16 team round robin with 8 different games. No repeating match-ups or games.

[things]

I'm trying to set up a round robin with 16 teams and 8 different games. I want there to be 8 rounds so that every team plays each game once, and no repeating of team match-ups.

With 16 teams, each team as a possible 15 different match-ups but I only need 8 and I'm still having trouble either having no team repeat a game or no teams repeat a match-up.

I tried using the circle method with 1 fixed team. I have to move the fixed team down a row every time though to make sure they are playing a different game but I'm get repeated match-ups this way.

I have attached my excel sheet if anyone can take a look and tell me why I am being dumb here.

If there's a way to automate this based on a given number of teams and games, that would be cool but I'd settle for figuring out why I can't even do this exact number of teams and games manually right now.

[Ian Wakeling]

The problem is hard to solve and there is no cyclic algorithm that will work for all choices of the number of teams.

If you look at this message thread the 1st schedule in Reply #5 should do what you want.  You can take either the 1st 8 rows, or the last 8 rows. 

[things]

Oh boy, so more complicated than I thought and that 16 team one just happened to work perfectly for my exact scenario.

Now looking at your other posts in that thread...

With the criteria of:
Players/teams playing each game once
Players not repeating any match-ups

Should any of these scenarios come into play I could use your tables to have:
5 games and any multiple of 10 players
6 games with any multiple of 12 players
7 games with any multiple of 14 players
8 games with any multiple of 16 players
10 games with any multiple of 20 players

Right?

And as far as partitioned balanced tournament design, if I am understanding correctly, one variable will have no repeats while the other will have some repeats, correct?

So I could technically have a tournament with any number of games with the number of participants being a multiple of the number of games and the players would never repeat a game (or all players play each game twice, etc) but repeat some match-ups, or am I off on this part? Do you know of a source that can automate something like that? I looked at your spreadsheet but if I understand this correctly, the "court" would be the games in my scenario but your spreadsheet chooses the number of courts automatically.

[Ian Wakeling]

I linked to the PBTD schedule because I knew where to find it, and it solves your problem.  But as you only need half of the schedule, it is overkill because it is a simpler problem to make just half the schedule - although even that can not be generalized with one algorithm that fits all!

The PBTD is just a special case of the court balanced schedules (for even n) from my spreasheet, both have each player once or twice in the columns, and exactly once in the rows.  In order to meet the latter property the number of courts is always n/2. I do mean "court" in the same sense that you are using "game".

It is possible to generalize to scenarios with n/2 courts or more. For example see here for 12 teams and 10 courts.  Reply #4 in that thread has a spreadsheet that constructs some more using a diagonally cyclic approach, including some n/2 schedules for 10, 14, 18 and 22 players.

You mentioned multiples of n players, I only see that this works if the players are split into equal sized groups and there is a separate schedule for each group.

Hope that helps.

[things]

You mentioned multiples of n players, I only see that this works if the players are split into equal sized groups and there is a separate schedule for each group.

Yea, I didn't word that well. I meant say I if have 32 teams and 8 games I could just break it into two groups of 16 and use the top 8 or bottom 8 lines in your ready made table per group. That ensures all 32 teams play each game once and never repeat an opponent. And I could use the other tables you have in that thread with the other number of games.

The goal I have is to always have each team play each game once and never repeat a match-up so I was thinking out loud that I could use your already made tables since doing it manually seems to be above my level. But to use your tables, the number of teams would always have to double the number of games to start and then the number of teams would have to double from there on, right?

So what I meant is that if I have 5 games I want to play I could set it up with either
10 teams
20 teams
30 teams
etc
and then just break it into groups of 10 and use your table for 10 teams to make sure no one repeats anything



I'm probably confusing myself at this point but basically what I am getting at is if I wanted to have a little tournament with say:

20 teams
8 games
Each team plays each game once so 8 rounds total
Each team does not repeat a matchup

there is nothing that would spit that out for me, I would need to do it manually, correct? Or have I gone and confused myself?