McMahon Regular

The McMahon Regular Tournament System is a variant of the standard McMahon Tournament System, where groups are not determined by rank step, but rather have a predetermined size. The players are strictly sorted by rank, rating and other criteria, and then divided into equally sized groups.

Determining Group Size

Although any group size works, it should preferably be a power of two, to postpone as long as possible the necessity to pair players with different scores (pairing up or down). If you do not use a power of two, try to use a multiple of four, to postpone pairing up or down somewhat.

You can determine any appropriate group size based on the number of players. To do this, take twice the number of rounds and find the closest power of two, choosing the lower power of two in case of doubt.

It may be necessary do deviate from these sizes in some cases, such as when you have very few, or very many, participants, or when you expect many latecomers to show up.

Sorting the players

Players should be sorted by predetermined criteria in such a way that no two players are considered exactly equal. Example criteria might be: Rank (dan/kyu) then Rating (EGF/AGA), then lottery.

Once the players have been sorted, they are divided into bands equal to the group size given above. If the total number of players is not a multiple of that size, which is quite likely, then the lowest group will be smaller.

Once players have been divided into bands, record the sorting criteria (rank/rating/lottery) of the weakest member of each group. Those criteria determine the group boundaries in case of latecomers that need to be assigned an initial score

Example

Suppose that you have a 5 round tournament with 56 players. The group sizes will be:

• 8 - 8 - 8 - 8 - 8 - 8 - 8

After the first round, the group sizes will be:

• 4 - 8 - 8 - 8 - 8 - 8 - 8 - 4

After the second round, the group sizes will be:

• 2 - 6 - 8 - 8 - 8 - 8 - 8 - 6 - 2

After the third round, the group sizes will be:

• 1 - 4 - 7 - 8 - 8 - 8 - 8 - 7 - 4 - 1

This is the fist point where it is necessary to pair players up or down. Group size in the middle of the field will continue to be 8 though.

If every player with more points wins those games where players were paird up or down, the sizes after round 4 will be:

• 1 - 2 - 5 - 8 - 8 - 8 - 8 - 8 - 5 - 2 - 1

Other considerations

• In lower groups with a considerable spread in playing strengths, you can use (reduced) handicap based on the player's reported ranks and/or ratings.
• Use a slide pairing in round 1 and 2 to minimize strength differences. Use fold pairings based on SOS in later rounds.

Discussion

willemien: to me it looks like SwissTournament/accelerated pairings only the group size is fixed. (instead of the number of groups)

Herman: Unlike Swiss (with or without accelerated pairings) this system does not start all players on the same number of points. It is pretty much exactly like McMahon, with only a small difference in how group boundaries are determined, really

willemien: you don't mention that in the description (or only as "in case of latecomers that need to be assigned an initial score" and I also think that gives an unfair advantage to the players in the topgroup.

Herman: The first line describes it as a variant on McMahon, that should be enough. Anyway, why promote accelerated pairings on this page?

willemien: I removed the promotion but it has similarities to it. But I still have my objections. for the players in the top group winning is unfairly easier than the ones in lower groups.

Herman: The reason behind this system is to avoid pairing players up or down as much as possible. With accelerated pairings, you pair players up and down by design, so I would say that this system is less similar to it than regular McMahon. With accelerated pairings, the weaker players have the same chance of winning as with McMahon variants, i.e. none at all. With McMahon, at least they have fun games.