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?

The chief procedural difference between the two tourneys is that the Open has a much more sensible way of handling late scratches. At the Western and Southern, four players (including three of the eight whose seeding entitled them to first-round byes) were replaced directly with “lucky losers”, with the result that three players who lost in the last round of the qualifying not only got to play in the main draw, but were seeded into byes. At the open, the late scratch by Andy Murray wasn’t replaced directly by Lukas Lacko, the “lucky loser”. Instead, number 5 Marin Cilic gets Murray’s line, number 17 Sam Querrey get’s Cilic’s line, formerly-unseeded Philipp Kohlschreiber gets Querrey’s line, and Lacko comes in on an unseeded line.

As with the Western and Southern, I’ve simulated the tournament two ways: with the actual draw, and with a hypothetical draw that’s as close to the aspiration of the actual draw as my simulator allows.

For both simulations, I use a player’s rank according to the consensus betting odds (this time from oddschecker.com) as the measure of skill rather than the ATP point counts used for the actual seeding. I’ve tweaked the parameters of the model first developed here. Because the field is so much larger, it stands to reason that they’ll be a wider distribution of skills, so I set the cutoff for the entrants at Z=1 rather than Z=2. I also found that nudging the luck factor down from 1.15 to unity seems to fit the punter’s predictions a bit better.

The biggest winners and losers, at least in terms of absolute dollar expectancies, are toward the top of the table, where the numbers are bigger anyway.

Both Federer and Nadal are big losers, chiefly I expect because they are put into the upper half of the draw, while the two best players in the bottom half, Alexander Zverev and Cilic, are the biggest winners, especially because they’re the only two from the top eight in the skill distribution in the bottom half – all of the rest are stuffed into the upper half with Federer and Nadal.

As at the Western and Southern, Kyrgios and Del Potro suffer from the fact that they’re ATP point totals suggest a seeding much lower than their actual skill as assessed by the punters, and also because they land in the same overloaded quarter of the draw as Federer. Thiem is fairly seeded, but has the misfortune to land in Federer’s quarter of death. Dimitrov is a little under-seeded, and he too suffers by being sent to the top half.

Down the table, the unseeded players fortunate enough to draw other unseeded players do well. For example, 107th ranked Santiago Giraldo has drawn 118th ranked Vincent Millot, Neither one would be likely to do well in a fully-seeded tournament, and their prospects are still iffy in the base case tournament, which is partially seeded through 32 places. But one or the other has to win the extra $36,000 one gets for advancing to the second round. To some, perhaps, such pairings are a flaw in the partial seeding system that tennis uses, but I find the existence of such matches part of the charm of the event. No such luck for Dusan Lajovic, the 120th best player, who drew Nadal, but at least he probably gets to play a match on one of the big show courts.

Here is the full list, with expectations from the actual draw, the base case that protects 32 players but does not randomize them within tiers, and the difference between the two: