For this post, David Reinstein gives us an overview of how the card system will work tomorrow.
On Saturday, HSNCT will feature 1200 matches: 240 teams each playing 10 matches, and 80 rooms each hosting 15 rounds. Each team will play in two of the first three rounds, two of the next three rounds, etc. There will be a lunch break after six rounds, when each team has played four matches. There are 44 conference rooms and 36 suites used by the tournament.
The tournament uses a card system. There are 240 cards which have schedules on them. At the beginning of each match, the teams give their cards to the moderator. At the end of the match, the moderator gives the winning team the card with a number closer to 1 and the losing team with a number closer to 240. There is some randomness in the card assignments, so teams should not assume that the best team starts the day with Card 1 and the worst team starts with Card 240, because that is not what happens. There is also some seeding in the assignments, so teams that have demonstrated during the year that they are among the top few in the nation will not play each other in the first few matches.
As much as possible, teams will play opponents with identical records. This will work out perfectly in the morning, after which there will be 15 4-0 teams, 60 3-1 teams, 90 2-2 teams, 60 1-3 teams, and 15 0-4 teams. Because there are odd numbers, there will be some matches in the afternoon that feature teams with unequal records. All such matches will feature teams with records that differ by one win. To do this, one 4-0 team will play a 3-1 team, one 3-1 team will play a 2-2 team, etc.
By the end of the day, here are the numbers of teams there will be with each record:
10-0: 0 or 1 team
9-1: 0 to 4 teams
8-2: 6 to 14 teams
7-3: 23 to 34 teams
6-4: 43 to 56 teams
5-5: 52 to 66 teams
4-6: 43 to 56 teams
3-7: 23 to 34 teams
2-8: 6 to 14 teams
1-9: 0 to 4 teams
0-10: 0 or 1 team
Here are the numbers of teams with each record or better:
10-0 or better: 0 or 1 team
9-1 or better: 1 to 4 teams
8-2 or better: 10 to 15 teams
7-3 or better: 38 to 44 teams
6-4 or better: 87 to 94 teams
5-5 or better: 146 to 153 teams
4-6 or better: 196 to 202 teams
3-7 or better: 225 to 230 teams
2-8 or better: 236 to 239 teams
1-9 or better: 239 or 240 teams
The most likely scenario has 41 teams in the top bracket (7-3 or better) and 50 teams in the bottom bracket (6-4) starting on Sunday, but don’t be surprised when the actual numbers are slightly different. On Sunday, teams in the top bracket get knocked down to the bottom bracket when they lose, and teams in the bottom bracket get eliminated when they lose.