Diagonal Tournament Format.

The Diagonal Tournament Format was developed on this site based on the tournament experiences since 2011 and used for two years now (2021 and 2022).
Format description finished October 2022.

Background.

If all the players are ordered by rating in a Round Robin table, then broadly speaking the outcomes of all the games in the NE and SW parts of the table are known beforehand, since the games are played by players with a large difference in rating.

Only the outcomes of games on the NW-SE diagonal part of the table are unknown, since the games are played by players of nearly equal strength.

So this format concentrates on those latter games and skips most of the rest.

Experience with the diagonal format.

The games are remarkably well played all across the board. Opponents of neighbouring strength have an opportunity to show their very best and probably have more fun too, and no matter where they are on the rating scale the games are certainly interesting to watch.

The format handles any number of players, a large number as easily as a small number.

All players meeting their nearest neighbours to both sides functions like one long continuous group of 3-5 players all way through from top to bottom, with every player in the middle of his group.

Since all the players are activated with decisive games from start and all results are carried over to next rounds, the players have fewer opponents at a time and thus more time for the games.

Double Elimination.

When a player lost games corresponding to losing to two opponents, he is eliminated.
Since two games must be played against each opponent, one black and one white, a defeat to two opponents corresponds to four lost games.

Performance Rating.

When the tournament has finished, the tournament result can be calculated for all the players, i.e. their Performance Ratings.

Tournament setup.

Round 1.

All players are ordered in a row by their ratings for this variant (possibly by maximum ratings).

First half of the row, each player plays against the second next player in line.
Second half of the row, each player plays against the second and fourth next players in line.
The difference is due to that the opponents in the first half-row are roughly double as strong as the opponents in the second half-row.
The numbers of opponents are now 2 2 2 ... 2 2 3 3 3 3 4 4 4 ... 4 4 4.
The setup works for 5 or more players, and at 4 players it becomes a Round Robin.

   00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23
00     x  x
01  x        x
02  x           x
03     x           x
04        x           x
05           x           x
06              x           x
07                 x           x
08                    x           x
09                       x           x
10                          x           x     x
11                             x           x     x
12                                x           x     x
13                                   x           x     x
14                                x     x           x     x
15                                   x     x           x     x
16                                      x     x           x     x
17                                         x     x           x     x
18                                            x     x           x     x
19                                               x     x           x     x
20                                                  x     x           x  x
21                                                     x     x        x  x
22                                                        x     x  x     x
23                                                           x  x  x  x

Round 2.

Players with two or more losses are eliminated.

If there are many players left, they're set up with two opponents like this:

   00 01 02 03 04 05 06 07 08 09 10 11
00              x           x
01                 x           x
02                    x           x
03                       x           x
04  x                       x
05     x                       x
06        x                       x
07           x                       x
08  x           x
09     x           x
10        x           x
11           x           x

If there are few players left, they are set up as a ring in such a way that the upper half of players plays against the lower half.
Fx. players A, B, F, H, K and M would be set up as
A-H-B-K-F-M plus A-M.

It is avoided, if possible, that players who already met, meet again.

Continuing with new rounds by this method until a winner is found. Losses are accumulated.

The winner.

Eventually only one player is left, the winner.

In case all players were eliminated in the last round:
The player with the fewest losses won.
If there are more players with the same fewest number of losses:

Direct comparison of the games of the tied players counted for all rounds.
If this is also even, the player who in the comparison won with the shortest sum of game lengths counted for all rounds, is the winner. (If a game was resigned, the number of moves it would take to finish the game, is added.) If the game lengths differ by less than 10%, they're considered equal.
Or new rounds between the tied players until the winner is found.

Tournament Simulator.

The Diagonal Tournament Format can be tested with this tournament simulator:
Diagonal Tournament Simulator.

Comments on the Diagonal Tournament Format.

Comments.

Aage Nielsen, October 26, 2022.
(Updated Sep 7, 2023).