Predicting Champs with 100,000 EPA Simulations

Strategos · April 13, 2023, 3:13pm

Inspired by the yearly NFL Madden simulation predicting the Super Bowl, I ran 100,000 simulations of Houston Champs using EPA data to predict the winning teams.

I simulated division assignment, schedule generation, qual matches, alliance selection, division eliminations, and Einstein. It’s not perfect but I’m excited to see how the predictions evolve once divisions are announced, schedules are released, and matches start. Let me know what you think!

Methodology

Each of the following is repeated 100,000 times:

Division assignment is completely random, the rookie-only shuffle is not implemented. For each division, I use Chezy Arena schedules and create schedules with 10 matches per team. Qualification matches are simulated and RPs are tabulated. No tiebreakers are used, ties are split randomly.

In alliance selection, I approximate the selection process with the softmax function applied to team EPAs. The higher a team’s EPA relative to the other candidates, the more likely they will be picked. I implement a rudimentary version of declining that allows teams to decline if they can guarantee a better alliance by at least 5 EPA by declining.

Playoff matches are simulated and the double-elimination bracket advancement structure is used. This results in the 8 alliances going to Einstein. The same code simulates Einstein and crowns the winning alliance.

Throughout the process I calculate stats which are aggregated and displayed at the end. Let me know if you have any questions about the methodology! Code is available here.

Caveats

In the simulation, each team is completely described by three numbers: their EPA, Link RP EPA, and Activation RP EPA. Clearly, some teams will make major improvements by next week, some teams will be picked for their complementary autos/climbs, and some teams will fill a valuable niche. This simulation does not account for that, so take everything with a grain of salt.
I haven’t modified EPA to handle supercharging, although I do not think any modifications are required. I made it 10% more difficult to get the Link RP in the simulation, but that is not completely accurate.
I have never simulated alliance selection before, so there might be room for improvement via fine tuning parameters or a completely different approach. Second and third picks especially are not well modeled.

Now onto the results! While they rankings follow the EPA rankings pretty closely (as expected), this will become way more interesting once divisions/schedules are released.

Most likely to seed high in quals

Rank	Team	Mean Rank	1st	Top 4	Top 8	Top 16
1	2056	5.32	29.1%	63.4%	81.1%	93.8%
2	1323	5.68	27.1%	60.7%	79.0%	92.9%
3	254	6.09	25.4%	58.4%	77.0%	91.7%
4	1678	7.68	19.0%	48.6%	68.8%	87.3%
5	3538	9.87	13.3%	38.5%	58.8%	80.5%
6	971	11.01	11.2%	34.5%	53.8%	76.6%
7	930	11.12	10.8%	33.5%	53.2%	76.3%
8	3005	11.19	10.9%	33.9%	53.3%	76.0%
9	6036	11.21	10.7%	33.4%	53.2%	76.2%
10	111	11.36	10.6%	33.1%	52.5%	75.6%
11	1987	11.45	10.2%	32.1%	51.8%	75.3%
12	176	11.64	9.9%	31.5%	50.9%	74.6%
13	5940	11.67	10.2%	32.0%	51.4%	74.6%
14	195	11.81	9.5%	30.9%	50.2%	74.2%
15	4414	12.44	8.7%	28.9%	47.8%	72.1%
16	3467	12.84	8.5%	27.8%	46.6%	70.7%
17	2910	13.01	8.0%	27.4%	45.9%	70.2%
18	6672	13.02	8.3%	27.7%	46.2%	70.2%
19	7157	13.1	8.3%	27.6%	46.2%	69.9%
20	1619	13.51	7.5%	25.9%	44.5%	68.7%
21	2767	13.61	7.4%	25.5%	43.7%	68.1%
22	2338	13.66	7.5%	25.8%	44.0%	68.2%
23	2539	13.66	7.3%	25.5%	43.7%	68.0%
24	1577	13.81	7.4%	25.3%	43.3%	67.5%
25	2468	13.82	7.1%	24.9%	43.3%	67.6%

