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The 17 team round robin?

Posted: Tue Mar 20, 2007 1:59 am
by pakman044
Since the limited 13 team round robin was brought up, it reminds me that maybe someone has an idea for a setup that I've never been able to quite puzzle out--how to do a round robin for 17 teams.

I assume the following preconditions:
  • I would like to give each team at least 5 rounds in prelims, but take not many more than 7 or so.
  • Round robin divisions are preferred.
  • Swiss pairing will not be used (there were some reasons for not using it in my situation, and in this theoretical case, it defeats the purpose of considering this question).
The problem this situation brings up is that I can conceive of two setups: a two division setup and a three division setup.

The two division setup would have two divisions broken up 9/8. The eight team division has a perfect round robin in 7 rounds. The nine team division has an imperfect round robin in 9 rounds (one bye per team).

My concerns with this setup were twofold when I considered it:
  1. The nine rounds to complete the round robin were more than I really wanted (the time could balloon out control).
  2. The eight team division plays in two fewer rounds than the nine team division, and thus will be sitting around a lot longer (there are creative ways to handle giving them byes, like giving them a first round and last round byes, but it doesn't conceal this issue).
On the other hand, three divisions are less than savory. The breakdown would thus be 6/6/5. The six team divisions perfectly divide into 5 rounds with no byes. The 5 team division imperfectly divides--and gives each of those teams only 4 games. That didn't seem like enough games.

As the number of teams increases in a round robin tournament, it becomes easier to handle weirder size divisions because the divisions can be broken up in more ways. After n=18, my limited investigation shows that things clear up tremendously (I wouldn't bet the farm on my supposition, but it seemed reasonable based on what I looked at).

The simplest solution would be to find an extra team for 18 teams. But sometimes that option just isn't possible, or someone drops late in the game, leaving 17 teams. It leaves a headache of a contingency issue.

Ideas anyone?

Patrick King

Posted: Tue Mar 20, 2007 3:03 am
by Zip Zap Rap Pants
Force teams at gunpoint to give up players for a spare team maybe? 18 works so well...

Posted: Tue Mar 20, 2007 10:20 am
by Coelacanth
We were faced with the 17-team scenario at our TRASH Regionals this past fall, until we cobbled together an additional house team to get us up to 18.

Our plan was to run two separate 9-team, 9-round round robins. We would then replace the missing team in the 8-team bracket with a 2nd bye for each team. (Basically, we replaced the team that had dropped out causing our issue with "Bye").

This means your 8-team bracket takes 9 rounds to play 7 games, with two byes for each team. If you schedule carefully, you can ensure that no team has their byes twice in a row.

If you are not constrained by staff and equipment (we were) you can have the two "bye" teams play each other during the rounds where you have two bye teams. (Basically every round except the one in which Bye is scheduled to play against Bye.)

This unbalances your schedule, as each team will play two games against exactly two other teams. You can apply some strength-of-schedule algorithm to normalize the final records, or you can simply consider these games exhibitions. Neither solution is ideal, of course, but at least you minimize the time spent sitting around by your teams.

Posted: Tue Mar 20, 2007 11:32 am
by tabstop
I think the 6/6/5 scenario would be best. Yes, some teams only get 4 prelim games, but everybody else only gets 5, which means there should be plenty of rounds left for playoffs of some kind. In fact, you could run a round-robin playoff (top two from each pool, etc.); four more rounds for (almost) everybody if you play only the "unique" games. And no one would have a bye more than once (the team that would expect to have a bye twice, the last-place team from the smallest pool, would have their bye eaten by the "missing" round in the playoffs). Not so bad, I think, provided you're willing to run 9-10 rounds.

--
AFeist

Posted: Wed Mar 21, 2007 6:00 pm
by emactruman
My response would be to throw out the idea of multiple divisions. Have a pre-determined schedule with teams randomly drawing that schedule. Granted this assumes that you can draw a schedule in a understandable way, while making it obvious that the schedules were predetermined. This wouold work especially well if you had a bunch of teams of a similair caliber.

Posted: Wed Mar 21, 2007 7:39 pm
by Frater Taciturnus
Matt Morrison wrote:Force teams at gunpoint to give up players for a spare team maybe? 18 works so well...
Im gonna have to agree with Matt. Find three or four people (off the street if it comes to it!) and form a scab team. 18 is just such a good number for RR that you almost have to do it.