2015, 07:36

Very intersting, I like this idea. One problem I can see is that there are some teams that their last regional was early in the season (week 1-3), and I think the OPR of those teams won't represent the amount of points they will score at the Championship (they got a lot of time to practice, but it wasn't in an official competition so there isn't any recorded data of their improvement).

Quote:

Originally Posted by themccannman

The problem with trying to use variation or standard deviation with OPR is that the number it spits out pretty much just tells you what their match schedule was like. OPR is already a calculation of how much an alliances score tends to change when certain teams are playing, calculating standard deviation for that basically just going backwards. OPR tries to determine how one robot affects an alliances score, where as SD (with unique alliances) would give you how each alliance affected that robots score.

Unfortunately it's not very useful unless you have actual scouted data for each team to use, in which case you can make much more accurate predictions about rankings. Our scouting system had a little less than an 80% success rate guessing the winners of each match in our division the last two years, and those games were very defense heavy. I would bet on this system approaching a 95% success rate guessing match results this year since the game is much more consistent.

Pretty high percentages. Can you tell more about the system? What data it's based on, and what are the calculations it does?

tr6scott · #11 19-04-2015, 09:49

Quote:

Originally Posted by Lidor51

Very intersting, I like this idea. One problem I can see is that there are some teams that their last regional was early in the season (week 1-3), and I think the OPR of those teams won't represent the amount of points they will score at the Championship (they got a lot of time to practice, but it wasn't in an official competition so there isn't any recorded data of their improvement).

So can you curve fit the the overall week to week improvement in OPR of the population, and then use that to bias the random factor up for these teams.

Our data for TORC is from Week 7 MSC, so our random is the standard +-10, but team X, data is from week 3 and we know since week OPR overall saw a 20% increase (for example, not actual data) so let the random from team X range from +12 to -8...

Or we could just play the match next week.

CVR · #12 19-04-2015, 10:46

I think that your calculation method, which is essentially the following:

Red score = Red1_OPR + Red2_OPR + Red3_OPR

Greatly overestimates qual scores.

I think it might be more accurate to seperate the co-op and auto scores from OPR. In a single match, only one team can do co-op, and only one team can do auto (not entirely true, but pretty close). By counting all 3 team's auto and co-op scores, you're triple-weighting those scores.
Example: Qual 24 has three red teams, each of which have a co-op OPR of 20 (100% consistent 3 tote stack) and an auto OPR of 40 (100% consistent co-op). However, their tote, RC, and litter OPRs are each zero, for a total OPR for each team of 60. The score for this match would be 60, as they would get one auto stack and complete co-op. However, your method predicts the score being 180 points. That's an extreme example, but it illustrates the issue well.
I think a better method would be to use the following:

Red Score =
Red1_(toteOPR + binOPR + litterOPR)
+ Red2_(toteOPR + binOPR + litterOPR)
+ Red3_(toteOPR + binOPR + litterOPR)
+ MAX(Red1_autoOPR, Red2_autoOPR, Red3_autoOPR)
+ MAX(Red1_coopOPR, Red2_coopOPR, Red3_coopOPR)

I think that method, while slightly more complex, will give more accurate results.

Citrus Dad · #13 19-04-2015, 13:35

Quote:

Originally Posted by CVR

I think that your calculation method, such is essentially the following:

Red score = Red1_OPR + Red2_OPR + Red3_OPR

Greatly overestimates qual scores.

I think it might be more accurate to seperate the co-op and auto scores from OPR. In a single match, only one team can do co-op, and only one team can do auto (not entirely true, but pretty close). By counting all 3 team's auto and co-op scores, you're triple-weighting those scores.
Example: Qual 24 has three red teams, each of which have a co-op OPR of 20 (100% consistent 3 tote stack) and an auto OPR of 40 (100% consistent co-op). However, their tote, RC, and litter OPRs are each zero, for a total OPR for each team of 60. The score for this match would be 60, as they would get one auto stack and complete co-op. However, your method predicts the score being 180 points. That's an extreme example, but it illustrates the issue well.
I think a better method would be to use the following:

Red Score =
Red1_(toteOPR + binOPR + litterOPR)
+ Red2_(toteOPR + binOPR + litterOPR)
+ Red3_(toteOPR + binOPR + litterOPR)
+ MAX(Red1_autoOPR, Red2_autoOPR, Red3_autoOPR)
+ MAX(Red1_coopOPR, Red2_coopOPR, Red3_coopOPR)

I think that method, while slightly more complex, will give more accurate results.

I concur this is correct method. However, it's also important this year to use the Max OPR, not average, as teams improved dramatically through the season. I've got a message into Ed Law on a method to extract the Max Auto and Coop OPRs from this database.

Spoam · #14 19-04-2015, 15:06

Quote:

Originally Posted by CVR

Red Score =
Red1_(toteOPR + binOPR + litterOPR)
+ Red2_(toteOPR + binOPR + litterOPR)
+ Red3_(toteOPR + binOPR + litterOPR)
+ MAX(Red1_autoOPR, Red2_autoOPR, Red3_autoOPR)
+ MAX(Red1_coopOPR, Red2_coopOPR, Red3_coopOPR)

Quote:

Originally Posted by Citrus Dad

I concur this is correct method. However, it's also important this year to use the Max OPR, not average, as teams improved dramatically through the season. I've got a message into Ed Law on a method to extract the Max Auto and Coop OPRs from this database.

We have all this data available here if anyone wants to use it. Click the download button to get a local copy in csv format. We'll run our own monte carlo analysis later today using various models and post it here, along with some regression analysis on which model gives the most accurate predictions, just for fun.

forbes · #15 19-04-2015, 16:44

Quote:

Originally Posted by Spoam

We have all this data available here if anyone wants to use it. Click the download button to get a local copy in csv format. We'll run our own monte carlo analysis later today using various models and post it here, along with some regression analysis on which model gives the most accurate predictions, just for fun.

Thanks!

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