A Big, Peculiar Bracket

With my co-conspirator Butch Meese (the dean of bracket constructors for backgammon in the midwest), I’ve been working on something rather unusual for possible use in an upcoming tournament. It bend the rules of bracket-building in a number of ways, and illustrates innovative approaches to a few awkward problems.

It’s a 96-team double elimination with full progressive consolation.

A couple of things are worth noting about this format. The first is that it has both a full double-elimination and a consolation. Heretofore, a consolation was just a double-elimination tourney in which the last few matches, including the one where the survivor of the lower bracket got one more chance at the overall championship, was truncated. But here there are not two, but three brackets: an upper bracket; a middle bracket (which does get a chance at an overall win); and a consolation bracket, which doesn’t. As might be guessed, having three brackets to care for makes things much more complicated.

The other rather notable feature of the design is the way it deals with an exceedingly awkward number of entries. Ninety-six is squarely between 64 and 128, and so would ordinarily entail 32 byes. This design has none at all. That’s because, rather than seeing the 96 bracket as a pruned-back 128, it’s looking at it as three intertwined 32 brackets. Six players: the winners of each of the three 32’s and the winners three ED shift losers brackets will play off for the championship. There’s a little awkwardness to it, as one of the undefeated players will draw one of the surviving losers in the first round of the playoff, and the correct bracket to use in the playoff depends on the outcome of that match. But one somewhat squirrelly match in the playoffs is a small price to pay for avoiding a bracket with 32 byes in it.

Having a bracket of 96 gives you lots of room to spread the drops around, so there are very few repeated pairings in the middle bracket. The trick, I found, is to color-code the drop slips according to which of the three upper brackets they drop from. Then, for each of the three middle brackets, you take A and B drops of one color, C’s of another, and D’s and E’s from the third. This works so well that there are no possible repeats until the final match of each middle bracket – not even the E drops can find themselves playing an opponent they’ve seen before.

The drops for the consolation are another matter entirely. This requires another whole set of drop slips (also color-coded). I sometimes feel that making drops slips is a little fussy, and most of the time my experience is enough that I could get by without them. But I defy anyone to come up with a sensible set of drops without using drop slips in this format. Here’s a picture of the consolation drop slips spread out on my lovely maple dining table (in the best pattern I’ve found so far, which keeps the first three rounds of the consolation free from repeat pairings):

One more peculiar feature is the nature of the progressive consolation. It was all very well to resolve the three-section bracket with a six-player playoff, but that’s not going to work with the consolation. Dropping from the middle bracket, in which (as with the upper) everything happens in threes is going to wreak havoc on any conventional bracket, where things somehow have to resolve themselves into a power of two.

My solution to this is not to solve it. I’m keeping the three-part structure by taking the drops from the three middle brackets into three separate consolations. They won’t be resolved – each of the three consolation winners gets a modest prize payout and a tiny little trophy.

Not everyone will like this solution, but the more I think about it, the better I like the idea. What’s the point of having a third bracket anyway? To give everyone who washed out of the the main competition another chance to play, and to let one more player leave the tournament feeling like a winner. (See A Nation of Losers.) Here you get almost as many additional matches, they play in one fewer round, and you get three more people all feeling like winners!

As it happens, there’s a reasonably compact way to accommodate the seven rounds of drops. And the alternatives are gruesome. Both Butch and I tried our hand at it, and he did better than I did. But even Butch’s best effort is still one of the ugliest brackets I’ve ever seen, with parallel drops going to different rounds and a bunch of sneaky, implicit byes. I suppose by that point in a tournament most players are too tired to argue, or maybe even to notice the inequities, but they’d bother me.

I won’t be posting these brackets for a while – they’re still works in progress.