In the last post, I brought the fairness (C) analysis up to date with respect to shifted and unshifted 16 brackets. In this post, I’ll do the same for 32s, with attention to the two different shifts available.
Recall that for 32 brackets there are two shifts available. The unshifted bracket, 32lowerus, A.B.|.C.|.D.|.E.X, an early shift, 32lowercd, A.B.C.D.|.|.E.X, and a late shift, 32lowerde, A.B.|.C.D.E.|.X. Here are the fairness (C) and (b:X) numbers for each (this time omitting the uninteresting upper-bracket rounds):
|luck = 1||ABvCvDvEX||ABCDvvEX||ABvCDEvX|
The early shift doesn’t have any obvious advantages (apart from saving one round). Fairness (C) is virtually the same. But the late shift is distinctly better. The critical round is the lower bracket final, which is M unshifted and L with either of the shifts. Only the late shift avoids giving the E drop the massive advantage of dropping directly into the lower bracket final.
With a greater role for luck, the benefits of the shift, particularly the late shift, are more dramatic. Again, the late shift’s L round is much better than that of the early shift – that’s not a surprise, as the L round doesn’t take a drop. But also look at the rounds that take the E drops: M, L, and K. The E drop into the lower bracket semi-final is in almost perfect balance with the rest of the table.
|luck = 3||ABvCvDvEX||ABCDvvEX||ABvCDEvX|
All in all, the best that can be said for the unshifted bracket is that it sometimes doesn’t hurt too much. Sometimes there will be some non-fairness reason, like a concern for timing, to keep the traditional bracket.
If there is to be a shift, if should be the late shift, again, unless there’s an unusual reason go do the contrary. The one obvious reason to do that is where the middle bracket is incomplete because the E1 loser doesn’t drop – that is, when the tourney is a consolation tourney rather than a real double elimination.
None of these are new conclusions. But it is a little comforting to find that the old findings are not being significantly compromised when challenged with teh additional analytical tools that are now available.
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