"Random" match Schedules

[Bongle]

Oh boy, hard numbers!

I wrote a C program to crunch the numbers of teams that teams played with or against at the first day of various regionals.

NASA/VCU Regional

S = set of teams that a given team played with or against
P = set of teams that a given team played against
A = set of teams that a given team played with
There were 66 teams at this regional
Team	Games		|S|	|P|	|A|
116 	7		23	15	15
122 	7		23	15	15
339 	7		23	15	15
343 	7		23	15	15
345 	8		23	15	15
346 	8		23	15	15
384 	6		20	13	13
393 	6		20	13	13
401 	6		20	13	13
405 	6		20	13	13
414 	6		20	13	13
422 	6		20	13	13
435 	6		20	13	13
510 	6		20	13	13
539 	6		20	13	13
540 	6		20	13	13
587 	6		20	13	13
600 	6		20	13	13
611 	6		20	13	13
612 	6		20	13	13
617 	6		20	13	13
619 	6		20	13	13
620 	6		16	14	13
623 	6		16	14	13
638 	6		16	14	13
843 	6		16	14	13
900 	6		16	14	13
928 	6		16	14	13
975 	7		18	16	15
1002	7		18	16	15
1033	7		18	16	15
1054	7		18	16	15
1086	8		18	16	15
1093	8		18	16	15
1095	6		16	14	13
1123	6		16	14	13
1137	6		16	14	13
1172	6		16	14	13
1184	6		16	14	13
1222	6		16	14	13
1236	6		16	14	13
1262	6		16	14	13
1413	6		16	14	13
1522	6		16	14	13
1541	6		20	13	13
1598	6		20	13	13
1599	6		20	13	13
1610	6		20	13	13
1655	6		20	13	13
1731	6		20	13	13
1748	6		20	13	13
1793	6		20	13	13
1829	6		20	13	13
1830	6		20	13	13
1885	6		20	13	13
1895	6		20	13	13
1907	7		23	15	15
1908	7		23	15	15
2021	7		23	15	15
2028	7		23	15	15
2068	8		23	15	15
2074	8		23	15	15
2106	6		20	13	13
2107	6		20	13	13
2108	6		20	13	13
2186	6		20	13	13

New Jersey Regional

S = set of teams that a given team played with or against
P = set of teams that a given team played against
A = set of teams that a given team played with
There were 59 teams at this regional
Team	Games		|S|	|P|	|A|
11  	7		21	14	15
25  	7		20	14	15
41  	7		20	14	15
75  	7		20	14	15
88  	7		20	14	15
102 	7		21	14	15
103 	7		21	13	15
136 	7		21	13	15
165 	7		21	13	15
177 	7		21	13	15
219 	7		21	13	15
223 	7		21	13	15
224 	8		21	13	15
237 	8		21	13	15
293 	6		19	11	13
303 	6		18	12	13
341 	6		19	11	13
359 	6		18	12	13
375 	6		19	11	13
381 	7		23	15	15
486 	7		23	15	15
522 	7		23	15	15
550 	7		23	15	15
555 	7		23	15	15
613 	7		23	15	15
637 	8		23	15	15
694 	8		23	15	15
708 	6		20	13	13
714 	6		20	13	13
716 	6		20	13	13
816 	6		20	13	13
834 	6		20	13	13
836 	6		20	13	13
869 	6		20	13	13
1048	6		20	13	13
1089	6		20	13	13
1155	6		20	13	13
1218	6		20	13	13
1279	6		20	13	13
1302	7		27	13	15
1367	7		26	14	15
1391	7		27	13	15
1403	7		27	13	15
1495	8		26	14	15
1547	8		27	13	15
1617	6		24	12	13
1672	6		22	12	13
1676	6		24	12	13
1689	6		23	11	13
1727	6		23	13	13
1807	6		23	11	13
1811	6		24	12	13
1881	6		22	12	13
1882	6		24	12	13
1923	6		23	11	13
2016	6		24	12	13
2140	6		23	11	13
2180	7		27	13	15
2191	7		27	13	15

St Louis Regional

S = set of teams that a given team played with or against
P = set of teams that a given team played against
A = set of teams that a given team played with
There were 45 teams at this regional
Team	Games		|S|	|P|	|A|
45  	7		25	14	15
148 	8		21	13	15
217 	8		21	13	15
292 	7		21	13	15
461 	7		21	13	15
525 	7		21	13	15
547 	7		21	13	15
829 	7		21	13	15
830 	7		21	13	15
868 	7		21	13	15
888 	7		21	13	15
931 	7		21	13	15
939 	6		17	11	13
967 	6		20	12	13
1094	6		21	12	13
1098	7		18	15	15
1178	7		21	15	15
1182	8		18	14	15
1208	7		19	13	13
1250	6		16	13	13
1288	6		16	13	13
1315	7		17	15	15
1329	7		17	15	15
1444	7		17	15	15
1451	7		17	15	15
1472	7		17	15	15
1502	7		17	15	15
1602	7		17	15	15
1625	7		17	15	15
1646	7		18	15	15
1658	7		23	14	15
1706	7		20	12	15
1723	7		24	14	15
1747	8		21	13	15
1752	8		23	13	15
1769	7		20	12	15
1939	7		24	14	15
1985	7		21	13	15
1986	7		23	13	15
2011	6		19	12	13
2014	6		21	13	13
2133	6		17	11	13
2167	7		21	13	15
2177	7		21	13	15
2219	7		22	14	15

Interpretation
First column is how many games a team played.

Second column (|S|) is how many teams that team played either with or against. Obviously P and A are subsets of this.

Third column is how many teams a given team played AGAINST. So this is the size of the set that ALL their opponents were chosen from.

Fourth column is how many teams a given team played WITH. So this is the size of the set that ALL their alliance partners were chosen from.

You can see how a small size in either P or A might be problematic. If a team has a small pool to draw partners or opponents from, it is easy for that pool to be full of very good or very poor teams, thus throwing off that particular team's rankings.

Edit: See my post a few posts down for some stats from 2006. In general, teams did play with a wider variety back then.