Round Robin Tournaments

[cmeld15]

I'm trying to start a round robin tournament with 14-20 teams. The thing is there is only 8 events. Each team needs to play every event only once without playing the same team twice. How can I get the teams to be completely random without doing the normal round robin setup?

[Ian Wakeling]

I am not certain what you mean by "completely random".  How about this if there were 16 teams A to P?

(N B) (I G) (A P) (H K) (F J) (M O) (D E) (L C)
(M J) (F O) (D K) (L P) (I B) (N G) (A C) (H E)
(L G) (A B) (I C) (M E) (D O) (H J) (F K) (N P)
(A E) (L K) (N O) (F G) (H C) (D P) (M B) (I J)
(D C) (H P) (M G) (I O) (L E) (A K) (N J) (F B)
(I K) (N E) (L J) (D B) (M P) (F C) (H G) (A O)
(H O) (D J) (F E) (N C) (A G) (L B) (I P) (M K)
(F P) (M C) (H B) (A J) (N K) (I E) (L O) (D G)

[cmeld15]

I just didn't want the typical set up of 1vs16, 2vs15, 3vs14,... and so on. I would like the matchups to be jumbled up. I'm not sure how many teams I'm going to have but I would assume between 14 and 20. would it be too difficult to come up with that many different possibilities? If so, that's ok.

[Ian Wakeling]

The only other scenario that works well, that is also within the range specified, is for 14 teams.

(B M) (G F) (D I) (L C) (J N) (---) (A E) (H K)
(D E) (A M) (B N) (H F) (---) (I K) (G C) (J L)
(L F) (I C) (G K) (B E) (A H) (D N) (J M) (---)
(A K) (---) (J C) (G N) (B F) (H M) (L D) (I E)
(H C) (J E) (---) (D M) (L K) (B G) (I F) (A N)
(G J) (D K) (A F) (---) (I M) (L E) (H N) (B C)
(I N) (H B) (L M) (J K) (G E) (A C) (---) (D F)
(---) (L N) (H E) (I A) (D C) (J F) (B K) (G M)

If there are more than 16 teams then things are going to become more complicated with people sitting out each round.  Is there any flexibility in the number of events?  With 10 events for example there are similar square schedules for 14, 16, 18 or 20 teams.

[cmeld15]

It doesn't need to be even. I just need to make sure every team plays in all the events and never plays the same team twice. I can't edit the amount of events.

[Ian Wakeling]

You can deal with 18 teams by taking this square:

(H N) (D I) (C R) (M E) (A F) (P G) (L O) (Q J) (B K)
(A E) (C K) (H G) (L F) (Q O) (M N) (D J) (B I) (P R)
(Q F) (H R) (A N) (D O) (B J) (L E) (C I) (P K) (M G)
(M I) (B E) (P O) (A K) (L R) (H J) (Q G) (D N) (C F)
(P J) (Q N) (B F) (H I) (M K) (C O) (A R) (L G) (D E)
(B O) (A G) (Q E) (C J) (P I) (D F) (H K) (M R) (L N)
(L K) (P F) (M J) (Q R) (D G) (A I) (B N) (C E) (H O)
(D R) (M O) (L I) (B G) (C N) (Q K) (P E) (H F) (A J)
(C G) (L J) (D K) (P N) (H E) (B R) (M F) (A O) (Q I)

If the 9 columns are the events then simply assign the final column to be a 'bye event' where people sit out.  Similarly for 20 teams take this square:

(C Q) (H I) (O T) (L K) (S R) (M G) (J A) (F D) (E P) (B N)
(O G) (E A) (C D) (S I) (B P) (F Q) (M N) (L T) (H K) (J R)
(H D) (C K) (E G) (J T) (M I) (L N) (B R) (S Q) (F A) (O P)
(F P) (S G) (L R) (H A) (J Q) (O K) (E T) (C N) (B I) (M D)
(B T) (O R) (J I) (E D) (F G) (H P) (L Q) (M K) (S N) (C A)
(J K) (B D) (M A) (F R) (H N) (S T) (C P) (E I) (O Q) (L G)
(L I) (J N) (S P) (C G) (O D) (B A) (F K) (H R) (M T) (E Q)
(S A) (M Q) (B K) (O N) (C T) (E R) (H G) (J P) (L D) (F I)
(E N) (F T) (H Q) (M P) (L A) (J D) (O I) (B G) (C R) (S K)
(M R) (L P) (F N) (B Q) (E K) (C I) (S D) (O A) (J G) (H T)

and assign the last two columns to be 'bye events'.  I think that's where I run out of advice, as I don't have any software that might handle an odd number of teams.

[cmeld15]

Ok that makes perfect sense...thanks!