Category: Uncategorized

A friend asks for help with pairings for a tennis league he runs.

There are eleven people in the league, and the league has two tennis courts reserved once each week for 24 weeks. Each week, the league will play a doubles match on each court, eight people playing in four partnerships, with three people getting a bye each week.

Here are the parameters he’d like to observe:

1. The schedule needs to be determined in advance, so that everyone knows which weeks they’ll be playing, and with which partner. It’s not necessary for them to know who there opponents are;
2. Each player should play nearly the same number of times over the 24 weeks;
3. Everyone should play with everyone else at least once, but no more than twice;
4. No one should draw a bye two weeks in a row; and
5. The pairings should, as far as possible, encourage “interesting” matches, with the better players tending to play other good players, and the weaker players drawing other weak players.

I’ve got a format for that. I’ll call it the “Social Swiss”. In this post, I’ll show how the first four criteria can be met, leaving the fifth criterion for a later post.

Continue reading “A Social Swiss”

The remarkable spectacle of last night’s women’s final at the U.S. Open tennis tourney brings to mind some past tourneygeek thoughts about the cheating and the nature of rules.

The central question is this: was Serena cheating?

Continue reading “Serenity Lost”

Watching this year’s U.S. Open tennis tourney has a certain morbid fascination, somewhat reminiscent of the last U.S. Open golf tourney. In both cases, the weather has been so extreme that any sensible person who had a choice would simply decline to play. This brings attention to the disconnect between two main constituencies for games: the players themselves, and those who like to watch. When a marketable spectator event has been scheduled, it matters little that the play itself has more to do with the players ability to withstand suffering than their ordinary game skills. The game must go on.

This seems to me to pose some clear ethical questions. When do spectator sports become so dangerous to the well being of the athlete that it’s no longer justifiable to present them as entertainment?

Continue reading “Whose Game Is It Anyway?”

There’s a remarkable pairing in the first round of the U.S. Open tennis tournament. At noon tomorrow (August 27), Grigor Dimitrov plays Stan Wawrinka, just two months after they happened to draw each other in the first round of Wimbledon (Wawrinka won).

Both Dimitrov and Wawrinka are among the elite of men’s tennis, and it’s matchups like this one that most tourneys are designed to avoid through the use of seeding. But there’s always some degree of variance between the ATP point totals used by tournaments to make their seedings and the actual skill level of the players. Let’s take a close look at the details of this particular pairing.

Continue reading “The Luck of the Draw”

The U.S. Open tennis tournament, like the other tennis majors, has a 128 draw that’s seeded in tiers along much the same lines as the Western and Southern. The first six tiers are the same: {1, 2, 3-4, 5-8, 9-12, 13-16}. To this, the U.S. open adds two new tiers: {17-24, 25-32}, which doubles the number of seeded players, from 16 to 32. There are no byes in the U.S. Open, so the tier boundary between 5-8 and 9-12 is less significant. But apart from this, the tiered seeding system has much the same effect on players’ expectations.

Next year, however, the Grand Slam Board – a body that sets policy for the tennis majors – has decreed that there should be only 16 seeds, which will presumably be accomplished by shedding the 17-24 and 25-32 tiers. For much interesting background on this change, see here.

[UPDATE: The Grand Slam Board has since reversed its decision, and will stay with 32 seeds, at least through 2019. The reason for the reversion is unclear, the GSB saying only that it had consulted especially with players and broadcasters.]

What effect should we expect from such a change?

Continue reading “Shedding Tiers”

The previous post discussed whether the new air-conditioned box seats in “1899 Room” in the new South Building at the Western and Southern Open tennis tournament were good seats for watching tennis. The upshot was that there are some very nice features of the 1899 room, but there are some problematic features too. The 1899 room is, in some ways, isolated from the rest of the stadium, and watching tennis there can be disconcertingly similar to watching tennis on television.

Today I traded tickets with one of my partner’s friends so that she could watch a set or two in the comfort of the 1899 room. I sat in her seat, which was high up (in the shade) along one of the sidelines of the center court.

From that vantage point, and from most of the seats in the stadium, you can see into the 1899 room. In fact, it draws the eye – the huge window wall that separates it from center court acts a little like a picture frame, and the different size and color of the 1899 seats attracts attention. Presumably many of the fans sitting in ordinary seats know that those seats on the other side of the window are the fabulously expensive air-conditioned ones.