Top 100

Rank	Team	Mean Rank	1st	Top 4	Top 8	Top 16
1	2056	5.32	29.1%	63.4%	81.1%	93.8%
2	1323	5.68	27.1%	60.7%	79.0%	92.9%
3	254	6.09	25.4%	58.4%	77.0%	91.7%
4	1678	7.68	19.0%	48.6%	68.8%	87.3%
5	3538	9.87	13.3%	38.5%	58.8%	80.5%
6	971	11.01	11.2%	34.5%	53.8%	76.6%
7	930	11.12	10.8%	33.5%	53.2%	76.3%
8	3005	11.19	10.9%	33.9%	53.3%	76.0%
9	6036	11.21	10.7%	33.4%	53.2%	76.2%
10	111	11.36	10.6%	33.1%	52.5%	75.6%
11	1987	11.45	10.2%	32.1%	51.8%	75.3%
12	176	11.64	9.9%	31.5%	50.9%	74.6%
13	5940	11.67	10.2%	32.0%	51.4%	74.6%
14	195	11.81	9.5%	30.9%	50.2%	74.2%
15	4414	12.44	8.7%	28.9%	47.8%	72.1%
16	3467	12.84	8.5%	27.8%	46.6%	70.7%
17	2910	13.01	8.0%	27.4%	45.9%	70.2%
18	6672	13.02	8.3%	27.7%	46.2%	70.2%
19	7157	13.1	8.3%	27.6%	46.2%	69.9%
20	1619	13.51	7.5%	25.9%	44.5%	68.7%
21	2767	13.61	7.4%	25.5%	43.7%	68.1%
22	2338	13.66	7.5%	25.8%	44.0%	68.2%
23	2539	13.66	7.3%	25.5%	43.7%	68.0%
24	1577	13.81	7.4%	25.3%	43.3%	67.5%
25	2468	13.82	7.1%	24.9%	43.3%	67.6%
26	118	14.44	6.2%	22.9%	40.4%	65.4%
27	3175	14.7	6.1%	22.3%	39.7%	64.6%
28	4522	14.74	6.3%	22.7%	40.0%	64.6%
29	694	15.06	5.9%	21.8%	39.1%	63.6%
30	4381	15.12	6.0%	21.8%	38.7%	63.2%
31	359	15.27	5.7%	21.6%	38.6%	63.1%
32	4028	15.38	5.9%	21.6%	38.6%	62.9%
33	2337	15.46	5.6%	20.9%	37.7%	62.2%
34	6090	15.55	5.7%	21.0%	37.8%	62.1%
35	2687	15.61	5.6%	20.7%	37.5%	62.0%
36	3357	15.72	5.2%	20.2%	36.8%	61.4%
37	1706	15.77	5.5%	20.6%	37.2%	61.4%
38	3683	15.89	5.5%	20.8%	37.1%	61.1%
39	6329	16.1	5.3%	19.7%	35.9%	60.2%
40	7890	16.11	5.2%	19.8%	36.1%	60.4%
41	4907	16.21	5.3%	19.6%	35.8%	59.9%
42	3015	16.42	4.9%	18.9%	34.8%	59.4%
43	1591	16.47	5.0%	19.3%	35.2%	59.4%
44	230	16.67	4.8%	18.5%	34.0%	58.6%
45	4499	16.95	4.8%	18.4%	34.0%	57.8%
46	1727	17.01	4.7%	18.0%	33.5%	57.6%
47	4613	17.07	4.5%	17.8%	33.3%	57.4%
48	2046	17.18	4.4%	17.3%	32.5%	56.7%
49	5913	17.31	4.4%	17.4%	32.7%	56.7%
50	973	17.31	4.2%	17.1%	32.3%	56.3%
51	870	17.37	4.2%	17.3%	32.3%	56.3%
52	604	17.59	4.3%	17.1%	31.9%	55.8%
53	1757	17.62	4.2%	16.7%	31.9%	55.8%
54	4270	17.62	4.2%	16.5%	31.6%	55.4%
55	148	17.64	4.2%	16.8%	31.7%	55.6%
56	1325	17.68	4.2%	16.7%	31.6%	55.5%
57	5895	18.05	4.0%	16.3%	31.0%	54.5%
58	1756	18.1	3.9%	16.1%	30.9%	54.3%
59	3310	18.26	3.9%	15.7%	30.2%	53.8%
60	2363	18.29	3.9%	15.9%	30.4%	53.8%
61	987	18.53	3.8%	15.6%	29.8%	53.3%
62	3663	18.54	3.8%	15.2%	29.3%	52.8%
63	4391	18.58	3.8%	15.4%	29.4%	52.8%
64	341	18.74	3.6%	14.9%	29.0%	52.4%
65	7457	19.2	3.4%	14.0%	27.6%	51.0%
66	2451	19.21	3.5%	14.0%	27.9%	51.0%
67	1114	19.27	3.4%	14.0%	27.3%	50.6%
68	2481	19.29	3.4%	14.1%	27.6%	50.7%
69	2052	19.35	3.2%	14.0%	27.3%	50.5%
70	3184	19.36	3.4%	14.1%	27.5%	50.6%
71	51	19.38	3.4%	14.1%	27.5%	50.6%
72	1339	19.38	3.3%	13.8%	27.3%	50.2%
73	3314	19.39	3.2%	13.9%	27.5%	50.4%
74	2521	19.6	3.1%	13.5%	26.7%	49.7%
75	1923	19.6	3.0%	13.4%	26.6%	49.7%
76	7021	19.62	3.2%	13.7%	26.9%	49.7%
77	1690	19.64	3.0%	13.3%	26.7%	49.6%
78	2075	19.69	3.3%	13.8%	27.2%	49.8%
79	1718	20.21	3.0%	12.9%	25.7%	48.2%
80	494	20.21	2.8%	12.6%	25.3%	48.0%
81	3937	20.31	3.0%	12.6%	25.3%	47.9%
82	4362	20.34	2.9%	12.4%	24.9%	47.6%
83	695	20.44	2.8%	12.7%	25.2%	47.5%
84	8033	20.49	2.8%	12.4%	24.8%	47.2%
85	1391	20.61	2.8%	12.2%	24.8%	47.1%
86	3476	20.67	2.7%	12.2%	24.7%	47.0%
87	461	20.77	2.7%	12.1%	24.5%	46.9%
88	67	20.78	2.7%	11.9%	24.3%	46.7%
89	2974	20.83	2.7%	11.7%	23.9%	46.2%
90	7769	20.89	2.7%	11.9%	24.2%	46.4%
91	6424	20.92	2.7%	12.0%	24.2%	46.2%
92	1796	20.93	2.6%	11.4%	23.7%	45.9%
93	4946	21.18	2.6%	11.4%	23.5%	45.5%
94	6002	21.29	2.5%	11.1%	22.9%	44.9%
95	4481	21.34	2.5%	11.1%	23.1%	44.7%
96	6328	21.37	2.6%	11.3%	23.4%	45.1%
97	125	21.41	2.5%	11.1%	23.0%	44.4%
98	1732	21.49	2.4%	10.8%	22.5%	44.3%
99	2992	21.61	2.5%	11.0%	22.6%	44.2%
100	5010	21.64	2.3%	10.7%	22.3%	43.9%

