## The Big, Peculiar Bracket, a Postmortem, Part III

In two earlier posts, I examined a set of brackets for a 96-team double-elimination tourney with a third consolation bracket. This format was originally discussed in a post called A Big, Peculiar Bracket (BPB).

These analyses identified a number of apparently sub-optimal features of the bracket. In this post, I’ll report the results of series of simulations of the BPB, and compare them with an alternative bracket that maintains the same overall structure, but addresses several of the identified issues. The result is that the BPB can be somewhat improved by fixing them.

A subsequent post will address the more fundamental issue of whether the unusual structure of the BPB makes it perform better than a more conventional bracket.

## The Big, Peculiar Bracket, a Postmortem: Part II

Having considered the process of adding a third bracket in a few simpler contexts, we now return to the Big Peculiar Bracket (BPB) to look particularly at the third bracket that worked with the upper two, which together constituted a double elimination.

In the first part of this analysis, we identified some questionable structural elements. But the apparent flaws in the upper two brackets pale in comparison to those of the third bracket.

Still to come in this series are the results of simulations, comparing the BPB to alternate formats for the same number of entries.

Adding a third bracket to a double elimination or a consolation tourney is uncommon, but not unknown. In this post, I’ll walk through the process of creating three third brackets.

One will be constructed on entirely conventional principles as a triple elimination 32 bracket. I’ll do only enough of this process to show why you probably don’t want to run such a tourney. The other two will be “last chance” brackets – third brackets added to a consolation tourney which are never reconciled to either of the other brackets. I’ll show the differences involved in doing this for brackets of 32 and 48.

In the next post, I’ll return to the post-mortem analysis of the Big, Peculiar Bracket to consider its third tier, which presented unusually difficult challenges.

## Double and Triple Eliminations

In principle, it’s possible to add another bracket to any knock-out tourney to make it a double-elimination format, and to turn a double elimination into a triple elimination by adding another bracket. In practice, however, there are a number of difficulties that need to be overcome.

Tourneygeek has spent a good many words on the way that these practical challenges may be met in the context of the double elimination, and I will presently offer some advice for those who want to run triple eliminations. First, however, I’d like to give some attention to the question of whether double- and triple-elimination tourneys make sense in the first place. As in other contexts, I’ll use the FEPS framework.

## The Big, Peculiar Bracket, a Postmortem, Part I

In an earlier post, I discussed a large bracket that was being prepared for a major backgammon tournament the summer in Michigan. The tourney was to be a full double-elimination format, with a consolation as well, capable of accommodating 96 entries.

For reasons I don’t fully understand (and would probably be impolitic to discuss if I did), the director chose not to use the bracket I prepared. The tournament was played using another very interesting and elaborate format that presents a number of bracket design issues.

In this post, I’ll discuss the structure of the format that was played. In subsequent posts, I’ll report some simulation results, and compare the format used to the unused one I suggested, and to a more conventional bracket.

## Using the New Tools: the Analysis of the 32 Bracket Continued

In the previous post, the new f(b) measure was used to gain a clearer picture of the way that the unshifted lower bracket for a 32-team double elimination tourney differed from either of the two available shifts. In this post, I’ll continue that discussion, and show how different levels of skill progression, resulting from different luck factors, affect the performance of the three candidates.

For those more interested in the practical result than the details of the method, here’s the result: The ED shift is to be preferred, except in the very low-luck scenario, where it’s a dead head between the unshifted bracket and the CD shift.

## Fairness Turned Upside-Down

For some time, I’ve been concerned that the fairness statistics I report are harder to interpret than I’d like. The new version of fairness (B) in particular has made the problem more apparent to me, and so I’m finally ready to make a change that I should probably have made long ago.

The difficulty is that the measures I’ve defined really measure unfairness more directly than they measure fairness. I define fairness (C) by adding up the instances of a less skillful player being rewarded in preference to the more skillful player. Fairness (B) is determined by adding up the inequalities in the result of similarly-placed competitors. In both cases, a higher number meant less fairness, not more.

To date, I’ve been flipping this around by then taking a reciprocal, and that makes higher numbers good and lower numbers bad. But it also has a tendency to scale the numbers in ways that make them hard to interpret. For the new fairness (B) measure, the difference between a score of 3 and a score of 4 is quite significant – a format scoring 3 is much less fair than one scoring 4. But the difference between a fairness (B) score of 70 and one of 100 is pretty trivial, nothing that the designer should worry about.

For this reason, I’m getting rid of the reciprocals. Henceforth, lower numbers are good, and higher numbers are bad.