Using the new tools: f(C), f(B) and f(b) in the 32 Bracket

Two posts ago, the fairness (B) statistic was generalized so as to be applicable to any round in a bracketed tourney. And in the last post, I inverted the fairness (B) and fairness (C) statistics to make them easier to interpret. It’s time to put these new tools to work to show how they can provide a clearer picture than the old ones. To do this, I’ll revisit the question discussed by one of the earliest of tourneygeek’s empirical results in Shifting a 32 Bracket.

n.b., this analysis was briefly posted using the old, un-inverted statistics and (much worse) with significant mistakes in the analysis – the current version is, I hope, not only clearer but more correct.

Continue reading “Using the new tools: f(C), f(B) and f(b) in the 32 Bracket”

Generalizing Fairness (B)

Fairness (B) has been defined as the quality of a tournament design that answers the desire to give everyone an equal chance. As discussed elsewhere, it is sometime in conflict with other forms of fairness.

The only fairness (B) metric defined so far is rather a crude measure, suitable only for assessing the equality of opportunity in first round of a tournament, and then in a form that was greatly affected by the structure of the prize fund. In this post, I’ll propose a new fairness (B) metric which can be applied to any round, and is normalized so as to be unaffected by the absolute value of the prize fund.

As will be made clear in future posts, this new fairness (B) metric will be a powerful tool for analyzing various aspects of a tournament.

Continue reading “Generalizing Fairness (B)”

Rolling the Bones, Part IV

In casino craps, there are specific requirements for a throw of the dice to be considered valid. The details vary a bit, but in all cases, the dice are thrown a considerable distance, and required to bounce off of a wall. This is impractical for backgammon because there are only a few inches of space to deal with.

One method of ensuring fairer rolls is the use of a device that attempts to ensure that the dice bounce around a good deal within a limited space. Such devices are generally called “baffle boxes”, though they are also sometimes called “dice scramblers” or “dice towers”. These devices have been used for many years, but have recently become more fashionable, and perhaps also more controversial.

Continue reading “Rolling the Bones, Part IV”

Rolling the Bones, Part III

The first two parts of this short series called attention to what I called the “kabuki” elements in the rules and customs surrounding the throwing of the dice in backgammon. This was perhaps, a little unfortunate. Recent figurative use of the term “kabuki” seems to be intended to be derisive, and often in a way that’s rather offensive to Japanese culture.

Most of the kabuki elements of the dice-throwing rituals in backgammon are said to be in aid of deterring dice cheats. And some, but by no means all, of them are actually useful for this purpose. In this post, I’ll discuss the extent to which the dice rituals of backgammon relate to cheating.

Continue reading “Rolling the Bones, Part III”

Rolling the Bones, Part I

As discussed elsewhere, backgammon players have varied reactions to the enormous role that chance plays in the game. Among of the interesting implications of this are the elaborate, and sometimes contentious, practices that surround the rolling of the dice. In serious backgammon, rolling the dice is not just a convenient way to inject a chance element into the game – it had grown into a kind of kabuki theater.

This post begins a short series on dice rolling in backgammon with a consideration of the dice themselves.  Continue reading “Rolling the Bones, Part I”


The Championships (better known as “Wimbledon”), one of the world’s premier bracketed tournaments, is due to start in a few days.

I’ll forgo a full FEPS analysis of Wimbledon’s bracket format. Presumably the All England Lawn Tennis & Croquet Club has thought things through very carefully, and settled upon a format that meets its needs. At a guess, I imagine that the two main factors were fairness (A), honoring the traditions of the event, and spectacle, maximizing the economic value of the event, not necessarily in that order.

One of the distinctive things about the Wimbledon bracket is its use of partial seeding. Only the top 32 players in the 128-player main draw are seeded, with the other 96 being allocated their initial bracket positions by blind draw. This means that even the top-seeded player could draw the 33rd-best player in the draw in the first round, and that the lowliest qualifier could draw another lowly qualifier in the first round. And the 32 players fortunate enough to be seeded are still slotted into the bracket in a somewhat random way.

Seeding of any kind tends to improve the fairness (C) coefficient of a tourney. This post reports the results of some simulations that show how big this effect is, and compares it to other possible ways of seeding (or failing to seed).

Continue reading “Wimbledon”