If two brackets is (arguably) better than one, shouldn’t three be better than two? Let’s see if we can fashion a triple-elimination bracket that can compete with Miss SE55779 and Miss DE32jCD for the title of Miss FOTA 32.
They all laughed when the province of Singletania announced that it was going to send a single-elimination candidate to the Miss FOTA 32 Pageant. How could a design with only one bracket be the fairest?
But they gasped when they got a look at Miss SE55779! They’d been expecting a frumpy design with fairness (C) near 100. But she piled lots of extra games into her svelte five rounds. Still, surely one could do better with a double-elimination tourney.
Better? Well, maybe, but there’s a price to pay.
Now to begin trying to find Miss FOTA 32. Let’s start simple.
The simplest tournament design that obeys the rules is a straight single elimination. Nothing easier! It plays in five rounds, but we only have to start the E round, not finish it, within the time limit.
Here’s a first run, to see what we’ve got to work with: f(C) = 96.87, T = 98.7. The bad news is that fairness (C) looks pretty awful, but the good news is that the base tourney is using less than 100 of our allotted 500 minutes. How can we best spent the rest of the time to bring down f(C)?
Hello folks! This is Buster Brackets, coming at you live and direct from the Geekery Dome in beautiful Bloomington, Indiana, USA, site of this year’s hottest contest: the Miss FOTA 32 Fairness Pageant. Alongside me is the man who always has his ear to the ground, Worm Tourney. How’s it going, Worm?
I couldn’t be more pumped, Buster! We’re about to see some of the world’s fairest brackets going head to head for the FOTA 32 crown. You ready to have some fun, fella?
You bet, Worm, and I know that dozens of tourneygeeks all over the world are as excited as we are. They’ll be one the edge of their seats from Malta to Maryland to see who carries off the crown. While we’re waiting for the action to start, let’s talk about some of the controversial new ground rules that the IATg directors have come up with.
The quest for the fairest-of-them-all bracket in the past few posts has led us to build a number of very peculiar-looking brackets, particularly the cascade bracket. A form of this bracket is used to good effect in the last stages of bowling tournaments. But it would, quite reasonably, be considered highly inappropriate in most other contexts.
So, let’s look for the magic mirror with a different set of constraints. The most significant one is this: in order to be eligible for the victory, the winning bracket must be fair as to both fairness (B) and fairness (C). This should yield a design that people might actually want to use.
The idea of a Dolly bracket is, I think, a useful one, and so deserves a more precise definition. A Dolly bracket is any bracket designed to return a specific unfair result (in the fairness (C) sense).
In devoting the next post or two to Dolly brackets I don’t mean to suggest that such brackets are to be encouraged. If there were a code of ethics for tournament designers, one of the first rules would be never to create a Dolly bracket. But this is probably reason enough to spend some time playing with them, if only because it’s important to know what does and what doesn’t count as a Dolly bracket.
In Magic Mirror on the Wall … I attempted to make use of a new formula for the fairness (C) statistic to determine what bracket configuration for an eight-team single-elimination tourney was the fairest of them all.
Some problems with the new measure became apparent, and after a little fruitless tinkering, it became apparent that the new measure was not fit for purpose. Revisiting the question of the fairest 8SE, we find that the defects in the bad measure weren’t just theoretical – they led to an incorrect result.