PDL - A fixture suggestion - replies wanted

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Re: PDL - A fixture suggestion - replies wanted

Postby AKFD » 24 Jun 2019, 08:21

The SHIV wrote:And like I said before, look to the Classicistististissss.........plenty of players there, supposedly reliable, and like to play so they say. Make it a "Classicistististissssss only tourney. "King of the Classicistsistsistsisssss".

And if they surrender, auto ban from the club.

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Re: PDL - A fixture suggestion - replies wanted

Postby mjparrett » 24 Jun 2019, 11:47

Sorry for my negative outlook! The problem with this (and lets be honest this could easily be applied to our real life politics) is that the vote turnout is shit, then everyone moans at the decisions that are made! This is the chance for people to have a say so the tournament is as enjoyable as possible.

I think the 4 game structure would work well (I could maybe step up to 5 rounds but everyone only plays 4 etc), as that seems to be what most people could stomach. I might start a separate thread, but essentially I'm calling all mathematicians here - I want a set of fixtures that keeps things fresh - means everyone plays all their league compadres at least once and preferably never thrice.

As for classicist only... tempting, but I don't want to make it too restrictive. How many active classicists are there? I know 1 or 2 surrenders were classicists first time round but they were generally strange circumstances and I'm prepared to give them the benefit of the doubt. Ambassador only? Although having said that you can become a bronze classicist about as easily as an ambassador, although perhaps a lot of people don't know about the 'club' or bother themselves applying. At least the diplomat/ambassador title is site driven and could be used to sort things? And with a potential start date of January 2020 there is enough time for people to attain ambassador status if they want (exceptions will be made for new members to the site I think - as I said I want to encourage new players as well as pampering to the old!)

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Re: PDL - A fixture suggestion - replies wanted

Postby jay65536 » 24 Jun 2019, 15:56

mjparrett wrote:I think the 4 game structure would work well (I could maybe step up to 5 rounds but everyone only plays 4 etc), as that seems to be what most people could stomach. I might start a separate thread, but essentially I'm calling all mathematicians here - I want a set of fixtures that keeps things fresh - means everyone plays all their league compadres at least once and preferably never thrice.


Mathematician here.

I think I remember trying to help with this the first time you were setting up fixtures, but I think you have to bend one way or another on these preferences given your parameters. Let me see if I can explain why without getting myself too far into the weeds here:

1) You want everyone to play 4 rounds at most. The number of different people it is possible to play in 4 rounds is 4*6 = 24, so the maximum league size you're looking at is either 21 if you don't use off rounds, or 25 if you do. But having more than 21 and giving people rounds off doesn't work out from a numbers standpoint, because the total number of slots you're looking at for the rounds off is 5*4 = 20, fewer than the number of people in the league. (Also, the fact that 7 is prime really works against the idea of cycling through off rounds.) The upshot is, if you want everyone to play each other at least once, you're looking at exactly 21 people in the league, unless you want to lower it to 14, which doesn't seem like what you want.

2) As I think you found the first time, when you have 21 people in a league, and 4 rounds (the minimum for everyone to play each other once, since 6*3 = 18 < 20), combinatorially you will have to have people who play each other 3 times.

Essentially I think that given what you wanted, your fixtures the first time were about as good as you could have had them.
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Re: PDL - A fixture suggestion - replies wanted

Postby Custer » 24 Jun 2019, 16:35

All excellent points MJ.

So is it any combo of 7 then? How bout 28? Or 35?

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Re: PDL - A fixture suggestion - replies wanted

Postby mjparrett » 24 Jun 2019, 17:58

I'm not set on 21 by any means.

3 games each would possibly work, as would 5. People don't seem to want more than 5, and less than 3 detracts from it being a league and the best player winning.

Maybe what I had was close to as good as it could be, but I can't help but feel there is a (slightly) better solution.
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Re: PDL - A fixture suggestion - replies wanted

Postby V » 24 Jun 2019, 19:02

jay65536 wrote:
mjparrett wrote:I think the 4 game structure would work well (I could maybe step up to 5 rounds but everyone only plays 4 etc), as that seems to be what most people could stomach. I might start a separate thread, but essentially I'm calling all mathematicians here - I want a set of fixtures that keeps things fresh - means everyone plays all their league compadres at least once and preferably never thrice.


Mathematician here.

I think I remember trying to help with this the first time you were setting up fixtures, but I think you have to bend one way or another on these preferences given your parameters. Let me see if I can explain why without getting myself too far into the weeds here:

1) You want everyone to play 4 rounds at most. The number of different people it is possible to play in 4 rounds is 4*6 = 24, so the maximum league size you're looking at is either 21 if you don't use off rounds, or 25 if you do. But having more than 21 and giving people rounds off doesn't work out from a numbers standpoint, because the total number of slots you're looking at for the rounds off is 5*4 = 20, fewer than the number of people in the league. (Also, the fact that 7 is prime really works against the idea of cycling through off rounds.) The upshot is, if you want everyone to play each other at least once, you're looking at exactly 21 people in the league, unless you want to lower it to 14, which doesn't seem like what you want.

2) As I think you found the first time, when you have 21 people in a league, and 4 rounds (the minimum for everyone to play each other once, since 6*3 = 18 < 20), combinatorially you will have to have people who play each other 3 times.

Essentially I think that given what you wanted, your fixtures the first time were about as good as you could have had them.



I knew we had mathematicians on PlayDip. Remarkably valuable folks. Good job someone was paying attention, when that guy started droning on & on, during the morning lecture on statistics (or similarly dull subject:-)
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Re: PDL - A fixture suggestion - replies wanted

Postby Woolgie » 24 Jun 2019, 21:24

Jay65536 speaks the truth.

This is a variant of the social golfer algorithm/conundrum. There are three variables:

N number of players in the group
P number of players in a game
R the number of rounds everyone must play

P is 7 (unless we have sit out rounds).

If R = 4 and N = 21 then to allow everyone to play once there is a pair that will have to play together in all four games.

I stated previously the best case scenario for R =4, N = 21 whereby most people you play once, some you play twice and some you don’t play. But at least you don’t play anyone three times. I believe this is the option we must pursue.

More generally, and if the above is not satisfactory, we must pin down some of the parameters if we are to select a programme. There is no generalised solution to the social golfer (only trial and error and semi-solutions) and multi-dimensional equations are difficult.
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Re: PDL - A fixture suggestion - replies wanted

Postby Custer » 25 Jun 2019, 00:01

How bout:

R=5
P=7
N=28

Then what happens oh great wise one?

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Re: PDL - A fixture suggestion - replies wanted

Postby V » 25 Jun 2019, 15:04

“I stated previously the best case scenario for R =4, N = 21 whereby most people you play once, some you play twice and some you don’t play. But at least you don’t play anyone three times. I believe this is the option we must pursue.“

Agreed on this approach. Playing someone 3 times in 4 games would be worse than missing some folks that particular season. Knew there was a reason I never played Golf. Too much mathematics:-)
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Re: PDL - A fixture suggestion - replies wanted

Postby mjparrett » 25 Jun 2019, 16:42

I think in PDL1 there were a few 3 timers? But that was probably just me not getting the optimum fixtures.

If Woolgie or Jay can send me how the fixtures would look based on the 21 player, 4 game season with no triples then I think we'll go with that.
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