Drawing the Western and Southern

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.

The draw was fair in that fairness (C) for the particular draw was better than it was for draws in general: 20.45 and 21.20, respectively. Recall that fairness (C) measures the tendency in a format for the better players to get a bigger share of the rewards – here I used prize money. So this particular draw was somewhat less likely to cause better players to crash out early, before they’ve earned as much prize money as their relative skill suggests they ought to earn.

But this is not to say that there weren’t some dramatic effects on the expectation of particular players. These are easiest to see by looking separately at the four quadrants of the draw.

Djokovic landed in the top quadrant, with the effect of reducing the expectation of all 13 of the other players in that quadrant. Among the highlights:

Nadal, -$74K

NOTE: Since this was first posted, Nadal has scratched, and been replaced by a “lucky loser”. Nadal is exempt from the usual ATP requirement to play all 1000-level tournaments, and, as he played in Cincinnati last year, can do so without penalty. He is not claiming injury, rather just a desire to conserve his energy for the U.S. Open. It’s reasonable to suppose that his awful draw in the W&S was a factor in his decision. 

Dimitrov, -$23K
Johnson (Djokovic’s first round opponent), -$16K; and
Raonic, -$12K

Djokovic himself was +$19K, apparently because his first couple of rounds are none too threatening.

In contrast, the second quadrant didn’t receive any hugely under-seeded players, and so is mostly a pretty happy place. The two seeds with byes, A. Zevrev and Cilic are each +$24K.

In quadrant three, Anderson is +$25K, but the other bye seed, Del Potro, is -$10K. Del Potro suffers because he’s likely to run into the best of the tier six seeds, Kyrgios, in the third round. Kyrgios himself is +$22K, apparently because he has a couple of easy-looking rounds before his probable face off with Del Potro.

Finally, in quadrant four the big winner is Federer, at +$27K. The largest beneficiary of the draw was bound to be either Nadal or Federer, depending on who avoided Djokovic. Schwartzman, who appears to be over-seeded, is -$14K because he meets an under seeded Wawrinka in the first round. Similarly, Pouille, who drew Murray in the first round, is -$10K. But neither Wawrinka nor Murray is particularly advantaged, +$7K and +$6K, respectively, probably because so much of their expectation comes from later rounds in which they’re likely to encounter Federer.

If all goes well, I’ll have a similar analysis of the women’s draw tomorrow.