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