The Dolly Bracket

Bad news for my plan to sell the simulator as a magic mirror. The marketing department tells me that I’m missing my key use case. It seems that the market for magic mirrors is composed almost entirely of insecure, vain old tyrants like the Evil Queen, who are not really looking for objective information about who’s the fairest, but for flattery. Apparently Donald Trump is willing to spend up to $5 Billion of our money, but only for a bracket that will always declare that he’s the fairest.

So, let’s go back to the Evil Queen use case. She wants the mirror to tell her that she’s the fairest, but the annoying mirror says that Snow White is more fair. Maybe I can fill a market niche by using the simulator to find a bracket that will make second-seeded Evil Queen win over a first-seeded Snow White. But the fairest of them all bracket we built is won by the Evil Queen only 22% of the time, and chooses Snow White in 56% of trials. Evil Queen is not going to pay the big bucks for that result. I’ll probably be thrown in the dungeon, or at least ridiculed for “fake tourneygeekery” in her tweets. My computer will be seized and disabled, giving new meaning to poisoned apple.

We need a new bracket, and, while we’re at it, a new marketing campaign.

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Magic Mirror on the Wall …

. . . 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%.

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A Fly in the Ointment

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.

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A New Fairness (C) Measure

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.

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TGT: Four Maxims of Tournament Design

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.

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