Tournament Bracket Methodology

April 28, 2006 8:06 AM

Is there a standard or generally accepted methodology for determining the optimal number of byes needed, and in which round they should occur, in a single-elimination tournament?

I am running a Heads-Up poker tournament, and i doubt that i will have a power of 2 as the number of entrants, so i will need to have some players advance in some rounds without competing. There is no seeding is this tournament, and i want to have as few players end up getting a bye as possible. I have never scheduled any sports tournament before, but i am guessing that there is a generally accepted method for determing how many byes and in which rounds.

posted by dafair to sports, hobbies, & recreation (13 comments total)

Interesting question that I've never thought about before. It seems like you could just have byes in the first round to so there are a power of 2 number of first round contests. Since there is no seeding system, randomly picking who gets the first round byes would be fair.

The only way I've seen byes occur in later rounds is if the tournament is round-robin, i.e. not single-elimnation. Is there a reason you think having all of the byes in the first round would not work?
posted by gus at 8:17 AM on April 28, 2006

If i understand correctly what you're asking, the following should work:

You have all the byes in the first round to ensure no-one gets more than one and that advantages are minimised. All you have to do is figure out the power of 2 below the number of players you have, which is the number you want to have left after round one.
Taking away the number of players you want left after round 1 from what you start with tells you the number of matches you need, (because 1 match = 1 elimination).
So if you have 28 players to start with (i.e. in round 1), you want to have 16 left in round 2, thus you need to get rid of 12 in round one, thus you need to have 12 matches in round 1. (12 matches = 24 players so 4 players get byes.)
posted by biffa at 8:18 AM on April 28, 2006

Gus and biffa have it right: schedule all your byes in the first round. Since there's no seeding in your tournament, you should probably determine who receives the byes randomly. Of course, it might be more interesting to allow people to bid on or buy the byes...
posted by jdroth at 8:32 AM on April 28, 2006

OK, to clarify a little. Lets imagine that I get 24 entrants. I could give 8 byes in the first round, and 8 people total in the tourney would get a bye.

I could also just have 12 games in the first round, 6 in the second, and 3 in the third round. In the 4th round, one randomly selected player would get a bye, the other two would play, and in the fifth round, the winner of that game would play the player who got a bye for the championship.

I don't think either of those seem optimal. The lateness of the bye in the second scenario seems to make it very advantageous, and the sheer number of byes in the first scenario seems to make that method unfair as well. Surely there exists some way of determining the best "middle ground" between these two extremes?
posted by dafair at 8:37 AM on April 28, 2006

biffa has it right, it's called the "Bye system". I learned it in taekwondo, and I remember we had a chart we had to memorize. That was one of the first times I've ever solved a math problem that wasn't posed to me. I figured out the "pattern" for figuring out the number of byes needed in the first round.
We also gave out the byes randomly, or based on the scores of previous competition (for a 5 person sparing round, the 3 bottom scorers in Forms got the byes)
posted by slactoid at 8:44 AM on April 28, 2006

Can you have the 4th round be "round robin" with each of the three players playing the other two head-to-head? You'd have to establish tiebreaker rules in case they each win one and lose one. (This is, of course, assuming the 24 players you describe in your followup. If you get more or fewer players, you'd have to play around with it...)
posted by arco at 8:47 AM on April 28, 2006

the sheer number of byes in the first scenario seems to make that method unfair as well

If it's random, how is it unfair? That is, it's equally unfair to everyone, and at a point when everyone (since nobody has played yet) is equally "deserving."

In any tournament, "luck of the draw" should matter less and less as the tournament goes on—the early rounds are designed to weed out the inferior players or teams. So I would think it's definitely preferable to have this element of luck (the random byes) be a factor only in the first round.

Look at it this way: Any player who's good enough to win the tournament is going to be good enough to win the first round. So it doesn't really matter if they get a bye. If a bad player gets a bye, fine, they'll lose in the second or third round. To give a bye in a later round, when you've already narrowed it down to the best 4 or 8 players, seems much more unfair.
posted by staggernation at 9:59 AM on April 28, 2006

If it has to be single-elimination, and you can guarantee a multiple of 2 number of participants, this is one way to do it. Have everyone play a first round game with the losers eliminated. The best players based on X criteria (number of hands needed to win? largest single pot in the match? etc) get the byes in the 2nd round.

You could also delay the byes to the 3rd or 4th round as you proposed. Use some aspect of play to "earn" the bye. I don't know poker well enough to suggest what that may be.

If you can do round-robin, you can opt to do round-robin at the beginning or the end and totally skip any byes or assign byes more equitably.

For example, with 30 players you could have four pods of 7 or 8 players do round-robin. Best 2 players out of each pod enter an 8-team single elimination tourney. Or have the best 3 advance, with top players getting first-round byes. This has the advantage of being a little flexible with respect to number of players, but you need to budget more time for games.

With 28 players you could have 2 rounds of single-elimination to get to 7 players. Then have round-robin for the championship.

You get the idea.
posted by Tallguy at 10:10 AM on April 28, 2006

As I understand the problem you could use a Swiss system tournament, which would have the added benefit that everyone would get to play every round. However, it's possible that I either misunderstood the question, or my answer.
posted by jefeweiss at 11:12 AM on April 28, 2006

I think that jefeweiss actually has a pretty keen idea: you may want to explore a swiss tournament. It's actually a pretty good system for more than just chess!
posted by jdroth at 2:55 PM on April 28, 2006

Like professional Magic tournaments! (sorry that I know this).

Are all of your poker matches jsut head-to-head? Normally I think you seat people in the largest even distribution possible, right?
posted by Four Flavors at 3:50 PM on April 28, 2006

Given that single elimination is the least accurate method due to selecting a winner via the least data (and is thus the quickest method), I like arco's idea - use single elimination for the bulk of it, but when it's down to the final, have a round robin. It puts more emphasis in the right places, and eliminates byes.
posted by -harlequin- at 7:07 PM on April 28, 2006

I talked to a guy at work about my dilemma. He is the commissionor of a *large* (42 teams) little league organization (i didn't know him very well, but another person reccommended him to me). He said I was looking at the problem wrong.

See, I was thinking of someone as getting a bye in a round as me giving out one bye, no matter what round he was getting it in. A better way of looking at it, he said, was to count the whole tree below that point (that would have been filled by opponents if we had them) as byes. Thus someone who won a first round match, but gets a bye in the second round really means that while the player only got one bye, but I have added two the number I am giving out. Basically, a bye is "worth" one in the first round, two in the second, four in the third, etc..., however many first round players would have been in that tree.

This philosophical shifting of perspective has brought me around to the "give all byes in round one whenever possible" point-of-view.

To answer some other questions. This is a special head-to-head only event, and is being modelled on the National Head-To-Head Hold'Em Championships. Thus we are going to go with SE (as they do) rather than Swiss or DE for now. We may do a Swiss or DE event later on. I have run Swiss style boardgame tournaments before, and even though it would eliminate my bye issues, it introduces more bookkeeping and administration, which i don't want to do yet, since I am administrating the tournament as well as playing in it.

Most of the tournaments i run are full-table (8-10 players per table) events where people are eliminated as they lose all their chips. You play until one player has all the chips, balancing the tables as needed as you go.

Thanks to everyone for all your help.
posted by dafair at 10:57 AM on April 30, 2006