Miss FOTA 32: Third Time’s the Charm?

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.

We’ll start, as before, with a basic triple-elimination bracket, and work from there. Triple eliminations are much less common that doubles, and there isn’t really a standard bracket. So I’ll create one, based on the assumption that the middle bracket is the late shift that we used as a base for the double-elimination entry, the 32lowerde.

Creating a third bracket is not only an unfamiliar task, but a somewhat fraught one, frequently tempting the designer to indulge some inequitable drops in order to save rounds in the third bracket. Here, however, there seems to be a nice, tight design, which disadvantages only the G drops. The pattern is FG.H.I.J.K.L.|.X.X, and the bracket itself is here: 32third3E. As always, it’s not possible to exclude the possibility of repeated pairings beyond the second round, and I doubt that the later drops are optimal, but I gave it a lick and a promise.

The performance of the base-case triple-elimination design is f(C) = 72.34 at T = 264.3. That’s more or less in line with the SE and the DE, which were 97.24 at 98.7 and 78.93 at 192.8, respectively. The question now is how much additional fairness we can buy by spending the remaining 235 minutes of our allotment wisely. (No, after the idea flopped in the DE context, I’m not the least bit tempted to try to add in any layers of recharges.)

With rounds A through T to consider, the possibilities for inserting extra games are daunting. I decided to augment two rounds close to the money, L and T, and all five rounds in the top bracket, A through E. The idea behind the latter choice is that extra fairness achieved in the top bracket would flow through to all parts of the design. I then went looking for extra games that could be inserted into the design with small effects on the overall time requirement. Because I’d already decided to expand B, C, D, and E, the expansion of middle bracket rounds that run in parallel with those rounds gave me a lot of extra play for not much time. So, rounds F, G, and H were also expanded to best of three. Everything else was left as a single game, except for the final U round, which took advantage of the free best of nine agreement.

Here are the final statistics from a qualifying run of 200,000 trials: fairness (C) = 49.89. fairness (B) = 0.883. Time = 490.4 minutes. All in all, a respectable showing. The entrant will be knows simply as Miss 32TE – there are not other well established triple-elimination formats, so she doesn’t need a longer name.

 

 

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