Category: Uncategorized

. . . who is the fairest one of all?

Now that we have (still tentatively) a fairness (C) measure that gives us a clear target to shoot for, 100%, let’s see how close we can get to that number. We’ll use the simulator, with the new fairness (C) as our magic mirror to see what design gets closest.

The ground rules are these: The contest is single-elimination. All designs have to have eight teams (which means there will be exactly seven matches). Skills are at random from at least half of a normal curve. Perfect seeding is available. Fairness (B) doesn’t count for anything, except that every player has to have some chance of winning the first prize. Any configuration of lines and rounds is acceptable. All brackets will be evaluated at luck = 1. Payout must be either winner-takes-all or 65%/35%.

Continue reading “Magic Mirror on the Wall …”

I started to apply the new fairness (C) measure to a number of different designs to see if it was working properly. I had a nagging suspicion that I must have had a good reason to reject the more obvious formulation of the statistic when I settled on the present measure. It didn’t take long for a problem to appear.

After a number of successes on larger brackets, I thought I’d check the measure out on some very small ones, like the 8SE I’ve been using as an example in my TGT series. It seemed to be working, until I looked more closely.

Continue reading “A Fly in the Ointment”

For some time, I’ve been worried in the back of my mind that the fairness (C) statistic was rather hard to interpret. I’d forgotten the details of how is was calculated, but suspected that whenever I got around to looking at it again, I’d be unhappy with the formula. I didn’t want to be unhappy with the formula because I couldn’t do anything about it without revising my simulator, and I was scared to do that.

Sure enough, the time came when I needed to look at fairness (C) again. I was getting ready to write the section on fairness (C) for TGT, and sure enough, the formula looked absurd to me. How could I have done that? Why have I lived so long with such a silly formula? The needed change was obvious.

Continue reading “A New Fairness (C) Measure”

Here’s another draft section from the proposed Tourneygeek’s Guide to Tournaments monograph, this one discussing Fairness (B): FairnessB.

Here’s a first draft for another section of the nascent Tourneygeek’s Guide to Tournaments manuscript: Skill and luck.

I’m linking to a PDF because I’m not clever enough to figure out how to get the thing to format properly in the blog itself.

As always, comments and corrections are more than welcome.

In Tourneygeek’s Guide to Tournaments I set out a proposed table of contents for a monograph I may (or may not) write some day. I’d like to present the important things I think tourneygeek teaches in a more straightforward manner.

In this post, I’ll share my first attempt to write a section of this book. It’s about the maxims of tournament design. Regular readers may recall that so far I’ve discussed only three maxims – the fourth is new. Scroll down to see what the fourth one is.

Continue reading “TGT: Four Maxims of Tournament Design”

The further this blog goes into the details of particular design issues, the harder it may become for the director who seeks advice on particular practical problems to find relevant information in the blog.

From the beginning, I’ve had in the back of my mind the possibility of another sort of publication – probably a monograph, with these more practical concerns in mind. Here is my first attempt at a possible table of contents for such a monograph: TGT Outline.

Comments and corrections are more than welcome. What isn’t here that should be? What parts of the outline should be rearranged? Is this worth doing at all?

 

The past several posts all amount to another negative result.

I started by revisiting the 16DE “Balanced Bracket” posted by Joe Czapski on his tournamentdesign.org page. The idea was to see if my earlier analysis, which had been done before I’d developed my current fairness (C) metric and tourney simulator, was still valid. Long story short: it was. The Balanced Bracket has some appeal, but it does sacrifice fairness, and that’s a significant disadvantage in my estimation.

This would have been a short single post but for the fact that I made a big mistake. But sometimes you learn more from your mistakes than from your successes, and that happened here. I learned that I need to be more careful about how fairness (C) is used.

Continue reading “Requiem for the Balanced Bracket”

Now it’s time to reconsider the 16DE brackets from a few posts ago, including Joe Czapski’s “Balanced Bracket” from tournamentdesign.org, to see whether any of those analyses was infected by the ugly bottom effect.

In addition to the designs tested before, I’ll include one new one proposed by the same commenter who suggested the Ugly8. I’ll call this the Ugly16, though perhaps that’s not entirely fair, because I’ve taken care in this case to mitigate the ugliness, a bit, by interleaving the A and B drops (a step I didn’t take while drawing the Ugly8). The Ugly16 has the pattern 16: {AB.C.|.|.D.X.R}, and looks like this: Ugly16.

And, just for fun, let’s also test “Medusa16”. This will be a maximally-ugly 16DE created the same way we created Medusa for the 8DE, on the pattern 16: {CD.C.B.B.B.B.A.A.A.A.A.A.A.A.X.R}, which, for the morbidly curious, looks like this: Medusa16.

Continue reading “Ugly Bottom Effects in 16DEs?”

Before I start looking into past results to try and root out the baleful influence of the ugly bottom effect, I though I’d try to find a pure example of the effect. And so I’ll try to design a tourney with the ugliest possible bottom.

The feature that earned the original Ugly8 format its name was dropping the A drops and the B drops together into the D round: 8DE: {AB.C.|.X.R}. But if we really want to make the worst possible bracket, we need not just to drop later rounds together, but to drop them before the earlier rounds. And let’s also spread this maximally-ugly bottom into a single cascade. Here’s my candidate for the ugliest possible 8DE: {BC.B.A.A.A.A.R.X}. Here’s what that looks like: medusa8. I dub this the Medusa8 bracket, in honor of the character from Greek mythology who was so ugly that whoever looked at her turned to stone.

Kids, don’t try this at home! This is a format that takes ten, or occasionally even eleven, rounds to play. And I guarantee that everyone who descends into the ugly bottom will complain. But computers don’t mind, so let’s see what the simulator thinks of Medusa8.

Continue reading “The Ugliest Bottom”