Most likely to win their division

Rank	Team	Winner	Finalist	3rd Place	4th Place
1	2056	67.4%	11.7%	7.0%	4.8%
2	1323	58.5%	14.0%	9.0%	6.0%
3	254	58.0%	14.3%	9.0%	6.1%
4	1678	41.5%	16.9%	11.9%	8.8%
5	3005	38.6%	17.1%	12.4%	9.2%
6	111	32.0%	17.5%	13.2%	10.3%
7	971	31.7%	17.3%	13.1%	10.5%
8	3538	30.9%	17.5%	13.3%	10.5%
9	5940	30.2%	17.6%	13.3%	10.6%
10	6036	29.5%	17.5%	13.5%	10.4%
11	930	25.0%	17.2%	13.9%	11.3%
12	6672	24.5%	17.0%	13.8%	11.5%
13	7157	23.8%	16.9%	13.9%	11.5%
14	1987	21.1%	16.5%	13.9%	12.1%
15	1619	20.9%	16.5%	13.9%	12.1%
16	195	20.6%	16.4%	13.9%	12.2%
17	2910	19.5%	16.1%	14.0%	12.3%
18	3683	19.0%	16.1%	14.0%	12.3%
19	176	18.7%	15.6%	13.9%	12.5%
20	4028	18.6%	15.9%	13.8%	12.4%
21	2338	18.5%	15.9%	13.8%	12.6%
22	1577	18.3%	15.7%	14.0%	12.5%
23	3467	18.1%	15.8%	13.9%	12.5%
24	4414	17.4%	15.8%	14.0%	12.7%
25	1591	16.9%	15.4%	14.0%	12.6%

