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91

Requests / Re: Round Robin - 8 Player Doubles

« Last post by tkam on January 17, 2024, 06:57:58 PM »

Ian, thanks a lot, that’s fantastic!

Could we tweak the schedule to ensure the games are closely matched in terms of skill? Ideally, we want each team to have a similar aggregate skill level, so that player 12, being the strongest through to player 1, being the least skilled, are distributed in a way that makes each game competitive and balanced.

I've approached this by assigning each player a numerical ranking, with the top player receiving 12 points and the lowest-ranked player receiving 1 point. I then added up the points for each team in a game and determined the absolute difference in points between the teams. This value indicates the level of skill balance for each game; a lower total signifies a more evenly matched setup. My best attempt is the below which maintains the structure you provided but with player numbers swapped around. This leads to an overall total of 132. Is it possible to arrange the players to achieve an even more balanced total?

6  1  2  5
6  2  1  5
7  4  8  3
7  8  4  3
9  11  10  12
9  12  11  10
1  11  12  3
1  12  11  3
10  2  8  4
10  8  2  4
9  5  7  6
9  7  6  5
11  7  5  4
11  5  7  4
6  12  2  8
6  8  12  2
9  10  1  3
9  3  10  1
7  10  3  2
7  3  10  2
1  5  8  12
1  8  5  12
9  6  11  4
9  4  6  11
10  6  4  12
10  4  6  12
11  3  8  5
11  8  3  5
9  2  1  7
9  1  7  2

92

Requests / Re: Round Robin - 8 Player Doubles

« Last post by Ian Wakeling on January 17, 2024, 12:34:57 PM »

Hi Tej,

Here is my schedule which has 11 pairs who never partner, and opposition pairs that vary from zero to 4.


 2  3  8 10
 2  8  3 10
 5  7 12  6
 5 12  7  6
11  4  1  9
11  9  4  1
 3  4  9  6
 3  9  4  6
 1  8 12  7
 1 12  8  7
11 10  5  2
11  5  2 10
 4  5 10  7
 4 10  5  7
 2  9  8 12
 2 12  9  8
11  1  3  6
11  6  1  3
 5  1  6  8
 5  6  1  8
 3 10 12  9
 3 12 10  9
11  2  4  7
11  7  2  4
 1  2  7  9
 1  7  2  9
 4  6 12 10
 4 12  6 10
11  8  3  5
11  3  5  8


My version of your two symmetric matrices are immediately below (partners and opponents counts), followed by the sum of the two matrices.  I have put zeroes down the main diagonals.

 0  1  1  1  1  0  1  2  1  0  1  1
 1  0  1  1  1  0  0  1  2  1  1  1
 1  1  0  1  1  1  0  0  1  2  1  1
 1  1  1  0  1  2  1  0  0  1  1  1
 1  1  1  1  0  1  2  1  0  0  1  1
 0  0  1  2  1  0  1  1  1  1  1  1
 1  0  0  1  2  1  0  1  1  1  1  1
 2  1  0  0  1  1  1  0  1  1  1  1
 1  2  1  0  0  1  1  1  0  1  1  1
 0  1  2  1  0  1  1  1  1  0  1  1
 1  1  1  1  1  1  1  1  1  1  0  0
 1  1  1  1  1  1  1  1  1  1  0  0

 0  1  1  1  1  4  3  2  3  0  3  1
 1  0  1  1  1  0  4  3  2  3  3  1
 1  1  0  1  1  3  0  4  3  2  3  1
 1  1  1  0  1  2  3  0  4  3  3  1
 1  1  1  1  0  3  2  3  0  4  3  1
 4  0  3  2  3  0  1  1  1  1  1  3
 3  4  0  3  2  1  0  1  1  1  1  3
 2  3  4  0  3  1  1  0  1  1  1  3
 3  2  3  4  0  1  1  1  0  1  1  3
 0  3  2  3  4  1  1  1  1  0  1  3
 3  3  3  3  3  1  1  1  1  1  0  0
 1  1  1  1  1  3  3  3  3  3  0  0

