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Seeding and Fairness

Is seeding fair? This would seem to be a fundamental question, but it’s one that doesn’t have a straightforward answer. Before further interrogating the data from the simulation of the Western and Southern, with its odd seeding style, for its effect on fairness, it may be well to revisit the question of just how fairness and seeding relate more generally.

In a nutshell, seeding usually enhances the meritocratic values embodied in fairness (C) at the expense of the egalitarian values embodied in fairness (B). But the decision whether to seed is not simply a way of expressing a preference for fairness (C) over fairness (B). The fairness effects of seeding may be incidental to some other goal.

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Further South

I’d planned to roll out my Western and Southern simulation today, but no such luck. There’s yet another scratch. And yet again, it’s a seeded player giving up his bye line – Milos Raonic, the sixth seed, is being replaced by Christian Harrison, who’s ranked 240th in the world according to the ATP. Harrison is the fourth lucky loser chosen to fill out the bracket, and the third to go directly into the second round by fluking onto one of the eight lines that get a first-round bye.

So, I’ll need to retool the simulation once again. It will be a matter of a few minutes to slot in Harrison and nudge nearly everyone else up a place in the simulator’s skill ranking, but it will take a few hours to run the trials, and all this has to be done in off moments stolen from actually watching tennis.

With four of the seven losers of the qualifying mini-brackets being chosen to fill lines in the main draw, and with three of those getting first round byes, it appears that, on average, the Q2 losers, collectively, will be on track to win more prize money than the qualifiers who actually won and entered the main draw by right. It will be close. And I think we’re probably done finding new lucky losers, so perhaps the next simulations will actually make it to the blog. Watch this space.

Western and Southern Brackets Gone South

Since the last post, there have been two more scratches from the men’s field at the Western and Southern. Roger Federer and Gael Monfils. So, two more lucky losers have been rescued from the qualifying, Ramkumar Ramanathan, who’s currently ranked 180th in the world, and Thomas Fabbiano, who’s 85th. Fabiano is perhaps the luckiest of the lucky losers because he got Roger Federer’s line, seeded second overall.

Ramanathan may have the last laugh on Tipsarovic and Fabbiano, however. On Monfils’ line, he drew Christopher Eubanks, the lowest-ranked of all of the qualifiers. That match was played tonight, on center court, no less. It’s fairly common for an unheralded player to get a center court match because they’re drawn in an early round against one of the popular favorites. But it must be very uncommon to see a first-round match on center court between a low-ranked qualifier and a lucky loser.

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Brackets at the Western and Southern

Today was day 2 of the Western and Southern Open (formerly Cincinnati Masters) tennis tournament. The qualifying rounds were concluded, and a few matches from the main draws were played.

The tennis was good. I’m reminded of a quote from David Foster Wallace: “TV tennis is to live tennis pretty much as video porn is to the felt reality of human love” (from page 119 of this book).

They’re pretty good at running tennis tournaments here. There’s a small army of volunteers, so many that each seems to have a very small job to do, and to do it reasonably well. The facilities are good. Everything is expensive, of course, but not outrageous. Even the weather has been reasonably nice, especially in the shaded seats my companion was clever enough to buy for us.

I’m not so sure about the brackets.

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Modeling Tennis

Your faithful tourneygeek will go to the ends of the earth to bring you the best information on tournament design. Or at least as far as Ohio. For the next week, tourneygeek will be operating from temporary quarters in the Baymont Inn & Suites in Mason, Ohio. I’m here to watch the Western and Southern Open – the last important tennis tourney leading up to the U.S. Open. Where better to expand on the work started with Wimbledon, studying the effect of the rather odd seeding system used in high-level professional tennis.

First, I need to fine-tune my simulator for elite tennis – that’s the subject of this post.

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Pay Now or Pay Later

Not all tournament organizers have the power, or perhaps the inclination, to limit the number of entries in a bracketed tournament to a power of two. In such cases, the usual practice is to use the next highest power-of-two bracket, filling empty lines with as many byes as needed. On the printable brackets page, the model top-level brackets all have seeding numbers that double as guides for allocating byes.

But there is more than one way to allocate byes. In this post, I’ll illustrate the possibilities by working through a very simple case, comparing four different ways to prune a basic 32 single-elimination bracket so that it accommodates 24 entries. By artfully arranging the byes so that they fall in later rounds, there can be fewer of them. So, should you pay now by putting all the byes in as early as possible, or should you pay later by putting fewer byes into later rounds?

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The Powers of Two

Visitors to the printable brackets page will see that all of the brackets there are designed for tourneys with a number of entrants that’s an even power of two: 16, 32, 64, or 128. There are reasons for that, relating to the basic fact that an individual match is between two players or teams. When the number of entrants is not a power of two, some measure of unfairness is usually unavoidable in any elimination-style format.

In this post, I’ll discuss the common practice of using the results of a preliminary competition, usually some sort of round-robin regular season, to seed a championship playoff that observes, at least in its later rounds, the power of two constraint. In the next, I’ll consider some other ways of dealing with the awkward situation of running a tourney with a number of entrants that’s not a power of two.

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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.

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