Wednesday, April 7, 2010

SWISS IS FOR CHOCOLATE! Seeding and Pairing in a Tournament Setting

So, here's another tournament subject ...

In most 40k tournaments, opponents are paired off in rounds (after the first round) by similar strength. So, the person with the highest net score plays the 2nd highest in round 2, 3rd plays 4th, 5th plays 6th, etc.

There are a lot of reasons for this, but I'm not really going to cover them - mostly b/c I don't care for the approach. What I will do instead is present my rationale for why we use Elimination Pairing until the final round(s), and then open the comments floor for input.

In our system, here's what happens ...

64 people are randomly paired up
With no ties, 32 will be 1-0 and 32 will be 0-1
They will be "seeded" with the following rating system:
Record x Factor (let's just "pretend" 10 for the sake of example making) + %Objective1 + %Objective2 + %Objective3

So, let's take a hiatus from pairing and talk about this rating system so it's super clear to everyone:
"Variables" being set as constants for EXAMPLE'S sake =
Our 3 objectives that will be active in every round as primaries or tiebreakers, and used for seeding, will be "VICTORY POINTS" (Objective 1), "LOOT COUNTERS" (5 of them, Objective 2), and "QUARTERS" (4 of them, Objective 3). Just so you all can feel "connected" to the situation here, we'll say that Quarters is captured by VP preponderance in a quarter, VP is straight VP, and Objectives are just like the book mission where you've rolled 5 or 6 on your d3+2

Let's presume after Round 1 that Player A has the following tallies ...
He is 1-0
He scored 1,000 VP
He captured 4 of 5 Loot Counters
He captured 3 of 4 Quarters
In our example (again, keep this as sample, and not fixed for the Open yet), his rating would therefore be:
((1.0 (record %) x10) + (0.50 (VP%)) + (0.80 (loot counter%)) + (0.75 (quarters%))
So 10 + 0.5 + 0.8 + 0.75 = 12.05 ...
in theory his "max" rating possible would be a 13, and would require him to table someone (therefore netting him 100% VP, 100% loot counters, and 100% quarters)

OK, so this guy has a rating of 12.05, and there's how the rating system works

After 1 round, our 32 1-0 finishers each have a rating, which nicely and quickly seeds them #'ed 1-32
This rating is apt to change dramatically each round within the span of 10.01 -> 13.0, which is always going to be your "undefeated" rating range.

In a swiss system, the higest seeded would play the second highest seeded
In an elimination system, the highest would play the lowest within bracket, so #1 would play #32, while #33 (0-1) would play #64

Wait a minute, you ask ... isn't that kind of unfair for #32? Isn't that kind of going easy on #1? NO, it's not, and here's why ...

In a real tournament, where you are an impartial tournament organizer, you theoretically want the best player to win. More importantly, you want the best player to win by beating the 2nd best player in the very last round(s). At the very least, you want the best to make it through to the end.

What is the "best?" Well, in the case of a tournament, it's the best for THAT TOURNAMENT. This isn't a season or league, and you don't have time for a "best of" series for every round. As nice as that would be, it's for our area leagues that we hold, not for the NOVA Open.

So, after Round 1, you've got a #1 and a #32 ... they both "won" their games by vastly different margins (presumably). What does that mean? Does that mean #1 is the best player at the tournament, and #32 is only the 32nd best? Not at all. Your first round is RANDOM paired (I'm not going to go through and try to evaluate the skill of 64 people, hell no). For all we know, #1 went up against #64 (in fact, by the ratings, he probably did, since 64 lost by as much as 1 won by, if they played each other in round 1). For all we know also, #32 went up against #33 (best loser), and #33 could have been #2 if he'd drawn #64, and ... GASP ... a dizzying amalgamation of possibilities.

Well, how do you enable 32 to climb the ladder, and how do you enable 1 to be "proven" without punishing ... say ... #2 unfairly? How do you ensure that #1 and #2 don't knock each other out of contention right away? How do you ensure that people don't game the system and "skim" to the final round undefeated by "barely" beating everyone and thus pulling easier draws in subsequent rounds (i.e. 31 playing 32)?

Well, the answer is elimination pairing.

If #32 is a player who will always win his games, but by his army design win them by smaller margins or eeking out bare wins, that doesn't mean he's not a winner. If he's a crappy player who got an easy draw and still barely won, he shouldn't get the easiest possible match-up. So, he plays #1. Now, if #1 really is #1, he'll crush 32 and stay #1 by rating for round 3. If he's not really #1, he might barely win, and drop to the middle of the undefeated pack. He might lose, and now you've learned that #32 simply had a really tough first draw, or has an army that wins that way. Lots of possibilities, NONE OF THEM BAD.

What you don't want is #1 to play #2 in round 2, have #2 lose, and have the 2nd best player in the tournament (if he really is) playing for an "at best" 5th place on pure competitive record (best 3-1).

