This is a short post extending the fairness analysis of shifting brackets to a larger example. A 64 bracket can take two shifts, which should be expected to show the same sort of effects as were seen in 16s and 32s. And that’s exactly what happens.
Below are the f(b:X) tables, with valued for the rounds that take drops in bold.
The most remarkable number, here, is the 0.0 (rounded from 0.015) entry for the final of the shifted, luck = 3 bracket. In fact, for the final the lower bracket winner is even a tiny bit better, on average, than the upper bracket winner (1.294 and 1.281, respectively). There are simply no conspicuously bad rounds in that bracket.
The pattern hasn’t changed. The shift is somewhat beneficial for low-luck events, chiefly because it has a great round N. And the shift really comes into its own in the high-luck events.
It’s still true that the shift would be worse for a high-skill seeded event. I won’t bother to show the entire tables, but using tennis-style seeding with five tiers, f(C) for a low-luck 64 is 19.98 for the shifted bracket and 19.27 without the shifts. For high-luck, the shift is still better, 79.18 to 81.40.
So, for almost all real tourneys, the shift is recommended – it not only saves two rounds, but it also improves fairness (C).
luck = 1 | f(C) = 24.72 | f(C) = 23.52 |
ABvCvDvEvFX | ABCDvEFvX | |
G | 8.4 | 5.9 |
H | 21.3 | 18.4 |
I | 4.6 | 23.4 |
J | 6.4 | 24.4 |
K | 2.6 | 6.7 |
L | 17.6 | 2.2 |
M | 1.0 | 5.1 |
N | 20.8 | 1.5 |
O | 0.1 | 4.3 |
P | 7.2 | |
Q | 4.4 | |
luck = 3 | f(C) = 89.37 | f(C) = 85.38 |
ABvCVdvEvFX | ABCDvEFvX | |
G | 6.9 | 4.2 |
H | 4.4 | 3.7 |
I | 3.1 | 3.5 |
J | 13.6 | 3.0 |
K | 2.5 | 1.4 |
L | 14.8 | 5.1 |
M | 1.4 | 2.7 |
N | 13.2 | 0.1 |
O | 0.0 | 0.0 |
P | 4.3 | |
Q | 0.3 |
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