Following a Round Robin and prior to a Finals, we like to use a system we call a cascade, which pits teams against other teams of similar skill. Other sports do this with pools, but there's a sharp transition from one pool to the next — if each pool has 7 teams, then team 7 gets a much harder draw (playing against teams 1 thru 6) than team 8 (playing against teams 9 thru 14).
We keep your victory points from the previous round(s) and add on victory points for your cascade games. (We give the same number of victory points for cascade games as round robin games.)
It's possible to create a "thin" cascade where each team plays 3 games, but I'm only able to generate good fixtures (where you play other teams near your skill, and every team's "difficulty" is in the correct order) in a "thick" cascade where each team plays 6 games.
Let's start by illustrating a 31-team cascade:
Games Difficulty # RBY Who-plays-who RBYB.YR....................................................... 4.17 1 222 \3312111....................... BR..B.YYR..................................................... 4.25 2 222 3\23.1111...................... Y.R..B..BYR................................................... 4.50 3 222 32\121.111..................... .Y..R..B..BYR................................................. 5.33 4 222 131\121.111.................... ..BR.....B..YYR............................................... 6.08 5 222 2.21\121.111................... ....YR.....B..BYR............................................. 6.58 6 222 11121\111.111.................. ...Y...R.....B..BYR........................................... 7.42 7 222 11.121\111.111................. ......B..R.....B..YYR......................................... 8.00 8 222 111.111\111.111................ ........Y..R.....B..BYR....................................... 9.00 9 222 .111.111\111.111............... ..........Y..R.....B..BYR..................................... 10.00 10 222 ..111.111\111.111.............. ............B..R.....B..YYR................................... 11.00 11 222 ...111.111\111.111............. ..............Y..R.....B..BYR................................. 12.00 12 222 ....111.111\111.111............ ................Y..R.....B..BYR............................... 13.00 13 222 .....111.111\111.111........... ..................B..R.....B..YYR............................. 14.00 14 222 ......111.111\111.111.......... ....................Y..R.....B..BYR........................... 15.00 15 222 .......111.111\111.111......... ......................Y..R.....B..BYR......................... 16.00 16 222 ........111.111\111.111........ ........................B..R.....B..YYR....................... 17.00 17 222 .........111.111\111.111....... ..........................Y..R.....B..BYR..................... 18.00 18 222 ..........111.111\111.111...... ............................Y..R.....B..BYR................... 19.00 19 222 ...........111.111\111.111..... ..............................B..R.....B..YYR................. 20.00 20 222 ............111.111\111.111.... ................................Y..R.....B..BYR............... 21.00 21 222 .............111.111\111.111... ..................................Y..R.....B..BYR............. 22.00 22 222 ..............111.111\111.111.. ....................................B..R.....B..YYR........... 23.00 23 222 ...............111.111\111.111. ......................................Y..R.....B..BYR......... 24.00 24 222 ................111.111\111.111 ........................................Y..R.....B..BY..R..... 25.08 25 222 .................111.111\.11121 ..........................................B..R.....B..Y..RY... 25.92 26 222 ..................111.11.\12112 ............................................Y..R.....B.R..BY.. 26.33 27 222 ...................111.111\1212 ..............................................Y..R....BB.Y..R. 26.75 28 222 ....................111.121\122 ................................................B..R...YY..R.B 27.00 29 222 .....................1111121\22 ..................................................Y..R..BB..YR 27.17 30 222 ......................1121122\2 ....................................................Y.R...RBBY 27.42 31 222 .......................1122222\
In the grid above at the left, each row is a team, and each column is a game. In the middle of the fixture (teams 8 thru 24), teams play opponents 1, 2, 3, 5, 6 and 7 spots above and below them. The Difficulty column is just the average of the ranks of the other teams that this team plays against; you can see that team 1 has a difficulty of 4.17, and each subsequent team has a higher difficulty number. Immediately after Difficulty is the team's rank. Each team plays twice on each colour. The who-plays-who shows how many times teams play each other: for example, team 1 plays team 2 three times.
(Technical digression: my Golomb ruler approach is visible. From game 6 to game 55, you can see that in every second game the competitors are team n, team n+2, and team n+5. In every other game, the competitors are team n, team n+1, and team n+7. This corresponds to Golomb rulers {0, 2, 5} and {0, 1, 7}, providing distances [2, 3, 5] and [1, 6, 7], covering in total distances [1, 2, 3, 5, 6, 7], skipping only distance 4, as visible in the who-plays-who. I am confident that it is not possible to pick better Golomb rulers than these.)
