Reader metzgerism alerts me to the fact that in curling, “three-game guarantees are practically sacrosanct”. He also mentioned a tourney being held right now. The City of Ottawa Men’s Bonspiel.
This event carries a concern for the value of participation to a level I have never before encountered in a bracketed tourney. The draw for this tourney can be found here. Participants are guaranteed not just three but five games (though it appears that for a particularly unlucky or inept team, one of the five games may be a bye).
This is a complicated structure indeed, but it’s worth taking a close look at it.
I stand in awe of the organizers of the Ottawa tourney, where 91 teams compete over five days at ten venues. It took me several hours to create a structure file so that I could simulate the tourney, and I didn’t have to do any of the really tricky parts, like assigning matches to individual sheets, or scheduling it all so that teams could get where they needed to be. As metzgerism noted, “schedule balancing is far more critical than fairness in these tournaments”. That’s just as well, because there are any number of features in the brackets that I know from past work cause fairness deficits. I won’t report any fairness (B) or (C) statistics from my simulations.
Instead, I’ll focus on the broad structural features that I find distinctive. There are ten separate brackets, each of which awards a named trophy to its champion. I’ve simulated them assuming that luck = 3.
The first bracket is the bracket for the Hogsback Trophy, and it could stand on its own as a single-elimination tourney. It’s basically a 128 bracket, truncated to a 96 by evenly distributing 32 byes. There are five additional byes, four of which are grouped in such a way as to cause byes to appear past the first round. It does not appear that there’s any seeding in the Hogsback bracket, but I can’t be sure – there are no seeding numbers, but perhaps someone familiar with the Ottawa curling scene would notice that the 32 byes went to the better teams. I’m assuming that it’s a blind draw, in which case the average Z score for the winner is about 1.367.
The next three brackets are populated by the A, B, and C drops from the Hogsback bracket. The A drops play for the Billings Trophy; the B drops play for the Colonel By Trophy, and the C drops play for the Laurier Trophy. The Billings bracket is the easiest to win because every team in it lost its first match, so that the average Z score about -0.240, and winner’s average Z score is 0.740. The teams in the Colonel By bracket are a little better because the B round includes some first-round winners. The average Z is -0.139, and the average trophy winner is 0.882. The Laurier bracket is won by a team averaging 0.911, not much higher than the Colonel By winner because while the average bracket team is now above average at 0.116, there’s one less round of skill progression.
The trophy for the fifth bracket is called the Open Grand Aggregate. This bracket, added to the first four, turns the tourney into a double-elimination. The top half is populated by the winner of the Hogsback trophy together with its D, E, and F drops. The bottom half is populated by the winners of the Billings, Colonel By, and Laurier trophies, and by the G drop from the Hogsback. The bracket is shifted in the pattern D.E.F.G.|.|, with the winners of the four trophies also dropping with the G. The top half, with the Hogsback winner and the D’s, E’s, and F’s, is somewhat stronger, winning the OGA trophy 52.3% of the time. There’s no recharge. The mean Z score of the winner is 1.507.
This curious arrangement led me astray in the first version of this post, as I swapped the position of the drops for the G winner (i.e., the Hogsback champion) and the G loser. This is one of the features of the bracket as a whole that would seem to compromise fairness (C), as it’s generally unfair to send the winner and loser of a match to the same round of the same bracket. And here, the unfairness to the Hogsback winner is greater because it drops into the somewhat stronger top half of the OGA bracket, so that its chances of winning the OGA trophy decline from 17.6% to 13.5%.
The remaining five brackets are all consolation brackets, absorbing teams that wash out of the first five without having played five games. The different brackets vary a good deal in strength depending on which drops they receive. The weakest of them is very weak indeed.
The sixth bracket awards the Heritage Trophy, and produces a winner with Z = 0.538. The seventh awards the Governor General’s Trophy, and weighs in at 0.975, making it the third most difficult trophy of the tourney, after the OGA and the Hogsback. The eighth awards the Pontiac Trophy to a team averaging 0.278. The ninth awards the Rideau Falls Trophy to a team averaging 0.386.
And the final bracket awards the Mackenzie King Trophy to one of eight teams, most of which are there because they have no wins and four losses. This trophy’s winner is well below average skill for the tourney as a whole at -0.534.
There are any number of ways in which this peculiar tourney design could, at least in theory, be make fairer. But I don’t know if any of those changes would be practical.
And I doubt that they’d make it any more fun to play. This a a design for people who love to curl, and who want to do a lot of it. I find the Mackenzie King Trophy, especially, completely charming.