Italian translation at settesei.it
Last week featured two events on the WTA calendar. First, both chronologically and by every conceivable ranking except for “most Hungarian,” was the Dubai Open, a Premier 5 event offering over $500,000 and 900 ranking points for the winner. The other was the Hungarian Open in Budapest, a WTA International tournament with $43,000 and 280 ranking points going to the champion. No top player would seriously consider going to Budapest, even before considering potential appearance fees and WTA incentives.
Fifteen of the top twenty ranked women went to Dubai, and the top seed in Budapest, defending champ Alison Van Uytvanck, was ranked 50th. Every Budapest entrant ranked in the top 72 got a top-eight seed, including a couple of players who would have needed to play qualifying just to earn a place in the Dubai main draw.
The rewards offered by the Dubai event and supported by the structure of the WTA tour make this an easy scheduling decision for many players. But at some point, if the rest of the field is zigging toward the Gulf, might it be better to zag toward Central Europe? Van Uytvanck would have been an underdog to reach even the third round of the richer event, yet she defended her title in Budapest. Marketa Vondrousova, who would have been stuck in Dubai qualifying, reached the Hungarian Open final. Opting for the smaller stage almost definitely proved the wise choice for those two women. Did other, better-ranked players leave money or ranking points on the table?
Motivations
Scheduling decisions depend on a lot of factors. Some women might prefer to play the event with the highest-quality field, both to test themselves against the best and to give themselves an opportunity for the circuit’s richest prizes. Others might head for the marquee events because of their doubles prowess: Timea Babos was part of the top-seeded doubles team in Dubai, but was the lowest-ranked direct entry in singles. Still others might choose to play closer to home or at tournaments they’ve enjoyed in the past.
For all that, ranking points should come first, with prize money also among the top considerations. Ranking points determine one’s ability to enter future events and to remain on tour. Prize money is necessary to cover the vast expenses necessary to bankroll a traveling support staff.
Dubai-versus-Budapest offers a fairly “pure” experiment, because both are played on similar surfaces and neither event is in the middle of a mini-circuit of events in a single region. Yes, Dubai immediately follows Doha, but that trip requires a flight, and most players headed back to Europe or North America after the tournament. Opting for one event over the other doesn’t substantially complicate anyone’s travel plans, like it would for an ATPer to mix and match destinations from the South American golden swing and the simultaneous European indoor circuit.
Revealed preferences
Let’s see which of the two main factors played a bigger role in scheduling decisions last week. To determine each player’s options, I tried to reconstruct as much as possible what information each woman had at her disposal six weeks earlier, on January 7th, when entry applications and stated preferences for Dubai and Budapest were due. I used the January 7th rankings to project how a player would be seeded at either event, and Elo ratings as of that date to forecast how far she would advance in each draw.
The major difficulty of this kind of simulation is the composition of the draws themselves. From our vantage point after the events, we know who opted for each draw as well as which players were unable to compete. In early January, none but the best-connected players would have known which of her peers would head in which direction, and no one at all could have known that Caroline Wozniacki would be a late withdrawal from Dubai, or that a viral illness would knock Kirsten Flipkens out of the Hungarian Open. Still, the resulting 2019 draws were very similar to what players could have predicted based on the player fields in 2018. So to simulate each player’s options, we’ll use the fields as they turned out to be.
Let’s start with Carla Suarez Navarro, the highest-ranked woman (at the January 7th entry deadline) who wasn’t seeded in Dubai. She ended up reaching the quarter-finals at the Premier event, in part because Kristina Mladenovic did her the favor of ousting Naomi Osaka from that section of the draw. For her efforts, Suarez Navarro grabbed 190 ranking points and almost $60,000. She would have needed to win the Budapest title to garner more points. And with a champion’s purse of “only” $43,000 in Hungary, she would have needed to rob a bank to improve on her Dubai prize money check.
However, that isn’t what Suarez Navarro should have anticipated taking home from Dubai. Sure, she should be optimstic about her own potential, but smart scheduling demands some degree of realism. I ran simulations of both the Dubai tournament (before the draw was made, so she doesn’t always end up in Osaka’s quarter) and the Budapest event with the Spaniard as the top seed and the rest of the field (minus last-in Arantxa Rus) unchanged. These forecasts suggest that Suarez Navarro only had a 12% chance of reaching the Dubai quarters, and that her expected ranking points in the Gulf were much lower:
Event Points Prize Money Dubai 76 $28.121 Budapest 111 $15.384
(prize money in thousands of USD)
In all of these simulations, I’ve calculated points and prize money as weighted averages. Suarez Navarro had a 37% chance of a first-round loss, so that’s a 37% chance of one ranking point and first-round-loser prize money. And so on, for all of the possible outcomes at each event. For the Spaniard, her expected ranking points were nearly 50% higher as the top seed in Budapest. But because the Dubai prize pot is so much larger, her expected check was almost twice as big at the tournament she chose.
Consistent incentives
The total purse in Dubai was more than eleven times bigger than the prize money on offer in Hungary, while the points differed by only a factor of three. Thus, it’s no surprise that Suarez Navarro’s incentives are representative of those faced by many more women. I ran the same simulations for 26 more players: All of the competitors who gained direct entry into Dubai but were unseeded, plus Bernarda Pera, who would have been seeded in Budapest but instead played qualifying in the Gulf.