This grid can be better ordered so there are no back-to-back games:
Games Difficulty # RBY Who-plays-who B..Y.Y..B.R.R................................................. 4.17 1 222 \3312111....................... R.B.Y..R..Y.B................................................. 4.25 2 222 3\23.1111...................... .Y.R.B.B.R..Y................................................. 4.50 3 222 32\121.111..................... Y.R.B....B...Y....R........................................... 5.33 4 222 131\121.111.................... .B.B....R..R..Y...Y........................................... 6.08 5 222 2.21\121.111................... ..Y..R.....B.B.Y...R.......................................... 6.58 6 222 11121\111.111.................. ....R.R.Y.....B.Y..B.......................................... 7.42 7 222 11.121\111.111................. .R....Y...B....B.Y..R......................................... 8.00 8 222 111.111\111.111................ .......Y.....R..B...B..Y....R................................. 9.00 9 222 .111.111\111.111............... .........Y....R..B...R..Y...B................................. 10.00 10 222 ..111.111\111.111.............. ...............R..B..Y.B.Y...R................................ 11.00 11 222 ...111.111\111.111............. ...........Y....R.....R.B.Y..B................................ 12.00 12 222 ....111.111\111.111............ .................R.Y..B..B.Y..R............................... 13.00 13 222 .....111.111\111.111........... ......B................R..B...Y..Y....R....................... 14.00 14 222 ......111.111\111.111.......... ....................Y...R..B...R..Y...B....................... 15.00 15 222 .......111.111\111.111......... .........................R..Y..B.B.Y...R...................... 16.00 16 222 ........111.111\111.111........ .....................B....R.....R.B.Y..Y...................... 17.00 17 222 .........111.111\111.111....... ...........................R.Y..B..B.Y..R..................... 18.00 18 222 ..........111.111\111.111...... ......................Y..........R..B...B..R.Y................ 19.00 19 222 ...........111.111\111.111..... ..............................B...R..B...R.Y..Y............... 20.00 20 222 ............111.111\111.111.... ...................................R..Y..B...B.Y.R............ 21.00 21 222 .............111.111\111.111... ...............................Y....R.....R...B..B.Y.......... 22.00 22 222 ..............111.111\111.111.. .....................................R.B..Y....B.......R...Y.. 23.00 23 222 ...............111.111\111.111. ................................Y............R.....B.R.B....Y. 24.00 24 222 ................111.111\111.111 ........................................Y.....R.Y....B...R.B.. 25.08 25 222 .................111.111\.11121 ...........................................B...R....R...Y.Y.B. 25.92 26 222 ..................111.11.\12112 .........................................Y..Y...B..R..R...B... 26.33 27 222 ...................111.111\1212 .................................................Y..Y.B.B..R.R 26.75 28 222 ....................111.121\122 ..........................................B.R.....B...Y..Y..R. 27.00 29 222 .....................1111121\22 ................................................R.R.B..Y.B...Y 27.17 30 222 ......................1121122\2 ............................................B.....Y..Y..R.R..B 27.42 31 222 .......................1122222\
Since this is just a re-ordering, difficulty, colour and who-plays-who are not affected.
The smallest cascade grid I can generate with smoothy increasing difficulty is for 11 teams:
Games Difficulty # RBY Who-plays-who B..Y.Y.B.R.R.......... 4.17 1 222 \3312111... R.B.Y....Y.B.......R.. 4.25 2 222 3\23.1111.. .Y.R.B.....Y..R....B.. 4.50 3 222 32\121.111. Y.R.B...Y...R.B....... 5.33 4 222 131\121.111 .B.B...R....Y...R.Y... 6.17 5 222 2.21\.21121 ..Y..R..B......Y.B..R. 6.50 6 222 1112.\12112 ....R..Y.....R.B..B..Y 6.75 7 222 11.121\1212 .R....R..B...B...Y..Y. 6.75 8 222 111.121\122 ........R.B..Y..B..Y.R 7.00 9 222 .1111121\22 ......B...R...Y.Y.R.B. 7.17 10 222 ..1121122\2 ......Y...Y.B..R.R...B 7.42 11 222 ...1122222\
That's the point where the middle regular repeating section is largely removed, and we're left with just the "head" and the "tail".
Here are some specific cascade grids. You can generate your own cascades using my GenerateCascade tool, available as part of my Zone Grids bundle. That tool will also let you re-order games to avoid back-to-backs. Or contact me for a specific cascade.
When using these grids, it's desirable that you put strongest teams at the top of the fixture as illustrated. This is because in the main part, there are games where the top two teams are close to each other in rank, and the third team is 6 ranks lower. This is much more desirable than a game that's the other way up, with one very strong team who will effectively determine the outcome.
There may be room for improvement — in particular, I'd like a replacement "head" where teams play each other at most twice.
(Here is an explanation of how to read a grid.)