Three Maxims of Tournament Design

In a very early post, I proposed what I then thought would be the first of several maxims of tournament design. Here it is, in a slightly altered form:

Unbalanced designs are likely to be inequitable, and so are to be avoided unless there is some good reason that the design needs to be unbalanced. (maxim 1)

The alteration is the substitution of “design” for “bracket”, so as to make it applicable to tournaments that are not run in brackets.

To date, I have had less occasion than I thought I would to make such grand pronouncements. But I think it’s time to propose another two maxims. Here’s a second:

In a well-designed tournament, there should never be a situation in which a team or player has an incentive to lose or draw rather than win an individual match. (maxim 2)

In addition to avoiding giving a team an incentive to lose, it is also well to avoid, as much as possible, situations in which a player or team is indifferent to winning or losing, especially where their opponent is not indifferent. This suggests a third maxim:

In a well-designed tournament, one should avoid as much as possible, matches for which the reward for winning, or penalty for losing, is very different for the two competitors. (maxim 3)

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Seeding Waves

As discussed before, seeding tends to enhance fairness (C), which measures the tendency of a tournament to distribute its rewards to the better players, at the expense of fairness (B), which measures the extent to which every entrant is given an equal chance.

But the extent to which the better players are given an advantage is not uniform through the skill distribution. Seeding creates a pattern of advantages and disadvantages that affect different parts of the skill distribution differently.

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Who Won the Draw?

The United States Open tennis tournament uses much the same procedures for draws and seeding as the Western and Southern. There are substantial structural differences, of course, as the Open has a draw of 128 with no byes, as opposed to the Western and Southern’s draw of 56 with 8 byes.

So, who benefits from the particular results of this draw?

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Small Ball

The Little League World Series (LLWS) is being played now. It is, as you might imagine, a tournament with some distinctive features.

As first blush, it would seem that little league baseball should be a competition that puts a high premium on participation, possibly compromising some other of the FEPS goals. And this is probably true, at least to some extent, of Little League Baseball in general. But a moment’s reflection should be enough to conclude that participation needs to be severely compromised in order to hold a Little League World Series.

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Fairness at the Western and Southern

So how does the seeding system in use at the Western and Southern (and most important professional tennis tournaments) affect the fairness of their brackets? First, we need to consider how the basic seeding structure affects the outcome. In a subsequent post, I’ll finally extend the analysis to this year’s actual Western and Southern.

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