Here is another draft from my slowly-growing manuscript, Tourneygeek’s Guide to Tournaments. TGT Fairness
Only the first five pages, discussing fairness in general and fairness (A), are new, but because this now completes a first full chapter I’m also including the previously posted parts of the chapter than discuss fairness (B) and fairness (C).
As before, comments and criticisms are welcome.
One interesting bit of NCAA tourney trivia is that this year, apparently for the first time ever, one of the tens of millions of brackets submitted to online bracket challenge games was entirely correct through the first two rounds, or 48 games, of the tourney.
The chance that this bracket will remain perfect through the remaining 15 games is very small, but there will be many eyes on it. One year, there was a $1,000,000,000 prize offered for a perfect bracket (though, apparently for legal reasons, that prize is no longer on offer).
In a related discussion, I ran across a tidbit of expert opinion that may be useful in helping calibrate tourneygeek’s simulator.
In the last post, I compared the double-elimination portion of the Ottawa Men’s Bonspiel curling bracket against a slightly revised version of itself. But the more important comparison to make is with the a more conventional version of a double-elimination for 91 teams. And, as I’ll show, comparing the Ottawa bracket to a more conventional approach unexpectedly seems to open new avenues of inquiry for bye management.
As discussed in BBBR: 128s, there are a number of suitably-sized brackets from which to choose a comparator. In deciding which to use, I came upon another surprising virtue of the Ottawa-adapted format: it runs in just ten rounds, and there are almost no long waits except those caused by byes. The quickest of the 128s is the “128supershift“, which takes 11 rounds. So, to capture as much of the virtue of the Ottawa adaptation as possible in a (not very) conventional format, I chose the supershift.
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.
The bracket from the City of Ottawa Men’s Bonspiel tourney discussed in the last post had a number of features that make it look like it would be fun to play. In this post, I’ll consider whether a truncated version of the Ottawa bracket might make a good double-elimination bracket for a 91-team tourney in some other event.
This post will show the way the Ottawa-style brackets would look, both (nearly) as drawn by the Ottawa organizers, and with a few of my own alterations to eliminate some small sources of unfairness that seem to me gratuitous. In a later post, we’ll test these designs against a more conventional bracket.
The result, I’m guessing, is that the Ottawa bracket gives up a good deal of fairness (C) in exchange for its other virtues. Chief among these virtues is the way the tourney is experienced by the vast majority of players who lose in an early round.
In an ordinary double-elimination tourney, losing in an early round is very dispiriting. You know that you have a path back to glory, but you also know that that path is a long one, and your chance of success small. But you have a different prospect in Ottawa. Here the A, B, and C rounds losers all drop into a pristine new bracket, a bracket in which you have as good a chance as anyone else to win a named trophy.
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.
One of the perceived disadvantages of knockout tournaments is that they don’t offer much play to weaker (or unlucky) players. They’re very efficient, but that efficiency comes at the expense of participation – half the field in a knockout tourney get to play only one match before being eliminated.
Running a double elimination will give all teams at least two matches, as will running a consolation bracket. To offer each team at least three matches, you can run a triple elimination (which is quite rare and tends to raise thorny issues of bracket design), or add a last chance as a consolation-to-the-consolation bracket.
There is another way to guarantee each team a third match that is much less complicated than running a full triple elimination, and yet still offers a team a chance to win the overall title after losing the first two rounds. Here is such a bracket for a field of 16: 16DE3GG. It’s essentially a double-elimination bracket with an additional round in the lower. It this fair? How does it play?
Here’s another first draft of a section from the potential monograph, Tourneygeek’s Guide to Tournaments: FairnessC.
As before I’m linking to a PDF rather than putting the text here because I use some formatting that won’t work well as a blog post.
I think that fairness (C) is one of the more important concepts, and hope you will find this new explanation a good deal clearer than the one that was initially floated early in tourneygeek’s run, and added to in fits and starts since.
In a comment, Donald the Potholer suggested that there was a way of getting the simulator to run a Swiss-style tourney. At the time I thought he was incorrect, but with further thought, I see that it is possible to do this in a limited way, specifically for 32 players in five rounds. I stand corrected (and somewhat in awe of a reader who can infer from other discussions capabilities of my simulator that I didn’t realize it had).
So how would a Swiss Miss have fared had she been allowed to join the FOTA 32 pageant?
I subscribe to The Cricketer, a glossy cricket magazine published in England. My copy arrives in Indiana by way of Budapest after about two months transit time. But it’s worth waiting for. In the last issue I received, there’s an interesting tournament design problem relating to the scheduling of round robins.
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