Today we’ll dig into the rather surprising result that the shifted version of our 16DE tournament was at least as good, and in several respects better, than the standard, unshifted version. Continue reading “Finding Fairness in Analyzed Brackets”
Yesterday I discussed a technique for squeezing a round out of the lower bracket in a double-elimination tournament by shifting some of the drops into early rounds. Now it’s time to discuss the other merits of that technique.
Here’s the bottom line: The round compression technique doesn’t just save a round so that the tournament runs faster, but it also improves overall fairness, and reduces the number of repeated pairings. It’s not just a plausible way to save some time in a round-intensive tournament, but it should probably be the technique of choice for almost any double-elimination tournament, whether or not there’s any benefit from running fewer rounds. Continue reading “Building a Better Bracket, Part II”
The double-elimination tournament is one of the most popular designs. But it has some well-known flaws. In this post, I’ll introduce another way to draw a double-elimination bracket that, at least in some contexts, is superior to the more familiar bracket. Continue reading “Building a Better Bracket”
So, having made a case for the importance of putting the drops in the right places, let’s turn to the issue of how to get them there.
As a practical matter, the easiest thing to do is to download or copy from some source that can be relied upon to get it right. Unfortunately, there’s no site, other than this one, that I think can recommend on this point. I hope, in the fullness of time, to build out the collection of sample documents I make available here to the point where a tournament organizer can find a useful sample for any but the most exotic tournament. But don’t hold your breath. In the meantime, let me explain a general approach that I’ve found useful. Continue reading “Getting the Drops Right, Part II”
Today’s topic is arranging the drops in a double-elimination tournament. By drops, I mean the guides that show where the loser of a winner’s bracket match should reappear in the losers bracket. The goal is to avoid, as much as possible, repeating a pairing that happened earlier in the winners bracket.
Today I’ll ruminate a bit more about fairness. It strikes me that elaborating fairness into the three elements of fairness I suggested might be useful in helping to explain how people can disagree so completely about what’s fair. I’ll see if I can apply that insight in the context of trying to determine what is and isn’t fair in the world at large.
To review, there are three somewhat distinct virtues that all get called “fairness”. I’ll restate them a little to help generalize the context:
Fairness A: Fairness is meeting people’s settled expectations, and honoring past practice;
Fairness B: Fairness is treating everybody equally; and
Fairness C: Fairness is rewarding good performance (and punishing bad). Continue reading “Fairness in the World”
Participation is the value players derive from playing in the tournament.
Unlike fairness, participation has a simple and obvious metric: the number of games played. Thus, a 16-team single elimination involves playing 15 games or matches, and so has a participation score of 15. The double elimination tournament gets a score of 30 involves 30 games (or possibly 31 – more about this in a future post).
This simple and obvious measure can be refined in any number of ways, most of which are more complicated and debatable. Continue reading “Measuring Participation”