Next up in my series of posts visualizing the 2022 USTA League Nationals schedules is the 18 & Over 4.5 men which will be played the second weekend of Nationals.
This schedule looks reasonably random, but there are some mini-pods. Southwest, Southern, and Texas all play each other, Caribbean, Missouri Valley, and PNW all play each other, and NorCal, New England, and Northern all play each other.
It would be interesting to compare two national tournaments with the same number of teams.
ReplyDeleteI am fairly certain nationals has an adjacency matrix that determines the schedule based SOLELY on the number of teams.
I hope this is not correct.
If true, this would mean every tournament (with same number of teams) would have the same structure up to a permutation of the labels on the nodes.
I'm posting them all, if there are similarities you should be able to see it.
DeleteI don’t think that having a matrix like the other commentator explained is a big deal, as long as it limits the maximum independent set of teams sufficiently. I.E. the maximum number of teams that don’t play each other is small enough that undefeated teams getting sent home is minimal.
DeleteIdeally, if they are using such a matrix, and not just random picking of matchups, the maximum number of undefeated teams for that matrix would hopefully be 5 or less.
As your simulations for previous years have shown, it appears to be a maximum of 5 undefeated teams in the worst possible scenario, but those odds have been relatively low.
DeleteI do wonder if there’s a possible schedule that makes it impossible to have more than 4 undefeated teams when you have 17 teams playing 4 matches each.