 0  2  2  2  2  4  4  4  4  0  4  2
 2  0  2  2  2  0  4  4  4  4  4  2
 2  2  0  2  2  4  0  4  4  4  4  2
 2  2  2  0  2  4  4  0  4  4  4  2
 2  2  2  2  0  4  4  4  0  4  4  2
 4  0  4  4  4  0  2  2  2  2  2  4
 4  4  0  4  4  2  0  2  2  2  2  4
 4  4  4  0  4  2  2  0  2  2  2  4
 4  4  4  4  0  2  2  2  0  2  2  4
 0  4  4  4  4  2  2  2  2  0  2  4
 4  4  4  4  4  2  2  2  2  2  0  0
 2  2  2  2  2  4  4  4  4  4  0  0

Note that the 12 players fall into two distinct groups with different patterns of partners and opponents (Group A = 1-5 & 12, Group B = 6-11).  Finally note that there are 6 pairs of players who never meet either as partners or as opponents.  Hope that makes some sense.

93

Requests / Re: Round Robin - 8 Player Doubles

« Last post by tkam on January 17, 2024, 04:52:16 AM »

Thanks for having a look Ian.

Actually your 10-11 pair gap and 0 to 4 against is much better than what i've discovered already. Would you mind sharing that?

Otherwise, what is the most evenly distributed possible schedule if the partner with everyone requirement is relaxed?

Currently, the best i've been able to get is the below, where partnering with is max 2, min 0 and playing against is more extreme with max 10, min 0 (it seems you have already got one a lot better than this).

Ultimately i'm happy with any schedule which ends up smoothing out the extremes and results in the same ratios for everyone for both WITH and AGAINST, albeit with instances of zero partnering occurrences...

94

Requests / Re: Round Robin - 8 Player Doubles

« Last post by Ian Wakeling on January 16, 2024, 05:49:38 PM »

I believe the partnering-with-everyone-once-with-the-exception-of-one-person part is not possible - at least I can't find a schedule like this - as I end up with 10 or 11 pairs who don't partner.   Then the opponent balance is terrible, it varies from zero times per pair to 4 times per pair.  You would be far better advised to pick a different format.

95

Requests / Re: Tournament 5 players , 2 games

« Last post by Ian Wakeling on January 16, 2024, 05:42:08 PM »

I think you can use the standard round robin twice and just swap around the games associated with each column.  For example:

Rounds 1-5
 Fifa  Darts
(1 4) (2 3)
(3 5) (1 2)
(2 4) (1 5)
(1 3) (4 5)
(2 5) (3 4)

Rounds 6-10
Darts  Fifa
(1 4) (2 3)
(3 5) (1 2)
(2 4) (1 5)
(1 3) (4 5)
(2 5) (3 4)

96

Requests / Tournament 5 players , 2 games

« Last post by Khayzr on January 15, 2024, 06:15:16 PM »

I want to organize a Fifa and darts tournament with 5 players.
Everyone plays against everyone on both games 
And every Round we have 1 person who has no game. (Because of the odd number of players)
So we have 2 games and 5 players 
I cant seem to figure this out..

97

Requests / Re: Round Robin - 8 Player Doubles

« Last post by tkam on January 15, 2024, 03:02:53 PM »

Sorry, I should have clarified.

- 10 games per person

- playing with: partnering with everyone one once only, with the exception of 1 person

- playing against: as balanced as is possible given the above constraints

Everything else as before i.e. 2 games before a court change.

98

Requests / Re: Round Robin - 8 Player Doubles

« Last post by Ian Wakeling on January 15, 2024, 12:54:50 PM »

Hi Tej,

12 is not a nice number!  I have thought about it, with this format of play, I think each player has to play 16 games in order to have all partners at least once, and all opponents at least twice.  Is that too many games?  If so how many were your thinking of?

99

Requests / Re: PBTDs for 24 & 28 teams

« Last post by Innesw20 on January 15, 2024, 07:14:35 AM »

Thanks Ian, that was precisely what I was after.

100

Requests / Re: Round Robin - 8 Player Doubles

« Last post by tkam on January 14, 2024, 06:20:33 PM »

Hi Ian,

Following on from the 2 court solution you helped me with above, please could you help me with an optimal round robin structure for 3 courts, 12 players, with the exact same requirements as before?