Repeatedly pair the highest-up unpaired players (e.g. pair 1 against 2, then 3 against 4, etc).
Avoid any rematch from the previous two seasons.
If 5 has played 6, try 5 vs. 7, then 5 vs. 8, etc.
If you reach the bottom of the list without finding an opponent that avoids a rematch, then un-pair the last paired players, and try the player against them (e.g. if 5 has played all players below 5, then un-pair 3 and 4 and try 5v3, then 5v4).
* note on random numbers:
Spoiler Alert!
Rather than use actual random numbers, we use a pseudorandom number generated by a function which uses the player's name in our database, the season number, and the round number as an input. From a practical perspective, these numbers are random, but because this is a deterministic function it makes it easier for one person to set up a round without any questions about whether the random number generator was "gamed" to set up a desired result.
0-loss and 1-loss tiers after the first round
Sort the players by their Strength of Schedule.*
While there are unpaired players in the tier:
Select the unpaired player with the highest Strength of Schedule. This is player A. To find a match for that player:
Find the the remaining unpaired player with the lowest ranking who has not already played that player in this event (or, for the second round, in the previous event). This is player B.
If player B has a strength of schedule in the top half of the remaining unpaired players, order the bottom half (by Strength of Schedule) of the remaining unpaired players by ranking, from worst ranking to best ranking. Find the player whose ranking position in the bottom half matches player B's strength of schedule position. Call this player C. If player C's ranking is lower than player A's ranking, then player B is not matched with player A, and you return to step 1 to find a new match for player A (now ignoring player B).
Example: There are four players in the tier: dok, Xorlof, awesomeunleashed, and Kinseth, and their strengths of schedule are in that order. Their order by ranking is dok, Kinseth, awesomeunleashed, Xorlof.
dok is selected as player A. Xorlof is selected as player B, as he has the lowest ranking of the other three. However, Xorlof is in the top half of the tier by SoS (#2) and has the option to refuse the matchup. So we order the bottom two players by reversed ranking, and find the #2 player. That is Kinseth, who is then player C.
Since Kinseth is ranked below dok, Xorlof is NOT matched up with dok. The selection process to find dok's opponent is repeated with Xorlof ignored, and dok is matched up with awesomeunleashed (the next-lowest ranked player). The process then repeats again; Xorlof becomes player A and matched with Kinseth.
If rematch avoidance prevents any unpaired players remaining in the tier from being matched up with that player, then repeat the process to find a match for player A again, but ignore step 2. If there are still no options, then un-pair the last matchup you set, and try to pair player A again, with those two players now available.
* Strength of Schedule formulation:
Spoiler Alert!
The SoS calculation is based on the rankings of your opponents in the tournament. Your strength of schedule is the expected winning percentage your opponents would have had against an average player, based on the prediction of the trueskill algorithm. The higher this expected winning percentage, the better your SoS. Byes are an automatic win for any player, so they hurt your SoS considerably.
Pair-up
When a player needs to be paired up from this tier, one is chosen at random from the bottom-half SoS players in the tier (median SoS is eligible). A player cannot be paired up twice in the same event.
Avoid any rematch from the previous two seasons. (Technique is the same as the first round of the event.)
If there is a need for a bye player in the round, that player is randomly determined before any matchups or pair-ups are done. The same player should not receive a bye twice in the event.
Pair-up
When a Pair-up is needed, the highest-ranked 2 loss player is added to the next highest tier before any matchups are done.
That player is considered part of that tier (their strength of schedule is automatically considered lower half in the case of feeding into the 1-1 or 2-1 tiers).
Playoffs
Sort the players by their record (most wins, then fewest losses), then by Strength of Schedule.
Use these rankings to determine byes/play-ins.
Re-seed each layer of the bracket (i.e. players who have the same number of bye rounds) as if they were a tier in the previous round, except that record is considered over Strength of Schedule when applicable. If the player has no opponent (e.g. 10 players in the bracket, 1 and 2 have no opponents in the tier) then those players are slotted solely based on record and strength of schedule.
The bracket is then set up in the classic top-plays-bottom style.
Seeding is done once - brackets are then set for the rest of the event (except for rematch avoidance).
Later-round rematch avoidance:
If a match has a rematch from earlier in the event, swap the bottom player in the matchup with the player directly below that player, by seed, if that does not create a rematch itself. (Lower seed is whoever was effectively the lower seed when the bracket was initially set up.)
If it does, instead, try swapping with the next player down.
If you reach the bottom of the tier without finding a non-rematch pairing, then swap with the next player up from the lower-ranked player (again, if that does not create a rematch itself).
If it does, try swapping with the next player up, and so on.
Example:
Initial MUs are 1A, 2B, 3C, 4D.
Say 3 vs. C is a rematch. Try 3 vs. D. If 3D and 4C are both not rematches, make that switch.
If one of them is, try 3B and 2C.
May 11th, 2014, 06:56 PM
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