Top 100

Rank	Team	Winner	Finalist	3rd Place	4th Place
1	2056	67.4%	11.7%	7.0%	4.8%
2	1323	58.5%	14.0%	9.0%	6.0%
3	254	58.0%	14.3%	9.0%	6.1%
4	1678	41.5%	16.9%	11.9%	8.8%
5	3005	38.6%	17.1%	12.4%	9.2%
6	111	32.0%	17.5%	13.2%	10.3%
7	971	31.7%	17.3%	13.1%	10.5%
8	3538	30.9%	17.5%	13.3%	10.5%
9	5940	30.2%	17.6%	13.3%	10.6%
10	6036	29.5%	17.5%	13.5%	10.4%
11	930	25.0%	17.2%	13.9%	11.3%
12	6672	24.5%	17.0%	13.8%	11.5%
13	7157	23.8%	16.9%	13.9%	11.5%
14	1987	21.1%	16.5%	13.9%	12.1%
15	1619	20.9%	16.5%	13.9%	12.1%
16	195	20.6%	16.4%	13.9%	12.2%
17	2910	19.5%	16.1%	14.0%	12.3%
18	3683	19.0%	16.1%	14.0%	12.3%
19	176	18.7%	15.6%	13.9%	12.5%
20	4028	18.6%	15.9%	13.8%	12.4%
21	2338	18.5%	15.9%	13.8%	12.6%
22	1577	18.3%	15.7%	14.0%	12.5%
23	3467	18.1%	15.8%	13.9%	12.5%
24	4414	17.4%	15.8%	14.0%	12.7%
25	1591	16.9%	15.4%	14.0%	12.6%
26	2539	16.3%	15.3%	14.0%	12.9%
27	4499	15.8%	14.9%	13.8%	12.9%
28	359	15.4%	15.0%	13.7%	13.0%
29	2468	15.3%	14.9%	14.0%	12.8%
30	1706	15.0%	14.9%	13.9%	12.9%
31	2767	15.0%	14.9%	13.9%	13.0%
32	7890	14.6%	14.5%	13.4%	13.1%
33	6090	14.6%	14.7%	13.7%	13.1%
34	987	14.2%	14.9%	13.7%	13.1%
35	2687	13.8%	14.2%	13.5%	13.1%
36	5913	13.7%	14.3%	13.7%	12.9%
37	1756	13.4%	14.1%	13.5%	13.0%
38	4907	13.4%	14.2%	13.7%	13.0%
39	1727	13.2%	14.1%	13.6%	13.1%
40	1538	13.2%	14.4%	13.5%	13.1%
41	604	12.9%	13.9%	13.4%	13.0%
42	4522	12.7%	14.0%	13.5%	12.8%
43	6329	12.5%	14.0%	13.3%	13.1%
44	4381	12.4%	14.0%	13.3%	13.2%
45	694	12.4%	14.1%	13.4%	13.2%
46	148	12.3%	13.6%	13.3%	13.1%
47	179	12.2%	12.3%	12.3%	12.2%
48	3847	12.2%	12.3%	12.5%	12.4%
49	70	12.1%	12.2%	12.4%	12.2%
50	4635	12.1%	12.2%	12.2%	12.2%
51	2930	12.1%	12.2%	12.6%	12.5%
52	5460	12.1%	12.1%	12.2%	12.6%
53	4607	12.1%	11.8%	12.0%	11.8%
54	2337	12.1%	13.8%	13.5%	13.2%
55	1868	12.1%	12.3%	12.4%	12.4%
56	2883	12.0%	12.2%	12.1%	12.4%
57	5166	12.0%	12.1%	12.2%	12.2%
58	2363	12.0%	13.8%	13.4%	13.4%
59	1468	12.0%	11.6%	11.9%	11.9%
60	4336	12.0%	11.7%	11.8%	12.0%
61	3668	12.0%	12.1%	12.4%	12.6%
62	876	12.0%	11.8%	12.1%	12.1%
63	5712	12.0%	12.4%	12.3%	12.5%
64	9312	11.9%	12.3%	12.4%	12.3%
65	4020	11.9%	12.4%	12.6%	12.3%
66	245	11.9%	12.4%	12.4%	12.3%
67	5895	11.9%	13.6%	13.4%	13.3%
68	1189	11.9%	11.8%	11.9%	11.7%
69	7211	11.9%	11.8%	12.0%	12.0%
70	3539	11.8%	12.1%	12.3%	12.4%
71	3647	11.8%	12.2%	12.4%	12.6%
72	1318	11.8%	12.5%	12.5%	12.3%
73	5804	11.7%	12.4%	12.6%	12.6%
74	7407	11.7%	12.3%	12.5%	12.6%
75	4476	11.7%	12.1%	12.2%	12.3%
76	5406	11.7%	12.2%	12.7%	12.6%
77	1771	11.6%	11.9%	12.2%	11.9%
78	4481	11.6%	12.7%	12.5%	12.5%
79	1403	11.6%	12.6%	12.4%	12.8%
80	862	11.6%	12.3%	12.5%	12.7%
81	461	11.5%	13.2%	13.3%	13.3%
82	5010	11.5%	12.5%	12.4%	12.7%
83	5232	11.5%	11.7%	11.8%	11.9%
84	1796	11.5%	12.4%	12.7%	12.5%
85	972	11.5%	11.8%	11.9%	11.8%
86	6919	11.4%	11.7%	12.0%	12.0%
87	2659	11.4%	11.6%	11.9%	11.8%
88	1732	11.3%	12.3%	12.5%	12.5%
89	1325	11.3%	13.3%	13.1%	13.0%
90	4362	11.3%	12.5%	12.8%	12.8%
91	5472	11.3%	12.4%	12.6%	12.7%
92	2974	11.3%	12.6%	12.6%	12.9%
93	3175	11.3%	13.1%	13.2%	13.2%
94	2075	11.3%	13.3%	13.2%	13.3%
95	1768	11.3%	12.0%	12.0%	12.4%
96	1241	11.3%	12.4%	12.7%	12.7%
97	6722	11.2%	12.3%	12.6%	12.7%
98	599	11.2%	11.2%	11.1%	11.2%
99	1757	11.2%	13.6%	13.3%	13.3%
100	3015	11.2%	13.3%	13.3%	13.1%

