How do I schedule 12 teams in a championship where 3-4 teams play at the same time in a round, while allowing 1 loss to still be the champion?

Question

I have a game where there are 12 teams. One round is where 3-4 teams play at the same time and only one team wins. I'm looking for how to put a schedule for all the rounds needed to determine the champion team.

Example: Let's say I have teams A-L (12 teams): First round teams A-D play, let's say team A wins. That would be 1 round, 1 winner. So I would need 3 rounds to get 3 winning teams, then a final round where the 3 winning teams play.

But I'm looking for a more "fair" way of getting a champ where teams could have a loss and still be the champ. And I can't figure out how to schedule the rounds to do that in a 12 team competition where 3-4 teams play at the same time in a round.

Answer 1

This is almost exactly how Vampire the Eternal Struggle, the TCG plays its tournaments, although they prefer players per "table". In this page vekn.net/downloads you can download "the Archon v1.5e", which is a generator for this sort of tournament.

In this case round 1 would be three games:

A,B,C,D in first
E,F,G,H in second
I,J,K,L in the third

Round 2:

A,E,F,I in first game
C,H,J,K in second
B,D,G,L in third 

Round 3:

A,B,H,I in first game
D,E,G,K in second
C,F,J,L in third 

Everybody does not play everybody, but using scores from these games you can get to final.

Answer 2

It seems that rankade, our ranking system for sports, games, and more, fits your needs.

It's free to use and it's designed to manage rankings (and stats, including matchup stats, and more) for small or large groups of players/teams.

Its algorithm (called ree algorithm), although more complex (here's a comparison), is similar to most-known Elo if you play 1-on-1 matches only, but - opposite to Elo - it can manage 3+ teams/players per match, as per your needs, allowing both all losers tied results or detailed standings.

You can schedule matches using ranking after previous turns to optimize teams sorting (lowering the number of turns needed to getting a champ), or play random matches for longer time, seeking for an optimal skill based ranking.

We host many 3+ factions games groups/clubs (boardgames, shooting sports, races, and more), as well as other sports/games ones. Here's our dojo.

Answer 3

I do not know what sport are you talking about so it is difficult to reply. Maybe you can use a swiss-system with variations.

I use it for curling tournaments and work in this way (for 12 teams):

1. draw for the first 6 matches (first round);
2. rankings after first round;
3. second round determined by rankings (1vs2, 3vs4, 5vs6, 7vs8, 9vs10, 11vs12)
4. rankings after second round;
5. third round determined by updated rankings (1vs2, 3vs4, 5vs6, 7vs8, 9vs10, 11vs12)

For your need maybe you can:

1. draw for the first 3 "matches" (first round) for 4 team per match;
2. rankings after first round (in every single mathc you can find the first but I do not know if is it posssible to determine a second/third/fourth classified);
3. second round determined by rankings (1vs2vs3vs4, 5vs6vs7vs8, 9vs10vs11vs12)
4. rankings after second round;
5. third round determined by updated rankings (1vs2vs3vs4, 5vs6vs7vs8, 9vs10vs11vs12)

You can go on with many round as you need then make the last final round for the first 4 teams: 1vs2vs3vs4

After the first few rounds this method guarantees matches between teams of similar level and you can a number of mathces as you need at the same time.

There are also a lot of variants (for example to avoid matches with the same teams..) you can check on wikipedia link