By now, it’s pretty well understood luck plays a role in just about every sport, and there are a bunch of good ways to measure it. Batting Average for Balls In Play (BABIP) measures how sustainable a hitter/pitcher’s level of play is, fumble recovery rates in football converge to 50 percent in the long term, etc. There are definitely some elements of randomness and luck that come into play in tennis matches as well, but the biggest impact of luck comes before a single match is even played in a tournament: the luck of the draw.
Quantifying luck of the draw in tennis
The biggest influence of luck in tennis happens before the matches even start. Here’s how to quantify it, and why it’s important.
Matthew Stockman
A tennis player’s chances of advancing depend significantly on how hard or easy his or her path is, and that path is largely determined by which players get drawn to which spots in the tournament bracket. This on its own isn’t problematic, since there will always be lucky and unlucky teams or players in each sport; but when you have a points-based ranking system like the ATP/WTA, which doesn’t acknowledge the influence of the luck of the draw, that ranking system moves further away from a merit-based evaluation method and more towards being a Powerball ticket. I don’t think the players would appreciate being told outright that whether or not they get into certain tournaments depends more on whether it’s their lucky day than how well they actually play.
For the unfamiliar, here’s how the tennis tournament draw process would look like if it were applied to the NCAA basketball tournament:
- The conference tournaments would be played first to see which teams earn a qualifying bid, after which the at-larges are selected.
- Once all teams have received their bids, the overall #1 and next-best #1 seed would be placed at the top of their regions.
- The two remaining #1 seeds would be randomly assigned to the top lines in the last 2 regions.
- The #2 seeds would then be randomly placed on the #2 lines.
- The #3 seeds would then be randomly placed on the #3 lines.
- The #4 seeds would then be randomly placed on the #4 lines.
- All remaining 48 teams would be randomly assigned to all remaining spots.
That should give a sense of how big luck of the draw is. If you’re not seeded, your first-round opponent could be a #1 seed like Louisville, a qualifier like Montana, or anything in between. In fact, the only way to guarantee you aren’t too affected by luck of the draw for a tournament is to be seeded yourself, but whether or not you get seeded depends on what your rank is ... and your rank is calculated by how far you’ve advanced in past tournaments ... which have been significantly affected by luck of the draw. This is the snake eating its own tail, and it encapsulates everything that is awful about the current ATP/WTA ranking system.
There are a couple ways to address this. You could introduce a purely performance-based component, like Advanced Baseline, into your ranking system to reward the players that perform better than others. Alternatively, if you have a good understanding of which players have received disproportionately unlucky draws over time (hi, Ryan Harrison!), you could give them some sort of explicit benefit to counteract their bad luck, like a wild card draw. To do that, there needs to be a way of measuring luck of the draw. One such method is outlined below.
(Before I go any further, I should note I was a lot more excited to write this article before I found out Jeff Sackmann at Heavy Topspin already outlined the same method. I have a couple semantic differences with his approach, but I agree with 95 percent of it, and he outlines it really well, so it’s worth reading.)
