Round Robin Tournament Scheduling

### 10 tennis players, 2 courts, 26 rounds

Offtopic · 20 · 13254

#### Offtopic

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on: September 25, 2016, 11:55:44 AM
I have a similar request as "8 players, 2 courts, about 36 weeks"

I have tried several round robin based distributions without optimal results.

Pre-requisites:
* 4 Players per round
* 26 rounds available
* 10 players
* 2 courts for 2 singles
* 1 court for 1 double
* A round consists of 2 singles and one double

So each player can play 10 or 11 times.  Each player should play at least one time against each other and there should be no double with same players (like screenshot).

I meet above conditions except that some players play never against each other (eg. A vs. D)
« Last Edit: September 25, 2016, 11:56:41 AM by Offtopic »

#### Ian Wakeling

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Reply #1 on: September 26, 2016, 03:42:44 AM
Do you mean that after the two singles games in a round, the same pairs that opposed each other in the singles, then partner each other in a doubles game?

As 10 players is not divisible by 4,  then there will always be imbalance, and it will be hard to find good schedules.  What happens if you try your search method with 22 rounds?  This gives 44 out of the possible 45 singles games, and would be the closest you will be able to get to balanced singles.  You may get a better schedule if you do this first, and then add a final 4 rounds to try to make up for any exceptions like A vs D.

#### Mary_Jo_Youngblood

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Reply #2 on: September 26, 2016, 10:07:49 AM
I need schedule for 10 players, 2 courts,  4 on a court, for 33 weeks. 2 players will be off each week. No singles...

#### Ian Wakeling

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Reply #3 on: September 27, 2016, 03:15:10 AM
I think the schedule below will be about the best possible.   I have not checked this in detail, but the way I constructed it, I believe players ABCFGH should all have 26 games while DEIJ should have 27 games.   Most pairs of players should partner 3 times, and oppose 6 times, however the three pairs AF, BG & CH will only partner twice and only oppose 4 times.   Finally, I think no player will have 2 byes in a row.

(C J v F H)  (B G v A I)
(D I v C G)  (B J v E H)
(C I v A E)  (D F v B H)
(G I v F J)  (C E v A B)
(A J v D E)  (H I v C F)
(G J v B C)  (D H v E I)
(B F v C D)  (H J v A G)
(F I v E J)  (G H v A D)
(B D v I J)  (E G v C H)
(B I v A H)  (D G v E F)
(F G v B E)  (D J v A C)

(D F v G I)  (C H v B J)
(E J v D H)  (C F v A I)
(D J v B A)  (E G v C I)
(H J v G F)  (D A v B C)
(B F v E A)  (I J v D G)
(H F v C D)  (E I v A J)
(C G v D E)  (I F v B H)
(G J v A F)  (H I v B E)
(C E v J F)  (A H v D I)
(C J v B I)  (E H v A G)
(G H v C A)  (E F v B D)

(E G v H J)  (D I v C F)
(A F v E I)  (D G v B J)
(E F v C B)  (A H v D J)
(I F v H G)  (E B v C D)
(C G v A B)  (J F v E H)
(I G v D E)  (A J v B F)
(D H v E A)  (J G v C I)
(H F v B G)  (I J v C A)
(D A v F G)  (B I v E J)
(D F v C J)  (A I v B H)
(H I v D B)  (A G v C E)

#### Offtopic

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Reply #4 on: September 28, 2016, 12:46:08 AM
Thanks for your efforts, I think I got it:

01      (F I)      (J G)
02      (A G)      (F H)
03      (D B)      (E I)
04      (C F)      (B A)
05      (J D)      (C E)
06      (H C)      (A J)
07      (H B)      (F G)
08      (E J)      (I D)
09      (F J)      (H A)
10      (A E)      (B C)
11      (G D)      (J I)
12      (C A)      (E J)
13      (B F)      (G H)
14      (I H)      (G B)
15      (B E)      (D C)
16      (D A)      (C J)
17      (C I)      (E D)
18      (J H)      (A F)
19      (D H)      (I G)
20      (B J)      (F I)
21      (F D)      (A G)
22      (E G)      (I B)
23      (A I)      (H C)
24      (G C)      (J D)
25      (E F)      (I H)
26      (H E)      (D B)

# of possible games:      52
Round Robin has 45 unique rounds

Rounds with unique players      38
Rounds with played twice      7
38 + 7*2 = 52
« Last Edit: September 28, 2016, 12:49:52 AM by Offtopic »

#### Offtopic

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Reply #5 on: September 28, 2016, 12:48:14 AM
Quote
Do you mean that after the two singles games in a round, the same pairs that opposed each other in the singles, then partner each other in a doubles game?