Most likely to win Einstein

Rank	Team	Winner	Finalist	3rd Place	4th Place
1	2056	31.8%	11.4%	7.3%	5.6%
2	1323	21.7%	10.7%	7.4%	5.9%
3	254	21.2%	10.8%	7.4%	5.8%
4	1678	10.0%	7.5%	5.9%	5.0%
5	3005	8.6%	6.9%	5.5%	4.7%
6	111	5.9%	5.3%	4.6%	4.2%
7	971	5.7%	5.3%	4.6%	4.1%
8	3538	5.6%	5.1%	4.3%	4.0%
9	5940	5.2%	5.1%	4.4%	4.0%
10	6036	5.1%	4.7%	4.3%	3.9%
11	930	3.6%	3.8%	3.6%	3.4%
12	6672	3.3%	3.8%	3.5%	3.4%
13	7157	3.2%	3.6%	3.4%	3.2%
14	1619	2.4%	2.9%	3.0%	2.8%
15	1987	2.4%	3.0%	3.0%	2.8%
16	195	2.3%	3.1%	2.8%	2.8%
17	3683	2.1%	2.6%	2.6%	2.6%
18	2910	2.0%	2.7%	2.6%	2.6%
19	4028	1.9%	2.5%	2.6%	2.5%
20	1577	1.9%	2.5%	2.5%	2.4%
21	2338	1.9%	2.4%	2.5%	2.6%
22	176	1.9%	2.6%	2.5%	2.6%
23	3467	1.8%	2.3%	2.5%	2.5%
24	3847	1.7%	1.5%	1.5%	1.5%
25	179	1.6%	1.6%	1.5%	1.5%

