Another Balanced Bracket

My friend Sean Garber send me a variation on the one drafted by Joe Czapski, which was discussed in the last post. Here’s an analyzed version, with luck = 1 (to facilitate comparison with Joe’s bracket): sg16bal

The two differ a little, but they both use the same contingent J1 match. Joe’s bracket keeps the A, B, and C drops together, while Sean’s spreads them out a bit. This I would expect to cause Sean’s to be a tiny bit better on fairness (C). But if there is a difference, it is indeed tiny. With Luck = 1, SG and JC are 15.82 and 15.86 respectively; and with luck = 3 it’s 68.42 and 68.45. Neither difference is not statistically significant, even after a million trials. The choice between them is, I guess, a matter of taste – if there’s one bracket that looks better to you, that’s a good enough reason to prefer it.

My taste runs to Sean’s bracket – it just looks right to me to interleave the drops as much as possible.

But in making the experiment I was reminded of one of the nice features of Joe’s bracket: that there’s no wrong way to order the drops. Sean’s bracket does require careful attention to the drops, and as luck would have it my first model had bad B drops. (Sean is not to blame – the drops were fine on the drawing he sent me. I just misplaced them when I was building a structure file for the simulator.) The bad drops caused a few early repeats in the F round, which in turn caused Sean’s bracket to lag, a bit, behind Joe’s. So, in the hands of anyone not careful to get the drops right, there’s less risk in Joe’s bracket.

I’m still not ready to anoint either one as a best practice and post drawings to my printable brackets page. I want more time to learn their features and limitations.

 

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