The 17 team round robin?

Dormant threads from the high school sections are preserved here.
Locked
pakman044
Rikku
Posts: 262
Joined: Sun Nov 23, 2003 3:56 am
Location: Carrboro, NC
Contact:

The 17 team round robin?

Post 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
User avatar
Zip Zap Rap Pants
Yuna
Posts: 780
Joined: Tue Mar 01, 2005 12:55 am
Location: Richmond/Williamsburg, VA
Contact:

Post by Zip Zap Rap Pants »

Force teams at gunpoint to give up players for a spare team maybe? 18 works so well...
Matt Morrison, William & Mary '10, Tour Guide &c., MA in History '12?

"All the cool people eat mangoes while they smoke blunts and do cannonballs off a trampoline into my hot tub..."
-Matt Weiner

“In beer there is strength,
In wine is wisdom,
In water is germs.”
-Unknown

new email: mpmorr at email dot wm dot edu
User avatar
Coelacanth
Rikku
Posts: 283
Joined: Wed Sep 06, 2006 7:41 pm
Location: Minneapolis, MN

Post 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.
Brian Weikle
I say what it occurs to me to say when I think I hear people say things. More, I cannot say.
tabstop
Wakka
Posts: 122
Joined: Tue Mar 20, 2007 10:48 am
Location: NNVA

Post 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
emactruman
Lulu
Posts: 92
Joined: Mon Apr 21, 2003 11:18 am

Post 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.
User avatar
Frater Taciturnus
Auron
Posts: 2463
Joined: Mon Dec 12, 2005 1:26 pm
Location: Richmond, VA

Post 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.
Janet Berry
[email protected]
she/they
--------------
J. Sargeant Reynolds CC 2008, 2009, 2014
Virginia Commonwealth 2010, 2011, 2012, 2013,
Douglas Freeman 2005, 2006, 2007
Locked