Top 100

Rank	Team	Winner	Finalist	3rd Place	4th Place
1	2056	31.8%	11.4%	7.3%	5.6%
2	1323	21.7%	10.7%	7.4%	5.9%
3	254	21.2%	10.8%	7.4%	5.8%
4	1678	10.0%	7.5%	5.9%	5.0%
5	3005	8.6%	6.9%	5.5%	4.7%
6	111	5.9%	5.3%	4.6%	4.2%
7	971	5.7%	5.3%	4.6%	4.1%
8	3538	5.6%	5.1%	4.3%	4.0%
9	5940	5.2%	5.1%	4.4%	4.0%
10	6036	5.1%	4.7%	4.3%	3.9%
11	930	3.6%	3.8%	3.6%	3.4%
12	6672	3.3%	3.8%	3.5%	3.4%
13	7157	3.2%	3.6%	3.4%	3.2%
14	1619	2.4%	2.9%	3.0%	2.8%
15	1987	2.4%	3.0%	3.0%	2.8%
16	195	2.3%	3.1%	2.8%	2.8%
17	3683	2.1%	2.6%	2.6%	2.6%
18	2910	2.0%	2.7%	2.6%	2.6%
19	4028	1.9%	2.5%	2.6%	2.5%
20	1577	1.9%	2.5%	2.5%	2.4%
21	2338	1.9%	2.4%	2.5%	2.6%
22	176	1.9%	2.6%	2.5%	2.6%
23	3467	1.8%	2.3%	2.5%	2.5%
24	3847	1.7%	1.5%	1.5%	1.5%
25	179	1.6%	1.6%	1.5%	1.5%
26	4414	1.6%	2.3%	2.4%	2.4%
27	1591	1.6%	2.2%	2.2%	2.3%
28	5460	1.6%	1.5%	1.4%	1.5%
29	4635	1.6%	1.5%	1.5%	1.5%
30	1468	1.6%	1.5%	1.6%	1.4%
31	2883	1.6%	1.5%	1.5%	1.4%
32	245	1.6%	1.6%	1.5%	1.5%
33	4336	1.6%	1.5%	1.5%	1.4%
34	5166	1.6%	1.4%	1.4%	1.5%
35	1868	1.6%	1.6%	1.5%	1.4%
36	2930	1.6%	1.5%	1.5%	1.5%
37	3668	1.6%	1.4%	1.5%	1.5%
38	70	1.6%	1.5%	1.4%	1.5%
39	9312	1.6%	1.5%	1.6%	1.4%
40	4476	1.5%	1.5%	1.4%	1.4%
41	5406	1.5%	1.4%	1.5%	1.4%
42	7407	1.5%	1.4%	1.4%	1.4%
43	5712	1.5%	1.5%	1.5%	1.5%
44	3539	1.5%	1.5%	1.5%	1.4%
45	3647	1.5%	1.4%	1.5%	1.4%
46	876	1.5%	1.5%	1.5%	1.5%
47	4020	1.5%	1.4%	1.4%	1.5%
48	1189	1.5%	1.5%	1.5%	1.4%
49	5804	1.5%	1.5%	1.4%	1.5%
50	4607	1.5%	1.4%	1.5%	1.6%
51	5232	1.5%	1.5%	1.4%	1.4%
52	4481	1.5%	1.4%	1.4%	1.5%
53	1732	1.5%	1.4%	1.4%	1.4%
54	1796	1.4%	1.3%	1.3%	1.5%
55	1318	1.4%	1.5%	1.4%	1.4%
56	972	1.4%	1.4%	1.5%	1.4%
57	2539	1.4%	2.1%	2.2%	2.2%
58	1403	1.4%	1.5%	1.4%	1.4%
59	599	1.4%	1.4%	1.4%	1.3%
60	1771	1.4%	1.4%	1.4%	1.5%
61	7211	1.4%	1.5%	1.4%	1.5%
62	5010	1.4%	1.4%	1.3%	1.4%
63	6045	1.4%	1.3%	1.3%	1.4%
64	3478	1.4%	1.3%	1.4%	1.4%
65	862	1.4%	1.4%	1.4%	1.4%
66	2659	1.4%	1.4%	1.4%	1.4%
67	1466	1.4%	1.3%	1.4%	1.4%
68	1241	1.4%	1.4%	1.4%	1.4%
69	4499	1.4%	2.0%	2.1%	2.1%
70	6919	1.4%	1.4%	1.4%	1.4%
71	1768	1.4%	1.4%	1.4%	1.4%
72	359	1.4%	2.0%	2.1%	2.1%
73	4373	1.3%	1.4%	1.3%	1.5%
74	1745	1.3%	1.4%	1.4%	1.3%
75	2240	1.3%	1.3%	1.3%	1.4%
76	2974	1.3%	1.3%	1.4%	1.4%
77	1706	1.3%	1.9%	1.9%	2.0%
78	4362	1.3%	1.3%	1.4%	1.4%
79	1690	1.3%	1.3%	1.3%	1.3%
80	8592	1.3%	1.3%	1.3%	1.3%
81	2468	1.3%	1.9%	2.1%	2.1%
82	5472	1.3%	1.3%	1.3%	1.4%
83	4422	1.3%	1.3%	1.3%	1.4%
84	6722	1.3%	1.4%	1.4%	1.4%
85	3218	1.3%	1.3%	1.4%	1.4%
86	316	1.3%	1.3%	1.4%	1.4%
87	4903	1.3%	1.4%	1.5%	1.4%
88	333	1.3%	1.4%	1.3%	1.3%
89	6002	1.3%	1.3%	1.3%	1.4%
90	5987	1.3%	1.3%	1.3%	1.3%
91	2767	1.3%	1.9%	2.0%	2.0%
92	6377	1.3%	1.3%	1.3%	1.3%
93	5907	1.2%	1.3%	1.4%	1.4%
94	4738	1.2%	1.3%	1.2%	1.2%
95	180	1.2%	1.3%	1.3%	1.3%
96	1807	1.2%	1.2%	1.3%	1.2%
97	8177	1.2%	1.2%	1.2%	1.2%
98	8033	1.2%	1.3%	1.3%	1.4%
99	1701	1.2%	1.2%	1.3%	1.2%
100	422	1.2%	1.3%	1.3%	1.4%

