FRC Ranking with Monkeys

Ranking FRC teams is a difficult task because teams play in alliances that are three on three. Who should get credit for the win? How much credit? Based on an idea that was used once for football teams. The method used here is to create a graph with nodes or each team and edges that represent that teams opponents. We start by associating some large numbers of monkeys to the all the nodes randomly. The monkeys monkeys are polled thousands of times, and some percentage of the time they chose to pick a new team (about 20%, right now). If the monkey changes from their chosen team, then it will move to own of their opponents with the oppenents that have beaten our given team being about 5 times more likely to be chosen than an opponent that lost. Of the three opponents that we are choosing from we weight by their season point-differentials. Then we move the next monkey. We keep doing this thousands of times, in the hopes that it will become steady.

Here are results from a recent run (num_monkeys=4000, num_iterations=20000):

Rank	Team Number	Point Difference	Number of Monkeys
1	176	45.19	218
2	5813	37.24	145
3	7407	36.17	134
4	3467	15.75	119
5	177	30.14	103
6	125	34.20	102
7	6328	32.33	101
8	95	21.61	79
9	2262	-2.28	73
10	88	9.39	64
10	228	13.46	64
12	133	26.19	63
13	230	17.26	61
14	131	14.94	58
15	4909	8.03	57
16	6329	23.44	52
17	2168	23.94	50
18	3566	-8.77	49
19	7907	-4.53	45
19	467	-4.50	45
21	126	7.57	43
22	663	3.00	41
23	155	11.88	40
23	8085	-0.89	40
25	8889	17.17	39
26	8724	1.69	36
26	8013	2.93	36
28	1153	11.21	35
29	1991	-3.55	34
29	1768	-2.06	34
31	4564	14.89	33
32	1071	-7.89	32
32	3654	-3.50	32
32	151	1.89	32
35	1729	-5.25	31
35	1277	-1.00	31
37	4905	5.88	30
37	6620	-4.13	30
37	58	12.94	30
40	7153	4.00	29
41	5563	12.95	28
41	1474	5.00	28
41	195	-0.78	28
44	2877	11.94	27
44	6895	-3.75	27
46	238	11.69	25
46	1027	4.75	25
46	811	-8.75	25
49	178	-8.29	24
49	2370	11.29	24
49	5687	-1.56	24
49	4906	-2.14	24
53	7127	16.50	23
54	4546	-4.57	22
54	1073	14.14	22
54	3146	-11.25	22
54	1699	-11.71	22
54	236	-2.81	22
59	7869	-13.25	21
59	4041	-0.29	21
61	4761	-12.11	20
61	1740	2.53	20
61	8046	-3.64	20
61	6763	-2.79	20
61	558	-1.21	20
61	7694	-4.33	20
67	6690	1.31	19
67	5856	1.29	19
69	78	2.00	18
69	4572	-3.92	18
69	1350	-1.00	18
69	2648	-2.93	18
73	319	-7.00	17
73	237	-2.19	17
73	3461	-0.65	17
73	716	-2.07	17
73	3451	-6.86	17
78	246	-1.83	16
78	1922	-13.86	16
78	3719	-4.43	16
78	8167	0.58	16
78	4628	-4.17	16
78	157	-4.50	16
78	5494	-3.71	16
78	190	-9.14	16
86	3464	-17.21	15
86	6933	-3.92	15
86	2064	-3.29	15
86	6333	-9.92	15
86	1831	-11.79	15
91	5491	-6.92	14
91	501	-11.50	14
91	5902	-4.42	14
91	7913	-3.92	14
91	3182	-5.71	14
91	999	-10.14	14
91	166	1.29	14
98	2713	-5.50	13
98	6723	-6.86	13
98	97	-4.67	13
98	571	-8.38	13
98	1058	-8.43	13
98	2067	-0.29	13
104	8708	-3.00	12
104	173	-3.00	12
104	1124	-4.42	12
104	8023	-5.00	12
108	5735	2.21	11
108	5112	-1.50	11
108	1721	-8.33	11
108	1307	-14.17	11
108	172	4.57	11
113	2084	-17.75	10
113	2423	-13.58	10
113	3958	-5.79	10
113	5752	-13.67	10
113	1965	-2.50	10
113	8709	-8.25	10
113	4987	-8.00	10
113	1099	-8.29	10
113	4473	-30.36	10
122	5962	-18.83	9
122	181	-9.58	9
122	4097	-14.83	9
122	2712	-17.79	9
122	1247	-10.71	9
122	2785	-7.42	9
122	6153	-11.50	9
129	5459	-11.43	8
129	6529	-10.50	8
129	7822	-5.92	8
129	8604	-9.00	8
129	3623	-14.50	8
129	4925	-11.25	8
129	1512	-8.42	8
129	6346	-9.25	8
129	6161	-17.57	8
138	348	-9.29	7
138	2342	-7.25	7
138	5347	-8.25	7
138	7462	-11.75	7
138	5265	-23.00	7
143	509	-4.57	6
143	2876	-8.42	6
143	5422	-22.07	6
143	1761	-6.42	6
143	4311	-7.08	6
143	6324	-17.33	6
143	4176	-23.67	6
143	61	-14.33	6
143	839	-9.67	6
143	6762	-19.67	6
153	175	-5.86	5
153	2170	-17.50	5
153	7314	-27.50	5
156	6201	-10.00	4
156	8567	-24.08	4
158	4169	-15.00	3
158	5142	-3.64	3