Seedy and Shiftless

Another surprising result today.

I ran a 16DE through the simulator, this time seeding the entries – all of my previous runs have been blind draw. On the basis of what I’ve seen so far, I decided to run only the shifted bracket, which is in line with my conclusion that the shifted bracket is, or at least should be, preferred. But there’s more to the story.

I expected a big boost in fairness, and I got one – 12.28. But I was really expecting a bit more. It wasn’t until I was painstakingly copying numbers into the analyzed bracket from my simulation printout that I noticed something really striking. The drops were creating huge mismatches in the lower bracket, and for all of those matches, the much stronger player was the team dropping in.

It makes sense. The seeding protected the better teams in the upper bracket, so they stayed up there longer. The lower bracket was filled mostly with bad teams that had been trounced by the good teams. So the dropping teams were better, and the rounds they were dropping into were filled with teams that were worse.

So, perhaps this is a case in which fairness is best served by the ordinary, unshifted structure. There’s nothing to be done about the B drops, but we can refrain from moving the C and D drops earlier. And, sure enough it helps a good deal.

The overall fairness for the unshifted bracket is 12.53! The gain from unshifting the brackets in a seeded tournament is much greater than the gain from shifting them in a blind draw event.

With respect to repeated pairings, the results are mixed. The unshifted bracket has a few more total repeats: 1.35 as opposed to 1.23. And it has five matches that can repeat, as opposed to four for the shifted bracket. But a greater proportion of the repeats are in the last two matches, which most people would expect to repeat frequently. Excluding the last two matches, the unshifted bracket, despite having one more match that can repeat, has fewer: 0.30 as opposed to 0.39.

The unshifted bracket comes into its own. Apparently it’s fairer and no worse for repeat matches when it’s used for a seeded tournament. So it was harsh for me to call it “shiftless”, and I hereby reprieve it, calling it “unshifted” instead. But the old name is useful as a sort of mnemonic for when it should be used: seedy and shiftless go together.

Is there any advantage to shifting the bracket in a seeded tournament? Well, it still has the advantage of saving a round, and if that’s what’s most important, perhaps you should reconcile yourself to the added unfairness. But the price is high.

It remains to be seen how general this result is, so perhaps it’s too soon to announce a rule that unshifted brackets are to be preferred for seeded tournaments. More on this tomorrow.

Here are the analyzed brackets for the tournaments discussed in this post: 16-upper-shiftless-analyzed-seeded, 16-lower-shiftless-seeded-analyzed, 16-upper-shiftless-analyzed-seeded, and 16-lower-shift-seeded-analyzed