In order to measure whether players got lucky or unlucky from the draw, first we’ll need to set some expectation of how they’ll do before the matches get underway. The easiest way to do that is make a tournament forecast using some kind of predictive model, whether it’s Advanced Baseline, Sackmann’s Jrank, or any other system. If you know what the tournament bracket is and have a way of estimating head-to-head probabilities, you can simulate the tournament a bunch of times and see how often each player makes it to each round. As an example, here is an Advanced Baseline-powered forecast for the women’s side of the just-underway Madrid Open, generated after the draw was completed:
Player | Round of 64 | Round of 32 | Quarterfinals | Semifinals | Finals | Winner |
Maria Sharapova | 94.6% | 88.0% | 77.2% | 64.1% | 51.4% | 31.5% |
Serena Williams | 93.8% | 87.1% | 77.7% | 61.5% | 41.3% | 25.8% |
Victoria Azarenka | 91.7% | 80.4% | 70.4% | 55.4% | 31.7% | 18.3% |
Agnieszka Radwanska | 88.4% | 74.4% | 44.4% | 28.2% | 10.7% | 4.1% |
Ana Ivanovic | 85.5% | 62.7% | 36.5% | 23.1% | 8.9% | 3.2% |
Na Li | 92.2% | 59.1% | 42.9% | 16.2% | 7.6% | 3.0% |
Sara Errani | 84.8% | 67.7% | 49.0% | 21.0% | 7.8% | 2.9% |
Samantha Stosur | 71.4% | 49.6% | 33.3% | 11.0% | 6.2% | 2.3% |
Svetlana Kuznetsova | 87.9% | 57.7% | 37.1% | 17.9% | 5.7% | 1.9% |
Angelique Kerber | 82.3% | 61.7% | 30.5% | 13.7% | 3.9% | 1.0% |
Venus Williams | 76.1% | 34.0% | 22.4% | 7.1% | 2.7% | 1.0% |
Petra Kvitova | 75.8% | 57.0% | 29.9% | 8.4% | 3.7% | 0.8% |
Roberta Vinci | 64.6% | 45.7% | 21.1% | 6.7% | 1.8% | 0.5% |
Nadezda Petrova | 73.6% | 33.0% | 18.8% | 7.7% | 1.9% | 0.5% |
Caroline Wozniacki | 62.7% | 43.9% | 17.5% | 4.6% | 1.5% | 0.4% |
Dominika Cibulkova | 74.8% | 48.7% | 10.4% | 4.8% | 2.0% | 0.4% |
Kaia Kanepi | 68.6% | 28.0% | 15.1% | 3.8% | 1.7% | 0.4% |
Jelena Jankovic | 71.2% | 25.4% | 9.7% | 4.2% | 1.0% | 0.3% |
Maria Kirilenko | 62.1% | 45.9% | 10.1% | 4.0% | 1.1% | 0.3% |
Francesca Schiavone | 69.9% | 44.2% | 10.8% | 4.1% | 1.0% | 0.2% |
Sabine Lisicki | 74.3% | 33.9% | 5.4% | 2.3% | 0.8% | 0.2% |
Carla Suarez Navarro | 28.6% | 14.5% | 7.2% | 1.6% | 0.4% | 0.1% |
Andrea Petkovic | 17.2% | 8.4% | 3.5% | 1.7% | 0.5% | 0.1% |
Yaroslava Shvedova | 37.3% | 21.3% | 6.5% | 1.5% | 0.3% | 0.1% |
Lucie Safarova | 56.7% | 10.1% | 5.6% | 2.3% | 0.4% | 0.1% |
