A common desire for many tournaments is to organize the competition to make the best use of limited time.

A friend runs a monthly backgammon tournament that, in the past year, has drawn from nine to 15 entries. It starts at noon on a Sunday, and needs to be finished by six. For some years, this tourney has been played with a rather unusual lower bracket. The upper bracket is a standard 16. The lower bracket is like a standard (unshifted) 16 double elimination bracket, except that takes only the first three rounds of drops, and has no provision for the winners of the two brackets to play for the championship.

My friend want to know if he would be better off by using a shifted 16 consolation bracket. We speculated on the effects of the change for a while, but I’ve been looking at brackets long enough to know that the best way to get a bracket to reveal its secrets is to run it through my simulator.  And, sure enough, comparative simulations help to show some features of his non-standard bracket that were not initally apparent to either of us.

In this post, I’ll report the results of the simulation with respect to the bracket architecture, and in the next I’ll explore some other questions, including the question of what payout schedule ought to be used.

Continue reading “Getting the Most from an Afternoon”

If there’s a single idea behind tourneygeek, it is that a lot of badly designed tournaments are being run, often because their organizers have simply never considered some of the available alternative designs. If some people think there’s only one right way to run a tourney, they’re likely to make a fairness (A) claim whenever those expectations are not honored.

The last post considered the strength or weakness of this objection based on the source of the expectation. This one will consider the extent to which the claim is stronger or weaker according to whether people have reasonably relied on those expectations.

Many, perhaps most, innovations in tourney design aren’t vulnerable to the strongest sort of fairness (A) objection because no one is likely to behave any differently in reliance on an unmet expectation. But where there is reasonable reliance, the objection is a strong one.

Continue reading “Fairness (A) and Reliance”

In the last post, I suggested that the strength of a fairness (A) claim can be assessed according to the the source of the expectation that it is based on, and according to the reliance placed on those expectations.

Let’s explore some of the possibilities in a particular context. There’s a 64-team double-elimination tournament. The winner of the upper bracket is defeated by the winner of the lower bracket in one game. There is no recharge round – the upper bracket winner does not get another chance to win the title. Is this fair?

From a fairness (C) perspective, there may be a reasonably clear answer: in a low-luck game like tennis, it is fairer to have a recharge round, but in a high-luck game like baseball it is fairer not to have one. But this result is not well known – the matter is more likely to be resolved by appealing to fairness (A). How strong is the fairness (A) claim that there should have been a recharge round?

In this post, I’ll discuss the source of the expectations, and in the next I’ll discuss reliance.

Continue reading “Fairness (A) and the Recharge Round”

Fairness (A) is the fairness of meeting expectations. Regardless of whether a particular practice is equitable (appealing to fairness (B)), or meritocratic (fairness (C)), tourneys are often judged to be unfair because they’re not run the way that people expect them to be run.

Most of the discussion of fairness on tourneygeek concerns fairness (B) or fairness (C). There’s a good reason for that – tourneygeek seeks, where it can, to provide clear answers to questions or whether something is more or less fair, and so tends to concentrate on the two sorts of fairness that are, at least to some extent, quantifiable. Fairness (A), in contrast, is unquantifiable because people’s expectations tend to be qualitative rather than quantitative. Thus disputes about fairness (A) can rarely be definitively resolved.

But this does not mean that fairness (A) is unimportant, or that there’s nothing sensible to say about why some fairness (A) claims are stronger than others.

The strength or weakness of a fairness (A) argument depends on two factors: the source of the expectation, and the degree to which that expectation is relied upon. Considering the source goes to whether the expectation is reasonable, and considering the degree of reliance goes to whether the expectation is consequential.

The next two posts will work through an example to show how considerations of source and reliance might help us assess the strength of a fairness claim in a particular context.

 

 

 

From time to time I look back at old posts. Recently I looked at my pair of posts on the issue of recharge rounds, particularly the ones that require the winner of a “losers bracket” to defeat the winner of the “winners bracket” twice in order to win the overall championship.

Here I considered recharge in terms of efficiency, participation, and spectacle, and concluded that none of those three considerations really supported the practice of including a recharge round. But here I did some simulations to see if recharges contributed in a positive way to fairness, especially fairness (C). I concluded, with some surprise, that fairness was enhanced by the use of a recharge round.

But in looking back at that post, I’m struck by the fact that I did all of the simulation work on 16 brackets. A 16 bracket is the smallest bracket that’s capable of being shifted. Perhaps the results would have been different if I’d used a larger bracket, where the number of additional rounds played by players coming up through the losers bracket is greater. So I re-did the experiment, recently, using 64 brackets rather than 16s. And, sure enough, the results are somewhat different.

Continue reading “Recharge Redux”

I recently revised the A drops on my 48 double elimination bracket so that the byes would be more evenly distributed when the bracket was run with only 40 entrants.

To validate the change, I’ve run extensive simulations, and reported the results in a form I haven’t used for a while: the analyzed bracket. It was an interesting exercise, and one that shows how errors of this kind can easily go undetected. The analyzed bracket does, indeed, show the problem, but it’s subtle enough that it would be easy to overlook if you didn’t know where it might lurk.

Continue reading “Where the Bodies are Buried”

I’m occasionally asked to draw brackets for upcoming backgammon tourneys, and one of the popular requests is for a 48 bracket – that seems to be the size of the field fairly often these days.

On my printable brackets page, I’ve supplied only brackets for the powers of two, with the idea that an in-between bracket like a 48 is really just a 64 with 16 fewer lines, so that you can run the tourney just fine by using the seeding lines on the 64 to allocate byes to the opponents of the lines seeded 49 to 64.

Some have complained, however, about the way that the 48 brackets I’ve supplied play. Specifically, they dislike the fact that some players get a second bye in the lower bracket before others have gotten a first bye anywhere. This is a valid objection, and one that I’ve  taken too long to address. But I’ve done so now, and posted a 48 to the printable brackets page that’s better than the ones I’ve been supplying in spreading the byes more evenly. Continue reading “An Improved 48 Bracket”

Now to complete the design of my friend’s tennis league. In the first post, we’d gotten as far as showing how the partnerships should be formed. Now we need to determine who plays who in the actual matches, taking into account a preference for “interesting” matches.

In an earlier post, the quality my friend calls “interestingness” was called “competitiveness”, and discussed briefly here. In that post, I speculated that the only format that seemed particularly designed to enhance competitiveness was the Swiss system. That led me, in an effort to meet my friend’s preferences, to incorporate the pairing logic of the Swiss system into the design for his tennis league.

Continue reading “A Social Swiss, Part II”

As discussed in the last post, there are some difficult problems associated with deciding what players are entitled to participate in what events. Perhaps it will comfort organizers who are wrestling with such problems to consider a context in which the sorting problem is exceptionally complex and difficult: the Paralympic Games.

Continue reading “Extreme Sorting: the Paralympics”

In my friend’s tennis league, the players prefer “interesting” matches, which in this context means matches between teams of roughly equal skill. In the last post, I showed how I generated partnerships, but not matches, for the league. Presently, I’ll discuss how the matches are done, which will also explain why I’m calling this format a “social Swiss”. But first it’s worth discussing the idea of interesting matches in general.

A concern for interesting matches is most common when choosing which players or teams are eligible to enter an event. The tournament will generate more interesting matches if the range of skills among the entrants is small.

Continue reading “Sorting Out the Entrants”