Misc Stats

Alliance	Win Probability
1	34.24%
2	16.70%
3	12.11%
4	9.57%
5	8.11%
6	7.13%
7	6.34%
8	5.80%

Average Division Alliance EPA: 168.9
Average Division “Favorite” EPA: 187.1
Average Division Winner EPA: 180.9

Average Einstein Alliance EPA: 180.9
Average Einstein “Favorite” EPA: 202.6
Average Einstein Winner EPA: 196.4

Let me know what other stats you are interested in, and I can try and compute them using the simulation. Happy to answer any questions as well.

Technologyman00 · April 13, 2023, 3:23pm

Congratulations to 930 and 1732 for being the top Wisconsin Teams! I’m rooting for ya!

(Disclaimer: I apparently designed a part of 930’s bot without knowing it Printables)

Amicus1 · April 13, 2023, 4:08pm

You designed that case? Nice! That was what we used in the early part of the season before we knew exactly where we wanted the cameras mounted. I had a feeling it was some FRC person’s design.

Ashray.g · April 13, 2023, 4:13pm

Super cool!

I’d be interested in the probability distribution of #of grids filled in quals and elims and einsteins

Technologyman00 · April 13, 2023, 4:16pm

I designed it for PhotonVision after playing around with it

MARS_James · April 13, 2023, 4:22pm

47th most likely to win our division but 25th most likely to win Einstein but not in the top 100 of likely to seed well.