Yes that's the plan, see my plan above

#### Offtopic

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Reply #6 on: September 28, 2016, 12:55:11 AM
Attached the whole plan with dummy player names and some macros/conditional formatting for highlighted player

Sorry for mixing up english and german

#### Ian Wakeling

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Reply #7 on: September 28, 2016, 08:36:06 AM
I don't think you are taking the doubles opposition pairs into account.  For example, consider player C who will play against player A 5 times, but will never play against F, G and H.   It may be better to use my 33 row schedule above.   Consider playing the 26 doubles games from rows 1 to 11,  row 13 and row 19.  An for the singles games divide each doubles game in two.
« Last Edit: September 28, 2016, 08:38:37 AM by Ian »

#### Offtopic

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Reply #8 on: September 29, 2016, 02:00:42 AM
new_schedule is now with better double distribution but not perfect (the last two columns has a count for all player pairs (some play 3 times in doubles against each other, some other never)

#### Offtopic

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Reply #9 on: September 29, 2016, 02:03:43 AM
Quote
I don't think you are taking the doubles opposition pairs into account.  For example, consider player C who will play against player A 5 times, but will never play against F, G and H.   It may be better to use my 33 row schedule above.   Consider playing the 26 doubles games from rows 1 to 11,  row 13 and row 19.  An for the singles games divide each doubles game in two.

I used also your plan as explained, unfortunately player A has only 8 games (double distribution looks very good -> count of 39 vs 54, single distribution is the same: 52)
I also want to consider that all players have not to long waiting times.
As highlighted in the screenshot player H plays in the first round (10th oct) and the next time 9 weeks(!) later, in Februrary he plays every week - it's really  annoying to generate such a plan

#### Ian Wakeling

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Reply #10 on: September 29, 2016, 02:56:07 AM
I think you have miscounted the rows,  I was suggesting you use rows 13 and 19 taken from the 2nd block of 11:

13 (E J v D H)  (C F v A I)
19 (G J v A F)  (H I v B E)

Both these rounds involve A and F and should improve the balance for the number of games.

Rather than playing all the games from the left column, and then all the games from the right column, I suggest you alternate left. right, left, right, left, etc., this should improve the wait times.
« Last Edit: September 29, 2016, 03:01:18 AM by Ian »

#### Offtopic

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Reply #11 on: September 29, 2016, 03:09:06 AM
Quote
I think you have miscounted the rows,  I was suggesting you use rows 13 and 19 taken from the 2nd block of 11:

13 (E J v D H)  (C F v A I)
19 (G J v A F)  (H I v B E)

Both these rounds involve A and F and should improve the balance for the number of games.

Oh, I used the line number from editor and counted also the spacing line (my fault)

Quote
Rather than playing all the games from the left column, and then all the games from the right column, I suggest you alternate left. right, left, right, left, etc., this should improve the wait times.

You are my hero now it's perfect for me, no longer waits than 4 rounds! Where should I send a create of beer

Many thanks Ian!

#### Offtopic

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• Posts: 8
Reply #12 on: September 29, 2016, 04:00:04 AM
Quote
I don't think you are taking the doubles opposition pairs into account.  For example, consider player C who will play against player A 5 times, but will never play against F, G and H.   It may be better to use my 33 row schedule above.   Consider playing the 26 doubles games from rows 1 to 11,  row 13 and row 19.  An for the singles games divide each doubles game in two.

1) how did you generate the 33 schedule rows
2) why do you (I) know, to use the rows from 1 to 11 AND row 13 and 19?

#### Ian Wakeling

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Reply #13 on: September 29, 2016, 06:29:00 AM
Here is what I did.  I took 44 player pairs, that's all possible pairs from A to J except the pair AF, and used a computer search program to arrange them as an 11 round schedule on 2 courts. The objective of the computer search is to get the best possible doubles opponent balance, and what it finds is a schedule with a 'hole', where A&F do not partner and do not oppose, otherwise it is balanced.

The next two blocks of 11 rounds are simply permutations of the first 11 rounds.  For the 2nd block I transformed  (ABCDEFGHIJ) to (BCDEAGHIJF).  Which means that the missing pairing is now B&G rather than A&F.

So the reason for choosing rows 13 and 19 should now be clear, as these rows have the missing AF partnership and a missing AF opponent pairing.

#### Offtopic

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Reply #14 on: September 29, 2017, 10:43:24 AM
Ian you helped me very much last year!

Unfortunately this year I need the same plan but only for 9 players (instead of 10)
To you have again such a cool table?