Tricky croquet league schedule

[jimthompson]

Great site btw, very helpful.  My scheduling problem is as follows:

- 10 players
- 12 week season
- play one night per week, 2 matches per night
- every player plays 8 times in a season
- every player plays each other at least once
- each player plays in the early match as often as the late match or close to it.

I'm not sure it can be done, but I think a fair comprimise is to play 4 players in match 1 and 3 players in match 2 each night.  On the last night of the season there would only be a single match of 3 players.  This adds up to 80 match positions for 10 players.  As for how to schedule this to get a good balance, I have no idea!

Thanks.

Jim T.

[Ian Wakeling]

Hi Jim,

This can work as there is a very nice schedule for the first 10 rounds as follows:

    foursome     threesome      bye
  ( 8  2  1  5) ( 7  3  9)    (4  6 10)
  ( 9  3  2  1) ( 8  4 10)    (5  7  6)
  (10  4  3  2) ( 9  5  6)    (1  8  7)
  ( 6  5  4  3) (10  1  7)    (2  9  8)
  ( 7  1  5  4) ( 6  2  8)    (3 10  9)
  ( 2 10  7  6) ( 1  8  3)    (4  5  9)
  ( 3  6  8  7) ( 2  9  4)    (5  1 10)
  ( 4  7  9  8) ( 3 10  5)    (1  2  6)
  ( 5  8 10  9) ( 4  6  1)    (2  3  7)
  ( 1  9  6 10) ( 5  7  2)    (3  4  8)

Notice that each player appears once in each of the first 7 columns, so one player gets 4 foursomes, 3 threesomes and 3 byes.  So one player has (4*3) + (3*2) = 18 opponents over the course of 7 games.  Above the schedule is arranged so that each player plays against all 9 possible opponents exactly twice each.

If you want to play the 8th game then you can choose any assignment of the 10 players to a foursome and two threesomes for the last two nights.  But if you keep score for the first ten weeks, then you could choose to make the 8th game a play off for a prize.

Hope that helps,

Ian.

[jimthompson]

That's great!  Thank you so much Ian.

Cheers,

Jim