I am guessing we are a 2nd/3rd round pick and in simulations where we make it out of our division we are doing fairly well on Einstein.

Zaque · April 13, 2023, 4:23pm

When simulating matches, do you just decide winners based on the higher summed alliance EPA or is it a random selection with probability related to alliance EPA? Or is there some random element added to each alliance’s EPA, and then the higher score wins?

Strategos · April 13, 2023, 4:38pm

Sounds like a great idea. I’ll give it a shot.

It looks like your Activation RP EPA is lower than most teams with 50+ EPA. Looking at that metric over time, it seems you got unlucky a couple times with auto and endgame at Rocket City Regional. The model thinks you won’t get as many bonus RPs and won’t rank as high, but are still valuable in playoffs. As to why you’re 47th in winning the division but 25th in Einstein, that might be noise. I suppose I could run 1 million simulations .

I sum up the EPAs of the red and blue alliance, and then apply the following equation to get the win probability:

\text{Red Win Prob}=\frac{1}{1 + 10^{-5/8\times(\text{Red EPA} - \text{Blue EPA}) / 29.36}}

I then award Red 2 ranking points with that probability, and Blue 2 ranking points otherwise. This helps simulate the range of ranking outcomes. Over many simulations, the mean RPs awarded to each team is the same as if I had given Red 2 * Red Win Prob and Blue 2 * (1 - Red Win Prob).

potato2 · April 13, 2023, 5:13pm

Are you able and willing to look at how a specific team ranks that isn’t in the top 100? If you can, can you look at how Team 3003 is ranked and the probabilities of the categories?

AGPapa · April 13, 2023, 5:24pm

This is really cool!

Could we get a breakdown of the probability of each team ranking within a certain decile or quintile? I’d like to do some analysis after champs is over about how accurate these predictions are.

I’ve previously looked at an Elo based prediction and found it was slightly overconfident, and I’d like to do the same sort of analysis here. Detroit Ranking Projections - #11 by AGPapa

EDIT: Even getting that “most likely to rank in the top 16” list for every team, instead of only for the top 100, would be very helpful.

joemost · April 13, 2023, 5:31pm

How accurate has your actual rankings projections been?

I was watching Statbotics match predictions all weekend, I think its said to be 81% accurate?

Felt like especially after a few matches our final standings prediction was pretty good. Most of the even it projected us to finish 18th, we finished 13th instead. Pretty good predictions

bbombei · April 13, 2023, 5:31pm

I’m taking those alliance percentages with a grain of salt. You seen the numerous upsets in week 6 and anything can happen in the championship playoffs. Think alliances 1-5 have the best chance to win the division. With only one win to advance I’m, betting a top 2 alliance will go 0-2 like in previous years.

Strategos · April 13, 2023, 5:33pm

Looking at score and game pieces scored distributions (only 1000 simulations)

Since an alliance scores their mean EPA plus or minus some noise, the frequency of high scoring matches is underestimated by the distribution of the mean. Therefore I add a uniform random noise from -10 to 10 to each score and uniform random noise from -2 to 2 to total game pieces.

Looks like we will be seeing a lot of filled grids and 200+ scores in division playoffs and especially Einstein.

joemost · April 13, 2023, 5:33pm

at NE Champs between the two divisions,
8 beat 1 in the Meir division, and 1 beat 8 by 1 point in the Wilson division. These tournaments are going to be wide open

Ashray.g · April 13, 2023, 5:34pm

Makes sense yeah

I wonder how many double-filled there will be…

hudsonsezhi · April 13, 2023, 6:50pm

100 422 1.2% 1.3% 1.3% 1.4%

EZ lol, coming for that win

Jared_Russell · April 13, 2023, 6:59pm

Checks out.

bbombei · April 13, 2023, 7:33pm

Yeah as long as you make the playoffs anyone can win it, at this level where the teams are fairly close in skill to eachother.

joemost · April 13, 2023, 11:01pm

Yeah. Just get yourself to the dance

Brandon_L · April 13, 2023, 11:04pm

Will this be re-run in some way now that we have divisions?