Where the Bodies are Buried

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.

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An Improved 48 Bracket

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”

A Social Swiss, Part II

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.

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Extreme Sorting: the Paralympics

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.

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Sorting Out the Entrants

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.

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A Social Swiss

A friend asks for help with pairings for a tennis league he runs.

There are eleven people in the league, and the league has two tennis courts reserved once each week for 24 weeks. Each week, the league will play a doubles match on each court, eight people playing in four partnerships, with three people getting a bye each week.

Here are the parameters he’d like to observe:

  1. The schedule needs to be determined in advance, so that everyone knows which weeks they’ll be playing, and with which partner. It’s not necessary for them to know who there opponents are;
  2. Each player should play nearly the same number of times over the 24 weeks;
  3. Everyone should play with everyone else at least once, but no more than twice;
  4. No one should draw a bye two weeks in a row; and
  5. The pairings should, as far as possible, encourage “interesting” matches, with the better players tending to play other good players, and the weaker players drawing other weak players.

I’ve got a format for that. I’ll call it the “Social Swiss”. In this post, I’ll show how the first four criteria can be met, leaving the fifth criterion for a later post.

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