Author: tourneygeek

Hearts full of youth,
Hearts full of truth,
Six parts gin to one part vermouth.
– Tom Lehrer, “Bright College Days”

In The Only Thing that Matters is October, I derived parameters for Major League Baseball that track Lehrer’s recipe for martinis, with luck taking the role of gin, and skill relegated to the role of vermouth.

In earlier posts, I’ve fretted a good deal about what I thought was a strikingly large role of chance in backgammon, e.g., All That Luck. Can it possibly be true that the ratio of such to skill in baseball is twice as large as it is in backgammon? What does that mean for the way baseball is played?

Continue reading “Hearts Full of Youth …”

One of the more peculiar features of the Major League Baseball playoffs (or “postseason”, as the league prefers to call it) is the fact that five teams from each league qualify. The three division winners each get a bye, and the two non-winners with the best records play a single game to see which will join the other three. Including the World Series, then, the MLB playoffs are, essentially a single-elimination tourney on a 16 bracket with six first-round byes.

Six byes? A single-game first round? My first reaction is that this has got to be one of the worst formats in use for a major professional sport. But, working through the ramifications, I’ve come to opposite conclusion. The Major League Baseball wild card system is a stroke of genius.

Continue reading “Wild Cards”

The Major League Playoffs begin tonight with the “wild card” game between the Twins and the Yankees. This event is being promoted by one of the networks with the tag line “The only thing that matters is October”. This reflects the structure of the playoffs, where the entire 2430-game regular season matters only for qualification and seeding for a relatively brief knockout postseason.

It would be hard to argue that this arrangement is designed to award the championship to the best team. Instead, it appears that the intention is to create as much interest as possible for a limited time. October, for baseball, is like March for NCAA basketball – a special time when the attention of less avid fans can be captured by a series of high-stakes games. Fairness, at least in the sense of fairness (C), is less important than creating good spectacle.

So how severely is fairness (C) compromised? This post, and a few to follow, will look at the structure of the playoffs, and compare it in fairness (C) terms to some possible variations.

Continue reading “The Only Thing that Matters is October”

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)

Continue reading “Three Maxims of Tournament Design”

In Seeding Waves, I suggested that fully seeding a tournament might sometimes result in an incentive for players to seek lower seeds rather than higher ones. Such cases are probably rare, but they’re certainly possible. And with the right payout schedule, the effect can be dramatic. Continue reading “Making 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.

Continue reading “Seeding Waves”

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?

Continue reading “Who Won the Draw?”

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.

Continue reading “Small Ball”

In the previous post, I showed how seeding affected fairness in general terms. In this one, I’ll relate it to the actual bracket that was played in the men’s singles draw at the Western and Southern.

Continue reading “Seedy Doings 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.

Continue reading “Fairness at the Western and Southern”