Learning from Ottawa, part II

In the previous post, I suggested that the first parts of the Ottawa Men’s Bonspiel design could be adapted to a large double-elimination tourney in other contexts. It’s time to put it to the test.

In the last post, I linked to brackets for the Ottawa design, both (nearly) as it was played in Ottawa, and with a few technical adjustments intended to improve fairness. In this post, I’ll look at the effect of those technical adjustments.

For the simulations, I used luck = 3, and a payout schedule that awarded 28% to the OGA winner, and 18% each to the winners of the other four named trophies. I doubt those payouts reflect the values of the Ottawa Men’s Bonspiel itself, but they’ll do for a generic 91-team tourney that wants to pay five places.

The two minor tweaks to the Ottawa-like format were these: I redistributed the byes, and  I interleaved the D, E, and F drops.

The effect on the overall fairness (C) result was negligible, 97.70 for the actual pattern, and 97.69 with my tweaks.

Looking to fairness (b:X), however, the results are quite visible:

f(b:X) original tweaked f(b:X) original tweaked
A 8.60 7.54 H 21.39 19.21
B 12.83 12.87 I 16.35 6.40
C 4.30 4.64 J 16.33 3.02
D 4.10 2.91 K 4.03 1.61
E 3.73 1.00 L 2.17 1.44
F 2.14 0.32 M 6.89 2.08
G 0.77 0.22 N 3.52 1.86
O 2.48 2.82
P 77.53 77.46
Q 65.69 65.58
R 56.50 56.32

There’s a significant difference for some of the rounds, but not others. The tweak doesn’t seem to help with a huge imbalance in the P, Q, and R rounds. M and N, as might be expected, benefit from the interleaving of drops. In the upper bracket (shown on the left), round B (where the byes land) is predictably bad. Apart from round C, which I cannot explain, the other rounds show some improvement, probably from the more even distribution of byes.

All in all, I think the tweaks were worth making, though hardly essential.

 

 

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