Elena Vesnina | 58.0% | 27.8% | 4.9% | 1.8% | 0.3% | 0.1% |
Mona Barthel | 58.5% | 22.2% | 5.9% | 1.0% | 0.2% | 0.1% |
Shuai Peng | 59.1% | 6.3% | 2.7% | 0.8% | 0.2% | 0.1% |
Sloane Stephens | 57.5% | 19.3% | 5.7% | 0.8% | 0.3% | 0.1% |
Julia Goerges | 74.6% | 29.8% | 9.4% | 1.9% | 0.4% | 0.0% |
Sorana Cirstea | 60.8% | 17.7% | 8.1% | 1.7% | 0.3% | 0.0% |
Klara Zakopalova | 37.9% | 24.2% | 3.4% | 1.0% | 0.3% | 0.0% |
Varvara Lepchenko | 35.4% | 19.9% | 6.7% | 1.5% | 0.2% | 0.0% |
Ayumi Morita | 39.2% | 8.5% | 2.9% | 0.4% | 0.1% | 0.0% |
Ekaterina Makarova | 43.3% | 6.1% | 2.9% | 1.1% | 0.3% | 0.0% |
Alize Cornet | 50.8% | 16.0% | 4.7% | 1.0% | 0.1% | 0.0% |
Magdalena Rybarikova | 65.1% | 15.3% | 4.4% | 1.1% | 0.1% | 0.0% |
Bethanie Mattek-Sands | 9.0% | 3.6% | 1.1% | 0.4% | 0.1% | 0.0% |
Lourdes Dominguez-Lino | 48.4% | 4.7% | 2.0% | 0.6% | 0.1% | 0.0% |
Silvia Soler-Espinosa | 62.5% | 21.2% | 2.8% | 0.6% | 0.1% | 0.0% |
Kiki Bertens | 49.2% | 15.5% | 4.2% | 1.0% | 0.1% | 0.0% |
Laura Robson | 34.9% | 5.4% | 1.0% | 0.2% | 0.1% | 0.0% |
Monica Niculescu | 10.3% | 3.3% | 0.7% | 0.1% | 0.0% | 0.0% |
Christina McHale | 10.5% | 3.1% | 0.7% | 0.1% | 0.0% | 0.0% |
Marion Bartoli | 42.0% | 15.6% | 2.3% | 0.7% | 0.1% | 0.0% |
Simona Halep | 51.6% | 5.1% | 2.2% | 0.7% | 0.1% | 0.0% |
Flavia Pennetta | 31.4% | 7.9% | 2.9% | 0.4% | 0.1% | 0.0% |
Yanina Wickmayer | 24.2% | 12.5% | 3.3% | 0.4% | 0.1% | 0.0% |
Kirsten Flipkens | 41.5% | 12.6% | 2.6% | 0.5% | 0.1% | 0.0% |
Chanelle Scheepers | 15.4% | 4.8% | 1.2% | 0.4% | 0.1% | 0.0% |
Mallory Burdette | 11.8% | 3.8% | 1.1% | 0.3% | 0.1% | 0.0% |
Daniela Hantuchova | 42.5% | 11.2% | 2.6% | 0.3% | 0.1% | 0.0% |
Anabel Medina Garrigues | 23.9% | 5.6% | 2.0% | 0.3% | 0.1% | 0.0% |
Urszula Radwanska | 15.2% | 6.2% | 2.1% | 0.3% | 0.1% | 0.0% |
Maria-Teresa Torro-Flor | 9.0% | 2.7% | 0.7% | 0.2% | 0.0% | 0.0% |
Tsvetana Pironkova | 11.6% | 4.9% | 0.9% | 0.2% | 0.0% | 0.0% |
Jamie Hampton | 8.6% | 2.8% | 0.6% | 0.2% | 0.0% | 0.0% |
Madison Keys | 5.7% | 1.6% | 0.5% | 0.1% | 0.0% | 0.0% |
Kristina Mladenovic | 37.5% | 8.6% | 0.6% | 0.1% | 0.0% | 0.0% |
Olga Govortsova | 4.1% | 1.0% | 0.2% | 0.1% | 0.0% | 0.0% |
Anastasia Pavlyuchenkova | 8.3% | 3.4% | 1.2% | 0.3% | 0.0% | 0.0% |
Su-Wei Hsieh | 17.7% | 6.8% | 1.4% | 0.1% | 0.0% | 0.0% |
Lauren Davis | 6.6% | 1.4% | 0.2% | 0.1% | 0.0% | 0.0% |
