It’s time to address the thorny issue of byes in elimination tournaments.
So far, we’ve been considering only tournaments that conveniently happen to have a number of entries that’s an even power of two: 16 or 32. If you’re running an elite tournament, with people clamoring to get it, you can, if you like, decide to accept only such an convenient number of entries. But many tournaments are not at all elite, and gratefully take more of less everyone who shows up. And if the number of people who show up is not a power of two, you generally award the number of first-round byes necessary to bring the number of entries up to a power of two for the second round.
In this post, I’ll begin to discuss the effect this has on the tournament. In later posts, I’ll look at a number of other issues, but here I’ll just offer one analyzed bracket so that you can begin to see the effect byes have on a tournament.
Continue reading “Good Byes to All That”
Tourneygeek grows in a haphazard fashion. For me, that’s what makes it fun to write – I can speculate when I’m feeling speculative, analyze when I’m feeling analytical, draw new brackets when I’m feeling (slightly) artistic, or add new features to my tournament simulator when I’m feeling geeky.
But readers can be forgiven for not sharing my mood of the moment. So in this post, I try explain how the various threads – theory, practice, individual games, resources, and geekery – have developed, and show how to follow the main themes from post to post.
Continue reading “A Guide to Tourneygeek”
As promised, I’ve created a page for printable bracket forms. They’re free – please download and enjoy. I want them to be useful, so I haven’t locked the PDFs, but I’d appreciate it if you’d leave the tourneygeek.com tag that shows where they come from.
Continue reading “Printable Brackets Have Arrived”
In the last post, I suggested that game play is constrained by four kinds of limitation: explicit rules, implicit rules, background rules, and physical limitations. Here I’ll explore the different sorts of rules, and how they interact, in the context of line calling in tennis and in table tennis.
Continue reading “Ins and Outs”
Let’s build on our definition of game playing to define some related terms. Today we’ll talk about rules and other limitations.
By our previous definition, game playing is the pursuit of arbitrarily assigned value. In almost all cases, there are, in addition to the assigned values, constraints on the way the arbitrary value can be earned. These constraints are of two kinds – limitations that the player is welcome to strive against and overcome, and rules that (usually) need to be observed.
At my undergraduate school, St. John’s College in Santa Fe, there was an end-of-the-year festival we called the “Real Olympics”, or simply “Reality” for short. One of the activities in the Real Olympics was a game called Spartan madball. It was played on a soccer field. There was a ball, and two goals. But there were no other rules. Continue reading “Rules and Limitations: Spartan Madball”
Yesterday I discussed converting the competition model in the tournament simulator to use Gaussian factors rather than uniform factors. Today I’ll show the results for eight versions of the 16-team double elimination tournament.
As predicted, this has so far yielded results comparable to the old model. And tweaking the new parameters for luck and the elite entry cutoff have yielded results in the expected direction. Continue reading “Taking the New Model for a Spin”
Tourneygeek has now gone Gaussian.
I’ve had some misgivings about my initial efforts on the tournament simulator. The individual match model simply added a uniformly-distributed random number representing the skill of the player (which didn’t change over the course of each iteration of the tournament) to another uniformly-distributed random number (fresh each time) for each of the two players.
But uniform distributions are rare in the real world. Continue reading “Retooling the Simulator”