Dropping Seeds

I’ve exchanged a few emails with a reader who runs a small softball tourney. With his permission, I’ll work through the issues surrounding his particular tourney, showing where I see design issues, and suggesting a format.

First, however, I’d like to spend a post on a more abstract question he posed in his first email to me. The question is whether the drop patterns I suggest, and have tested primarily in blind draw tourneys, should be reconsidered when used in a seeded tourney.

Here’s part of the first note I received:

I have a question regarding the drops for seeded DE brackets. I see that you would arrange drops in a 16-team seeded DE tournament in a way that results in the least possible repeat match-ups later on in the lower bracket. However, is that necessarily the most important goal to achieve? Arranging the drops that way results in, assuming higher seeded teams win, match-ups of 6v9, 7v12, 8v11, and 5v10. Two teams play a team ranked 3 below them while the other two get to play teams ranked 5 below them, which would be a decided advantage for the latter two. Seeing that highest vs. lowest, next highest vs. next lowest, etc. match-ups in this round would be rematches from the first round, couldn’t it be argued that the next “fairest” way to arrange the drops would be such that all the teams have the same “rank difference” between them and their opponents (i.e 5v9, 6v10, 7v11, & 8v12) regardless of the slight increased possibility of rematches later on?

He runs his softball tourneys as full double-elimination, with recharge, fully seeded with seeds based on the teams’ regular season performance. He’s confident that his seeds are accurate, and that they’re also highly predictive or results – in three years of running his tourneys, there have just been a handful of instances in which a lower-seeded team has defeated a higher-seeded team. These factors suggest that he would do better not to shift the bracket, and he doesn’t. His basic pattern, then, is A.B.|.C.|.D.X.R.

In subsequent emails, he suggested two different drops patterns, each intended to improve fairness at the possible expense of additional repeat pairings. And it’s plausible that such drops might exist – when doing what I consider the standard drops, which can be found on the exemplar on the printable brackets page, I didn’t consider the ramifications of seeding at all.

Did his seed-sensitive drops patterns help? My simulations suggest that they do not. I used skill-heavy parameters such that the best team won about 65% of the time in all of the simulations.

Here are the fairness (C) figures and mean number of repeat pairings for my standard drops and the two alternative patterns:

standard:       67.11      1.38 repeats;
alternate1:     67.04      1.88 repeats;
altermate2:   66.95       1.74 repeats.

Neither of the alternate drops patterns was fairer than the standard bracket, and both of them increase the number of repeats. But maybe that’s because we’re not being thorough  enough with the drops. So I did a fourth set of drops, this time with the sole criterion of giving the advantage to the better-ranked team (assuming, of course, that the upper bracket goes according to form):

alternate3:    67.01      4.17 (!) repeats.

I suspect that the reason none of these alternate drops patterns improves fairness (C) is that the repeat pairings that the drops are no longer trying to avoid are themselves features that impair fairness.

There are many possible parameters I haven’t tweaked, so I can’t exclude the possibility that somewhere there’s a bracket where you can gain a little fairness at the expense of accepting a few more repeats. But so far, at least, this looks to be a pretty strong result, and a comforting one.

It appears that you don’t need different drops for seeded and unseeded tourneys.