The following table shows each player’s expected points and prize money for Dubai (D-Pts and D-Prize), along with the corresponding figures for Budapest (B-Pts and B-Prize):
Player D-Pts D-Prize B-Pts B-Prize
Dominika Cibulkova 96 $36.794 130 $18.291
Lesia Tsurenko 84 $31.528 119 $16.695
Carla Suarez Navarro 76 $28.121 111 $15.384
Aliaksandra Sasnovich 75 $27.920 111 $15.364
Dayana Yastremska 72 $26.716 107 $14.803
Anastasia Pavlyuchenkova 72 $26.590 106 $14.721
Barbora Strycova 67 $24.809 102 $14.096
Donna Vekic 66 $24.143 100 $13.717
Katerina Siniakova 63 $23.157 95 $13.062
Ekaterina Makarova 58 $21.543 90 $12.265
Player D-Pts D-Prize B-Pts B-Prize
Petra Martic 57 $21.019 88 $11.960
Su Wei Hsieh 54 $19.863 84 $11.396
Belinda Bencic 53 $19.813 84 $11.372
Ajla Tomljanovic 53 $19.530 82 $11.181
Shuai Zhang 49 $18.350 77 $10.416
Sofia Kenin 46 $17.109 72 $9.659
Ons Jabeur 45 $17.077 71 $9.624
Viktoria Kuzmova 45 $17.009 70 $9.432
Alize Cornet 44 $16.823 69 $9.280
Saisai Zheng 40 $15.436 62 $8.307
Player D-Pts D-Prize B-Pts B-Prize
Vera Lapko 37 $14.618 57 $7.695
Mihaela Buzarnescu 36 $14.465 56 $7.548
Alison Riske 35 $14.309 55 $7.445
Kristina Mladenovic 34 $13.910 51 $6.969
Timea Babos 32 $13.354 48 $6.572
Yulia Putintseva 32 $13.407 48 $6.484
Bernarda Pera* 25 $11.830 36 $5.061
Every single player could have expected more points in Budapest and more money in Dubai. The ratios are all similar to Suarez Navarro’s. The one possible expection is Pera (hence the asterisk). My simulation assumed she came through qualifying to make the main draw, and calculated only her expected points and prize money from main draw matches. Yet simply qualifying for the main draw is worth 30 ranking points, plus whatever points a player earns by winning main draw matches. Pera was no lock to qualify, but she was favored, and usually a couple of lucky loser spots make the main draw even more achieveable. It’s possible that if we ran all those scenarios, Pera is the one player for whom Dubai offered better hopes of prize money and points.
Loss aversion and game theory
It’s no accident that Van Uytvanck was one of the few players to choose the high-points, low-prize money route. She was defending 280 points from last year’s Hungarian Open, meaning that opting for a bigger check in Dubai would have a negative impact on her ranking. The thought of losing a couple hundred ranking points has a greater influence on behavior than the chance of gaining the same amount for a player who has few to defend.
For the majority of women who will face the same decision in 2020 without many points to defend, what should they do? Assuming, as I do, that they and their coaches will all carefully study this article, what happens if more top-70 players decide to chase ranking points and flock to the smaller event?
If the Budapest field gets stronger, each entrant’s expected points and prize money will decrease; if Dubai’s field weakens, each player there can anticipate a better chance of more points and even more money. As the entry system is currently structured, in which each player must state their preferences without knowledge of their peers’ choices, we can’t count on reaching an equilibrium. Even if every single player aimed solely to maximize ranking points, there wouldn’t be enough information available to reliably make the right choice. It’s conceivable, though unlikely, that a Budapest could attract a stronger field and end up offering lower expected prize money checks and ranking points.
But don’t fret, dear readers and schedule optimizers. There are external factors and there always will be. And in this case, virtually all of those factors pull players to the bigger money event. (Even Hungarian heroine Babos skipped her home tournament.) At least a half-dozen of the players listed above are doubles elites, making it likely they’ll choose the Premier event. Others–probably many others–will go where the money is, because they like money.
Even those who don’t play doubles and don’t like money will chase the biggest available pot of ranking points, not entirely unlike the way people play the lottery. The WTA offers a very limited set of opportunities to earn 900 points in a single week. You can get close to 900 points with three International championships, but there’s a finite number of weeks on the annual schedule–not to mention a limited number of matches in each player’s body! Lots of people stock up on lottery tickets despite unfavorable odds, and players will continue to enter higher-profile events even if their expected points are higher on smaller stages. The chance of a prestigious title, however slim, doesn’t show up in a purely actuarial calculation.
The success of Belinda Bencic–expected Dubai points, 53; expected Budapest points, 84; actual Dubai points, 900–will keep players chasing the big prizes. That’s good news for level-headed would-be optimizers. Those players willing to forego the skyscrapers, the shopping malls, and the prize money next year aren’t about to lose this opportunity. Budapest will almost certainly remain a better option for players who want to improve their ranking.