Lucie Hradecka | 7.3% | 1.8% | 0.3% | 0.1% | 0.0% | 0.0% |
Tamira Paszek | 7.8% | 1.3% | 0.3% | 0.0% | 0.0% | 0.0% |
Lesya Tsurenko | 3.7% | 0.9% | 0.1% | 0.0% | 0.0% | 0.0% |
Karolina Pliskova | 4.2% | 0.8% | 0.1% | 0.0% | 0.0% | 0.0% |
Sofia Arvidsson | 25.7% | 6.1% | 0.5% | 0.1% | 0.0% | 0.0% |
Mirjana Lucic | 2.6% | 0.8% | 0.2% | 0.1% | 0.0% | 0.0% |
Jie Zheng | 12.1% | 2.9% | 0.7% | 0.1% | 0.0% | 0.0% |
Stefanie Voegele | 7.2% | 1.9% | 0.3% | 0.0% | 0.0% | 0.0% |
Bojana Jovanovski | 25.4% | 4.5% | 0.7% | 0.0% | 0.0% | 0.0% |
Aravane Rezai | 4.3% | 0.8% | 0.2% | 0.0% | 0.0% | 0.0% |
Johanna Larsson | 4.9% | 0.9% | 0.1% | 0.0% | 0.0% | 0.0% |
Annika Beck | 6.2% | 1.0% | 0.1% | 0.0% | 0.0% | 0.0% |
Alexandra Dulgheru | 4.5% | 0.9% | 0.2% | 0.0% | 0.0% | 0.0% |
Marina Erakovic | 3.1% | 0.5% | 0.1% | 0.0% | 0.0% | 0.0% |
Camila Giorgi | 3.6% | 0.7% | 0.1% | 0.0% | 0.0% | 0.0% |
Garbine Muguruza | 5.2% | 1.2% | 0.2% | 0.0% | 0.0% | 0.0% |
Andrea Hlavackova | 1.1% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Mathilde Johansson | 2.6% | 0.6% | 0.1% | 0.0% | 0.0% | 0.0% |
Olga Puchkova | 0.8% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
Anna Tatishvili | 2.5% | 0.4% | 0.0% | 0.0% | 0.0% | 0.0% |
Donna Vekic | 1.3% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Melanie Oudin | 1.2% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Maria Joao Koehler | 0.4% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
Yulia Putintseva | 2.2% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Sara Sorribes Tormo | 0.9% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
How much of each player’s odds of advancing is due to their skill level versus their draw? We can measure that by generating tournament forecasts across all possible bracket draws (or if not all possible draws, at least a lot of them). This involves simulating the draw process itself and generating a lot of tournament brackets, then simulating how each of those tournaments play out. Here is the tournament forecast for Madrid across 1,000,000 possible bracket draws:
Player | Round of 64 | Round of 32 | Quarterfinals | Semifinals | Finals | Winner |
Maria Sharapova | 92.4% | 84.6% | 73.8% | 61.4% | 45.6% | 28.8% |
Serena Williams | 92.0% | 83.8% | 72.6% | 59.9% | 43.2% | 26.4% |
Victoria Azarenka | 95.2% | 85.1% | 71.8% | 57.1% | 33.0% | 19.8% |
