OHS event pairing rules

[dok]

First Round

• Sort the players randomly.*
• 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:

1. 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.
   
   
2. 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.

3. 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.

2 and 3 loss tiers

• Sort the players by ranking.
• Pair adjacent players (1 plays 2, 3 plays 4, etc)
• 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.

[dok]

Any thoughts on implementing these rules for pair up/down for round 4 of the current event?

[dok]

Originally Posted by dok

Any thoughts on implementing these rules for pair up/down for round 4 of the current event?

How about, any objections?

[Xorlof]

I finally looked at them close enough to give an opinion. Yes, I like. Good work.

[dok]

Well, it ended up not mattering this go-round, as there are 4 3-0 players and 8 2-1 players. But we'll go with these rules for future events, barring further announcements.

[dok]

We've decided to change our Strength of Schedule metric, starting in season 15, as the current one arguably places too much emphasis on the more experienced opponents you've faced when calculating your strength of schedule. The new approach, instead of using inverse-variance weighting, will be derived by averaging the means and variances of all of your opponents, and backing out a ranking from there.

[dok]

Just a heads up that these rules will probably be changing next season. We have noticed some perverse effects in the way these SoS-based matchups play out, and more than one person has pointed it out.

We'll figure it out - we already have a basic sketch of a fix, just trying to figure out if it's the best way to go. If you want to chime in feel free.

[kevindola]

Obviously this topic is quite meaningful to the community hence all the chatter, but alright I'll play along.

Originally Posted by dok

Just a heads up that these rules will probably be changing next season. We have noticed some perverse effects in the way these SoS-based matchups play out, and more than one person has pointed it out.

Do tell about these 'perverse effects'. sounds naughty.

It seems to me that the ranking systems have done what they were supposed to be doing. Those who get ahead on the SoS (almost always someone who pulled off 1-2 upsets in the first two rounds) gets matched up with the worst ranked of the lower SoS schedule.

I always thought the problem with that is that it tends to do the same thing. The lower ranked players have high SoS and the higher ranked players have low SoS so they wind up getting matched up against each other anyway.

One way around that I can think of is to solely reward the top player in SoS. (or at least give them primary priority) Everyone except the top SoS player gets ranked by their online ranking and the bottom player is matched up against top SoS. Then you repeat the process with those 2 players eliminated from the list. (so the 2nd ranked SoS gets matched up with the worst remaining ranking...unless the 2nd ranked SoS was already the worst ranked player and got matched up with the #1 SoS player. That means #3 SoS would get the lowest ranked player left....confused yet?)

[dok]

Originally Posted by kevindola

confused yet?

Sorry to disappoint, but given that you've actually suggested one of the options I've put forward internally, I was able to follow it.

The issue arises when the top half SoS players in a tier all (or mostly) have lower rankings than the bottom half SoS players. When that happens, the pairings that round will actually serve to further exacerbate the SoS divide (because the high ranked, low SoS players get the weaker opponents, while the low ranked, high SoS players get stronger opponents).

The approach you suggest gets rid of the worst case scenarios, but it doesn't solve everything. Example: One player has the highest SoS and ranking, and the next-highest SoS belongs to the player with the lowest ranking. While the #1 SoS player is rightfully rewarded with the easiest matchup, the next-highest player is now pushed into a matchup that will further ratchet up his high SoS.

I've tossed out some other options that get rid of these sorts of corner cases, although they don't have quite the elegant simplicity of the approach you suggested.

[Dad_Scaper]

Assign each player a rating based on performances against various opponents, weighted such that you gain more for beating stronger opponents, and lose more for losing to weaker opponents. Initiate a metric by using historical strength of schedule data. For each win, you gain (for instance) 10+x, where x=[some function based on the difference between your rating and your opponent's, and you can't gain <1 (hypothetically (rating difference)/10 or something)], and something similar for losing.

Maybe assign everyone the same rating, dated Jan. 1 2012 (or whenever is the earliest start date), and run the formula forward from there. So you had a 1600, like everyone else, on 1/1/12. Then on June 5, 2012, you beat Cap, who (like everyone) had a 1600 rating. You would get 10+x, where x=[(no rating difference)/10 = 0], so your rating would become 1610.

Once everyone has a rating, maintaining such a system is easy.

Ratings in hand, you then take each new tournament and lay out all the players in order by rating. In a tournament of 16, have 1 play 8, 2 play 9, and so on. After each round, sort by wins & losses within the tournament: 1-0, 3-1, whatever. As you already do. Within each category, sort (again) by rating. Then, of the 4 (hypothetically) players who are 2-1, have 1 play 3 and 2 play 4. Got it? And so on.

New players will enter the system with a predetermined rating, which will go up or down quickly as their performance dictates.

You can call this system the Universal Scaper Championship Formula. It'll work! And I invented it!

[awesomeunleashed]

Originally Posted by Dad_Scaper

Assign each player a rating based on performances against various opponents, weighted such that you gain more for beating stronger opponents, and lose more for losing to weaker opponents. Initiate a metric by using historical strength of schedule data. For each win, you gain (for instance) 10+x, where x=[some function based on the difference between your rating and your opponent's, and you can't gain <1 (hypothetically (rating difference)/10 or something)], and something similar for losing.

Maybe assign everyone the same rating, dated Jan. 1 2012 (or whenever is the earliest start date), and run the formula forward from there. So you had a 1600, like everyone else, on 1/1/12. Then on June 5, 2012, you beat Cap, who (like everyone) had a 1600 rating. You would get 10+x, where x=[(no rating difference)/10 = 0], so your rating would become 1610.

Once everyone has a rating, maintaining such a system is easy.

Ratings in hand, you then take each new tournament and lay out all the players in order by rating. In a tournament of 16, have 1 play 8, 2 play 9, and so on. After each round, sort by wins & losses within the tournament: 1-0, 3-1, whatever. As you already do. Within each category, sort (again) by rating. Then, of the 4 (hypothetically) players who are 2-1, have 1 play 3 and 2 play 4. Got it? And so on.

New players will enter the system with a predetermined rating, which will go up or down quickly as their performance dictates.

You can call this system the Universal Scaper Championship Formula. It'll work! And I invented it!

@Dad_Scaper : Have you read this thread?

[Dad_Scaper]

Heh.

No, I had not.

If you already have rankings, then adopting my suggestion for pairings is easy-peasy. I'd do it locally, but I wouldn't force rankings on my ftf buddies. Or their kids.

Just abandon strength of schedule as a factor. Ratings are a substitute for it, for the purpose of pairings. The only reason why SoS is important to the FTF scene is because there aren't ratings in it.