Here, as promised, are the f(b:X) tables for the five different versions or our hypothetical 128-player double elimination tourney.
(As the formal notation gets a bit unwieldy for a bracket as large as a 128, I’ve named the shifts after the files in the last post.)
The take-aways: the best of the shifted brackets are always better than the unshifted bracket. In the high-luck scenario, all five versions do a remarkably good job of equalizing the final. The “early” shift (which is the only shift that, like the unshifted version, sends the G drop to the lower final) does consistently worse than the other shifts, and for high-skill events it’s even worse than the unshifted bracket.
Somewhat to my surprise, the “super” shift, which squeezes an extra round out of the tourney, does quite well – event to the point of being the best performer for a high-luck event. I’m not ready to anoint it a best practice and post it to the printable brackets page, but it certainly bears further investigation.
|luck = 1||26.45||26.57||24.93||25.01||25.45|
|luck = 3||97.12||96.16||93.46||92.85||92.41|