Agnieszka Radwanska | 90.5% | 71.7% | 50.9% | 32.5% | 13.0% | 4.7% |
Ana Ivanovic | 80.8% | 63.8% | 25.6% | 16.3% | 7.2% | 2.7% |
Na Li | 81.5% | 65.0% | 45.6% | 20.3% | 9.3% | 3.7% |
Sara Errani | 79.8% | 62.3% | 42.3% | 17.8% | 7.7% | 2.8% |
Samantha Stosur | 78.9% | 60.9% | 37.5% | 15.3% | 6.4% | 2.3% |
Svetlana Kuznetsova | 66.1% | 37.7% | 19.8% | 8.8% | 3.3% | 1.1% |
Angelique Kerber | 71.3% | 49.3% | 28.2% | 9.3% | 3.1% | 0.9% |
Venus Williams | 66.0% | 37.6% | 19.8% | 8.8% | 3.3% | 1.1% |
Petra Kvitova | 73.7% | 52.8% | 31.7% | 11.1% | 3.9% | 1.2% |
Roberta Vinci | 69.5% | 46.7% | 23.3% | 7.2% | 2.3% | 0.6% |
Nadezda Petrova | 67.7% | 44.2% | 21.1% | 6.2% | 1.8% | 0.4% |
Caroline Wozniacki | 70.8% | 48.5% | 24.9% | 8.0% | 2.6% | 0.7% |
Dominika Cibulkova | 68.2% | 44.8% | 12.2% | 5.7% | 1.7% | 0.4% |
Kaia Kanepi | 57.1% | 26.9% | 11.5% | 4.1% | 1.2% | 0.3% |
Jelena Jankovic | 54.7% | 24.3% | 9.8% | 3.2% | 0.9% | 0.2% |
Maria Kirilenko | 67.0% | 43.2% | 11.3% | 5.2% | 1.5% | 0.4% |
Francesca Schiavone | 54.1% | 23.7% | 9.4% | 3.0% | 0.8% | 0.2% |
Sabine Lisicki | 49.1% | 19.0% | 6.6% | 1.9% | 0.4% | 0.1% |
Carla Suarez Navarro | 51.5% | 21.2% | 7.9% | 2.4% | 0.6% | 0.1% |
Andrea Petkovic | 33.2% | 16.0% | 7.0% | 2.5% | 0.7% | 0.2% |
Yaroslava Shvedova | 49.9% | 19.7% | 7.0% | 2.0% | 0.5% | 0.1% |
Lucie Safarova | 53.3% | 22.9% | 8.9% | 2.8% | 0.7% | 0.2% |
Elena Vesnina | 47.2% | 17.4% | 5.8% | 1.6% | 0.3% | 0.1% |
Mona Barthel | 46.8% | 17.1% | 5.6% | 1.5% | 0.3% | 0.1% |
Shuai Peng | 42.0% | 13.4% | 3.9% | 0.9% | 0.2% | 0.0% |
Sloane Stephens | 43.3% | 14.4% | 4.3% | 1.0% | 0.2% | 0.0% |
Julia Goerges | 45.7% | 16.2% | 5.2% | 1.3% | 0.3% | 0.0% |
Sorana Cirstea | 45.8% | 16.3% | 5.2% | 1.3% | 0.3% | 0.0% |
Klara Zakopalova | 46.5% | 16.9% | 5.5% | 1.4% | 0.3% | 0.1% |
Varvara Lepchenko | 46.7% | 17.0% | 5.5% | 1.5% | 0.3% | 0.1% |
Ayumi Morita | 36.6% | 9.9% | 2.4% | 0.5% | 0.1% | 0.0% |
Ekaterina Makarova | 47.7% | 17.8% | 6.0% | 1.6% | 0.4% | 0.1% |
Alize Cornet | 38.8% | 11.2% | 2.9% | 0.6% | 0.1% | 0.0% |
Magdalena Rybarikova | 42.3% | 13.6% | 3.9% | 0.9% | 0.2% | 0.0% |
Bethanie Mattek-Sands | 25.9% | 10.6% | 3.9% | 1.2% | 0.3% | 0.1% |
Lourdes Dominguez-Lino | 41.2% | 12.8% | 3.6% | 0.8% | 0.1% | 0.0% |
Silvia Soler-Espinosa | 39.3% | 11.6% | 3.0% | 0.6% | 0.1% | 0.0% |
