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.
Here is a compact representation of its structure for a 16-team tournament. I’ve drawn it so as to show how the rounds work – thus, the first round of the lower bracket is even with the second round of the upper bracket because each has to wait for teams to become available from the first round of the upper bracket.
The upper bracket is resolved in four rounds, but the lower bracket drags on for three more increasingly sparse rounds before it finally resolves and sends a player to the grand final.
Consider how this design plays out for chess or backgammon, where the most severely limited resource is usually the number of rounds that can be played. It starts out briskly, with everyone playing in the first two rounds. Later on, however, it’s anything but brisk. The last three rounds all have only one match. It goes late into the evening, when the folks from the venue want to get you out of there so they can close up. Most people have gone home. Two players are in action, and a couple of others are waiting to play their own late match. Maybe there are one or two people who had the misfortune to carpool with a friend who happened to do well. And there’s one very bored tournament director, fielding complaints for the umpteenth time – the tournament always finishes late.
This is enough of a problem that organizers often take fairly drastic steps to shave a round or two from the tournament. The first expedient is to eliminate the possible rematch between the upper bracket winner and the lower bracket winner if the latter prevails at the beginning of the grand final. I’ll do a post or two on this issue later on, but you can probably infer my preference from the fact that there haven’t been any such grand final rematch lines in the tournaments I’ve discussed so far.
A more drastic way to save a round is to dispense with the grand final altogether. The winner of the upper bracket collects the trophy and gets to go home, while whoever’s left among the losers slog it out for a smaller trophy. When you do this, it’s not really a double elimination tournament any more, but rather a single elimination with a consolation.
There is, however, another way to squeeze out a round that compromises the design much less. It’s done by rearranging the lines, like this (the difference is only in the lower bracket):
Hey, presto! Now there are seven rounds rather than eight. I works by dropping the last two rounds of drops into earlier rounds. In essence, a round that was going to have two games, and another than had only one, have been smashed together into a round with three games.
So does it really work? What are you giving up to get that extra round? Come back tomorrow for a surprisingly clear answer.