This is a morass, it can be. If you think it through, things are "fair." By Round 4, the 8 undefeated are almost always going to be the best 8 there. So, do you do 1 vs 8? Well, in this case, you actually don't. If we had 6 rounds in one day, where everyone played, I would say yes you do. But here, you want the whole field to be present for 1 playing 2, 3 playing 4, 5 playing 6, 7 playing 8. Unfair to 1 and 2? Well, no, not really. The next day the winners all play each other through in the Final Four, but you also have swiss paired the round that determines the top commander award.

Got you thinking, don't I? Now, all this logic seems to imply 1 vs 8, doesn't it? Well, maybe it does :) ... food for thought, for sure.

- Mike

PS - Rhett Austin has settled on ETC Comp for our Fantasy Side, and he'll be guest authoring on the blog about it shortly.


  1. Elimination Pairing for the win!

    I approve. It's a lot more work for the tourney organizer, but worth it. I HIGHLY suggest already having the algorithms programmed into an Excel sheet so that all you have to do is data entry.

    Makes me wish I could make NOVACon...

  2. Ok, my head is spinning a bit trying to poke a hole in this, but after just reading it I like the system. I guess I am wondering why, if your awarding the 4 top winners, you would not stick it out with the elimination pairing instead of switching to swiss for the final round (did I understand that correctly?)

  3. Yeah, you understood that correctly. There's not a good reason, necessarily ... half of the point was to get the average swiss-lover to "break the mold" by pointing out that flaw. /touches nose lightly

  4. Ok, thanks for that explanation, now it all makes a lot more sense.

    I'll most likely be there, but it'll depend on how my knee heals up.

  5. If this tournament format were a woman, I would have sex with it.

  6. I will allow that, if you actually make it, DI.

  7. Maybe you could clarify some questions for me. First I wanna say this sounds fantastic, i am now a huge fan of this pairing style. But how would the rest of the tournament play out? If this elimination then is it like a bracket and do losers then go into a loser bracket? I may not be reading it right, it may already have been answered.

    Also, if its elimination then someone who gets a loss or even a draw is out of the running for overall? I agree that this will truly prove the best player but you may have some people leave knowing they are out of the running. This would affect the pairings as well.

  8. Ultrabob - sorry I didn't catch this sooner.

    With regard to Overall, that's not tied to an undefeated status.

    That's to say, that winning all your games is required on the first day to win a Top General prize ... as is winning all your games to win the Tourney Champion (our equiv of "Best General) prize and 2nd Vegas ticket (2nd day activity).

    BUT the Overall, coined Renaissance Man in our system, is only 33% your record/competitive score, then 33% sports and 33% appearance ... so if you're a real nice sport and have a good looking army, you're going to be in the running for it as long as you win about half your games or more.

    As for leaving ... we're adopting the Adepticon stance - leave our event early for reasons such as "I lost, boo" and you're disinvited on a perpetual basis. Sounds harsh at first, but makes sense.

    It does affect the pairings if people leave, but the "loss" brackets are a little easier to pair out than the win brackets, and presumably people won't depart if they're undefeated.

    More importantly, the more you've lost, the higher your odds of winning random swag (your name goes in the raffle box once for every loss).

    Hope that helps, and that you get it!
    - Mike

  9. Good stuff Mike and it makes logical sense. Reminds me of the ice hockey tournaments in High School I used to play in. They ALWAYS used elimination and it always made sense.

    Plus, nothing is better than being that #4 team going into the finals and pulling out that big Cinderella win against the #1 team (and then go on to win the tournament). Elimination is truly the fairest and most accurate way to find the "best". Yeah the #4 player/team is "the worst" out of the Final 4, but he/they is probably as good, if not better than the other 3 teams there, so the only way to get the best representation of this is to finalize it through Elim.

    Granted I understand in your tourney the final rounds are Swiss Pairings, but I think they'd work as well as Elim.

  10. The Swiss style system you're describing (rank players each round after the first, 1-2 in every round, duplicates prohibited) is only one variation of the Swiss style system. I believe it's the one used most often because it's the easiest to implement. The one most often used in chess tournaments is to pair of the top half winners against the bottom half winners. For example, 8 winners would lead to a pairing of #1-#5, #2-#6, #3-#7, #4-#8. I believe this is called Standard Swiss.

    Elimination pairing can lead to a (not too) pathological case where the best player in the tournament gets paired with the next n best players in an n round prelim tournament. In round one he plays the second best player, and unsurprisingly, ekes out a victory. Then he gets paired against #3, because #3 smashed his first round opponent. Repeat as necessary, all due to an unfortunate first round pairing. Standard Swiss makes this much less likely. It's still possible, but even more pathological because for best to be paired against third best in round 2, third best would have had to win but been average points among the remaining winners. The same holds true for following rounds.

    The much more common case is that a winner who ekes out a victory will be paired with someone with a much better record, which seems to satisfy the reasons for Elimination Pairing in the first place. Additionally, Standard Swiss can hold all the way through final rounds as #1 vs #2 is still the most likely outcome for the final round pairing.