round robin for 22 competitors, 7-11 in a race

[skyywalker]

Hi there,

I need help again please for a trial event for the 2024 olympic sailing competition.

We have 22 competitors and as it is a test it does not have to be a perfect round robin, but of course the more fair it is the better...

We need to split the 22 competitors in races of something between 7 and 11 in a race (the less the better), and rotate them so that they sail as much as possible against all other competitors

We have limited time for this test, so if we get them somehow sailing against each other (even if not same amount of racing for a complete schedule) then it is fine.

Can anyone help please ? I need it for Wednesday...

Thanks a lot in advance !

Cheers,
Markus

[Ian Wakeling]

Hi Markus,

How many races are possible in the limited time?  Of course mathematically speaking, the more the better...

Ian

[skyywalker]

12-16 in an afternoon session, 8 or so more if we take the morning as well... (which means getting up VERY early  )

[Ian Wakeling]

This is a little smaller than you are asking for, but I think it may work (11 rounds/rows,  10 competitors per race).

Code: [Select]

  21 17  4 19 12  8  5  3 11 22
  22 18  5 20 13  9  6  4  1 12
  12 19  6 21 14 10  7  5  2 13
  13 20  7 22 15 11  8  6  3 14
  14 21  8 12 16  1  9  7  4 15
  15 22  9 13 17  2 10  8  5 16
  16 12 10 14 18  3 11  9  6 17
  17 13 11 15 19  4  1 10  7 18
  18 14  1 16 20  5  2 11  8 19
  19 15  2 17 21  6  3  1  9 20
  20 16  3 18 22  7  4  2 10 21

This gives exactly 5 races per competitor and everyone does compete together at least once and at most 3 times.  I could make something with 22 races which would be better mathematically, but that would mean an extra 6 in the morning.

Ian

[skyywalker]

Hi Ian,

cool - I will play a bit around with it.

Could you save it as an xls by chance in this thread ?

Cheers,
Markus

[Ian Wakeling]

xls is attached

[skyywalker]

Hi there,

I have looked at it and some competitors need to compete in 4 races after each other or so... is there a chance to spread it out a bit more ? Even with a different number of competitors in a race ?

Otherwise I go with that and need to have some breaks between the races.

Cheers,
Markus

[Ian Wakeling]

I can't find anything better - in all the schedules this size I have looked at, there are always 4 common boats in any two races - this makes runs of 3 races in a row quite likely.  All you can do is identify the longest runs of 4 and try to reorder the rounds to avoid them.

If I consider 8 boats per race, and 11 races, then there are always some pairs of competitors who do not race together.

Best,

Ian