Social Squares - Group Round Robin

A topic I have been doing some research on is the idea of a round-robin, but a group match play round-robin as opposed to head-to-head to see there’s a way that you can play every opponent once and only once but still have games of either 3 or 4 players.

I came across this concept of a Social Square which seems to allow for just that (in specific cases):

https://www.devenezia.com/round-robin/forum/?topic=774

The example they cite is for 16 players:

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If you are player A, then you need to face 15 unique opponents so you will need (15 / 3) = 5 Group Play matches to face everyone exactly once. Scoring is straight ahead. How many opponents did you win against?

I thought that this would be an interesting way to get what would essentially be head-to-head results over the course of five group-play matches as opposed to 15 rounds of Round-Robin.

I also thought that it would be an interesting way to conduct a Finals if you identity a Top 16. That being said, there’s a problem with the match-ups as laid out when it comes to seeding purposes. If you assume the order of the letters is the choice order, over the course of the matches it looks something like this:

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You’re essentially locked into your position except when you’re playing in the match close to your “tier”.

I played with some of the letter/seed pairings to see if I could accomplish the following:

  • Smooth the curve of the number of 1sts, 2nds, 3rds, and 4ths based on you seeding
  • Avoiding playing everyone close to you in a single match (i.e. no match of 1-2-3-4, but spread those pairings out across those matches.

Here’s what I’ve come up with:

Long story short, I plan I conducting this type of Finals at an upcoming event that we’re running and will report back how it goes. My thought at the moment is that we’ll run qualifying, then these five rounds of Match Play and then do some kind of final round with the Top 4.

Beyond just 16 players, I think there’s an opportunity to make something like this work for a number of different player configurations, especially when there’s the opportunity to have either 4, 3, or 2-player matches.

For 9 players, you could do four 3-player matches and have everyone play everyone once. I haven’t optimized the seeds yet for this one to avoid a 1-2-3 matchup.

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Source: https://www.devenezia.com/downloads/round-robin/social-square-prime.html

My spreadsheet: https://docs.google.com/spreadsheets/d/1b3n27p9KxDacZ6wc4-gP7f-JyX5zFHThFAgseFlmiCw/edit?usp=sharing

I’m interested to spend time over the next few weeks working out if configurations are possible from 9 players and up (can it work with 11? can it work with 24?) but wanted to put this out there for thoughts and feedback.

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What event? I’d be down to be a part of your math adventure.

We’ll probably try it out at the PinCrossing Summer Classic on Aug 24.

What’s the advantage of this over 1v1 round robin?

TGP!

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5x 4 player games @ 2 TGP = 10 TGP
15x 2 player games @ 1 TGP = 15 TGP?

or is my understanding of TGP even worse than I think?

If you are constrained on games, you would need less physical games per round (5 vs 8).

I would imagine it would take a lot less time to run 5 rounds of four-player games than it would to run 15 rounds of head-to-head, especially if you are waiting for the completion of an entire round before starting the next one.

Yes, it would be 10 TGP vs 15 TGP, but I would also assume your TGP Per Hour (TGPPH?) is going to be higher.

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You gotta trademark that :slight_smile:

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New TD/tourney Efficiency rankings lol

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We use a similar system at the nationals in Australia. The 48 qualifiers are split into three pools of 16 players each. Players each play 5 rounds (with three games per round), and are matched up with each of the other 15 players in their pool exactly once.

This seems a more equitable way of grouping players in a group match play tournament than other available methods, and feedback from competitors has been positive.

After the group match play rounds, the top 5 players from each pool, along with the highest-scoring sixth-placed finisher, advance to head-to-head best-of-5 single elimination finals.

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Neat! I had heard about the pool play on a Head-2-Head episode recently, but didn’t realize it was a very similar format. If I may ask, how do you assign the players to the different rounds? Does qualifying seeding have any affect on placement within which group of 16 they end up in and within the group of 16 itself?

Yes, players are placed in different pools according to their qualifying rank:
Pool A: 1,6,7,12,13,18,19,24,25,30,31,36,37,42,43,48
Pool B: 2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47
Pool C: 3,4,9,10,15,16,21,22,27,28,33,34,39,40,45,46

Players are assigned to the different rounds according to the table you linked to in the original post (the highest seed in a pool is player A, the second-highest is player B, and so on). The rounds are played in the reverse of the order listed.

Players are not given play order choice. Play order is assigned, with an attempt made to equalise the number of times played in each position (though it’s impossible to do this perfectly across 15 games).

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In case it helps, the general problem appears to be known as “The Social Golfer Problem” as described here.

http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html

Here is a computer algorithm (presented in various languages) which produces solutions.

https://www.localsolver.com/docs/last/exampletour/socialgolfer.html#program

This code does not appear to handle taking seeding into account, but perhaps it could be modified to do so.

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