So what do folks see when they look into the 1899 room from the outside?

Continue reading “The 1899 Room, Outside Looking In”

Let me digress, for one post, from discussing austere abstractions about the design of tournaments to some unusual aspects of being among the spectators at the one I’m attending now: The Western and Southern Open tennis tournament (W&S).

There are good reasons to go and see top-class tennis in person. As so often, no one said it better than David Foster Wallace: “TV tennis is to live tennis pretty much as video porn is to the felt reality of human love.”

There are also, however, some good reasons not to watch tennis live. Watching live tennis often means sitting on hard seats or benches in the hot sun for hours at a time.

This year, for the first time, the folks who run the W&S have a new viewing option for wimpy heliophobes like me: the First Financial 1899 room. “First Financial” is the sponsor who snagged naming rights for the new room, and “1899” celebrates the antiquity of the tourney, which was first held in 1899.

The 1899 room is part of a large new building that has been constructed between center court and the grandstand court. It contains 252 seats which look out through huge windows onto center court, all more or less at the baseline viewing angle familiar from television, and all reasonably close to the action–in the front row there are only eight rows of ordinary box seats between you and the court. The seats are upholstered. The room is air conditioned. There’s a special restaurant that only the holders of 1899 room tickets get to eat at, with tables looking out and the action on center court, and even a few looking the other direction for a good view of the grandstand court. There are squeaky-clean and little-trafficked rest rooms reserved for 1899 room denizens.

These comforts do not come cheap. But leaving aside the cost, it’s worth considering whether this way of watching tennis loses the qualities that David Foster Wallace prizes in live tennis. You’re watching tennis from a comfortable chair in an air-conditioned room through a wall of glass with the accustomed baseline angle used for television. Do these elements combine to create a viewing experience that’s disengaged from live tennis in the same way as viewing tennis on television in your living room? Continue reading “Tennis Under Glass in the 1899 Room”

The distinctive tiered seeding system used in professional tennis avoids the phenomenon of seeding waves – local effects in the seeding order in which it may be beneficial to be seeded lower rather than higher. This is a good thing.

But it does it at the expense of creating another seeding anomaly – the equal treatment of players with a given tier. Thus at the Western and Southern, where the tiers are 1, 2, 3-4, 5-8, 9-12, and 13-16, it makes no difference to a player’s prospects whether he is seeded 3 rather than 4, 5 rather than 6, 7, or 8, and so forth.

But it does matter, and matter a good deal, when a player crosses a tier boundary, being seeded 2 rather than 3, 8 rather than 9, and so forth. In this post, I’ll try to put a dollar figure on the gain or loss associated with each of these boundaries.

Continue reading “Tiers, Idle Tiers”

In the women’s draw at the Western and Southern, something very similar happened to what happened with the men. The punter’s number one choice, in this case Serena Williams, is entirely unseeded, which is bound to cause some serious loss of expectation in whatever quadrant of the draw she lands.

As with the men, I’ve run a pair of simulations to show the particular effects of the women’s draw. First, I ran 500,000 trials with a new, properly tiered draw each time, and then another 500,000 trials of the bracket with the draw that did happen.

Continue reading “The Women’s Draw”

Last night in Cincinnati, the Western and Southern had its “draw party”. I had imagined this as a rather small event, but it was anything but. Hundreds of eager tennis fans crowded into a large tent to eat an indifferent buffet supper and watch as volunteers from the audience, mostly cute kids, came up to the stage one by one to get a picture taken with Angelique Kerber and pull a number from a bowl to allocate one of the 16 seeds to a line in the draw.

This year, there was the potential for dramatic draw effects. Serena Williams is unseeded, and so could have ended up anywhere. And Novak Djokovic, who enters the event as the punter’s favorite but only a modest tier five (9-12) seed might be even more destabilizing, causing other players’ expectations to crash in whatever section of the draw he landed in.

I ran simulations to estimate the effect of the draw. First, I ran 500,000 trials with a fresh draw for each trial to establish a baseline for expectations. (These trials were slightly different from those reported a couple of posts ago because there have been some late scratches, including a couple of the tier six seeds.) Then I ran 500,000 trials with this particular draw.

Continue reading “Drawing the Western and Southern”