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A Guide to Tourneygeek

Tourneygeek grows in a haphazard fashion. For me, that’s what makes it fun to write – I can speculate when I’m feeling speculative, analyze when I’m feeling analytical, draw new brackets when I’m feeling (slightly) artistic, or add new features to my tournament simulator when I’m feeling geeky.

But readers can be forgiven for not sharing my mood of the moment. So in this post, I try explain how the various threads – theory, practice, individual games, resources, and geekery – have developed, and show how to follow the main themes from post to post.

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Remaking the NBA Playoffs

National Basketball Association Commissioner Adam Silver has floated the idea of changing the way that teams qualify and are seeded in the NBA playoffs. Instead of qualifying eight of the fifteen teams in each conference, and seeding those eight into separate knock-out bracket, with the winners of those two brackets playing in the finals for the championship, perhaps the league should qualify the 16 teams with the best record, regardless of conference, into a single 16 bracket.

The reason that alternatives are sought is that the two conferences of the NBA are widely regarded as being badly our of balance. According to the gnomes at fivethirtyeight.com, eight of the nine best teams in the league, including the top three, are in the Western conference.

One of the possible objections, anticipated by Mr. Silver himself, is that the regular season schedule is not balanced between the two conferences. In the 82-game season, each team plays each other team in the league at least twice, but each team plays ten of the teams in its own conference four times, and the other four in-conference teams thrice. Is this a problem?

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Hearts Full of Youth …

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?

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Wild Cards

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.

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The Only Thing that Matters is October

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.

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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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