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.
As with the men, the women’s draw was relatively fair: fairness (C) for all draws was 22.79, and for the W&S actual draw it was 21.05 (recall that for the current version of fairness (C), lower numbers are better).
In the men’s draw, there are seven spots for qualifiers. For some reason in the women’s draw there are more – 12 qualifiers, and one “lucky loser” (necessitated by the late withdrawal of Venus Williams), which for purposes of the simulation is much the same. In the simulations, I assume that all of those people can be considered to be the least skillful entrants. This assumption is, no doubt, not entirely correct, but I suspect that it’s reasonably close, especially given the fact that qualifiers have to play two rounds before they enter the main draw, and are thus likely to be at least a little tired.
One of the eye-catching factors in this years draw is that the qualifiers (and lucky loser) are not very evenly distributed. There are five in the top quadrant, only one in the second quadrant, five in the third quadrant, and two in the fourth.
As with the men, I’ll consider each quadrant separately, and mention those players whose expectation for the actual draw is significantly higher or lower than for the average of all draws. For the women, however, the numbers run smaller than the draw bonuses and penalties I reported in the last post. This is because the prize fund for the women is a good deal smaller than the one for the men. (I won’t go into why this is true in the supposedly gender equal world of professional tennis.)
The first quadrant, with five qualifiers and no conspicuously under-seeded players is a calm, and reasonably happy place. The two bye seeds, Halep and Muguruza, enjoy a draw bonus of +$8K and +$9K, respectively. No other entrant has a large gain or loss.
The second quadrant is a strong one, with only one qualifier. Kerber does well at +$10K, but the other bye seed, Garcia, is -$9K. Garcia is not the victim of any one strong competitor, but rather faces several better-than average players in her part of the bracket.
The third quadrant is where the draw effects are most pronounced. Serena Williams, herself a healthy +20K, is a tough draw for her first round opponent, Gavrilova (-$7K), and also for Kvitova, who is -$31K because she’s likely to face Serena in the second round. On the other side of the quadrant, Stevens is nearly even at +$1K, with the relatively weak opposition she’s likely to face early on compensating for the prospect of having to face Serena in the quarter finals.
In the fourth quadrant, Svitolina draws relatively unthreatening early opposition (including both of the quadrant’s qualifiers), to emerge at +$8K, while Wozniacki, who attracted some better antagonists, is at -$11K.
Bear in mind, please, that these are tendencies rather than fate, and that in all likelihood there will be some players who prosper despite a tough draw, and others who succumb to relatively less threatening opposition.