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.
tourneygeek.com 