Kiki Bertens | 38.1% | 10.8% | 2.7% | 0.5% | 0.1% | 0.0% |
Laura Robson | 29.3% | 6.1% | 1.2% | 0.2% | 0.0% | 0.0% |
Monica Niculescu | 16.7% | 5.4% | 1.5% | 0.3% | 0.1% | 0.0% |
Christina McHale | 13.8% | 4.0% | 1.0% | 0.2% | 0.0% | 0.0% |
Marion Bartoli | 48.5% | 22.1% | 3.4% | 1.0% | 0.2% | 0.0% |
Simona Halep | 42.4% | 13.6% | 3.9% | 0.9% | 0.2% | 0.0% |
Flavia Pennetta | 40.0% | 12.0% | 3.2% | 0.7% | 0.1% | 0.0% |
Yanina Wickmayer | 40.2% | 12.3% | 3.3% | 0.7% | 0.1% | 0.0% |
Kirsten Flipkens | 38.7% | 11.2% | 2.9% | 0.6% | 0.1% | 0.0% |
Chanelle Scheepers | 16.7% | 5.3% | 1.5% | 0.3% | 0.1% | 0.0% |
Mallory Burdette | 15.2% | 4.9% | 1.4% | 0.3% | 0.1% | 0.0% |
Daniela Hantuchova | 35.9% | 9.5% | 2.2% | 0.4% | 0.1% | 0.0% |
Anabel Medina Garrigues | 41.7% | 13.2% | 3.7% | 0.8% | 0.2% | 0.0% |
Urszula Radwanska | 34.9% | 9.0% | 2.1% | 0.4% | 0.1% | 0.0% |
Maria-Teresa Torro-Flor | 13.8% | 4.3% | 1.2% | 0.3% | 0.0% | 0.0% |
Tsvetana Pironkova | 31.1% | 7.0% | 1.4% | 0.2% | 0.0% | 0.0% |
Jamie Hampton | 14.6% | 4.5% | 1.2% | 0.3% | 0.0% | 0.0% |
Madison Keys | 17.4% | 5.6% | 1.6% | 0.4% | 0.1% | 0.0% |
Kristina Mladenovic | 28.5% | 5.7% | 1.0% | 0.1% | 0.0% | 0.0% |
Olga Govortsova | 9.0% | 2.1% | 0.4% | 0.1% | 0.0% | 0.0% |
Anastasia Pavlyuchenkova | 39.4% | 11.7% | 3.1% | 0.7% | 0.1% | 0.0% |
Su-Wei Hsieh | 29.8% | 6.3% | 1.2% | 0.2% | 0.0% | 0.0% |
Lauren Davis | 9.8% | 2.5% | 0.5% | 0.1% | 0.0% | 0.0% |
Lucie Hradecka | 8.9% | 2.0% | 0.4% | 0.1% | 0.0% | 0.0% |
Tamira Paszek | 22.5% | 3.5% | 0.5% | 0.1% | 0.0% | 0.0% |
Lesya Tsurenko | 7.0% | 1.5% | 0.3% | 0.0% | 0.0% | 0.0% |
Karolina Pliskova | 5.5% | 1.1% | 0.2% | 0.0% | 0.0% | 0.0% |
Sofia Arvidsson | 26.9% | 5.1% | 0.9% | 0.1% | 0.0% | 0.0% |
Mirjana Lucic | 9.5% | 2.5% | 0.6% | 0.1% | 0.0% | 0.0% |
Jie Zheng | 25.8% | 4.7% | 0.7% | 0.1% | 0.0% | 0.0% |
Stefanie Voegele | 10.6% | 2.7% | 0.6% | 0.1% | 0.0% | 0.0% |
Bojana Jovanovski | 23.6% | 3.9% | 0.6% | 0.1% | 0.0% | 0.0% |
Aravane Rezai | 4.9% | 1.0% | 0.2% | 0.0% | 0.0% | 0.0% |
Johanna Larsson | 7.0% | 1.5% | 0.3% | 0.0% | 0.0% | 0.0% |
Annika Beck | 6.3% | 1.3% | 0.2% | 0.0% | 0.0% | 0.0% |
Alexandra Dulgheru | 4.5% | 0.8% | 0.1% | 0.0% | 0.0% | 0.0% |
Marina Erakovic | 4.1% | 0.7% | 0.1% | 0.0% | 0.0% | 0.0% |
Camila Giorgi | 6.6% | 1.5% | 0.3% | 0.0% | 0.0% | 0.0% |
Garbine Muguruza | 9.3% | 2.4% | 0.6% | 0.1% | 0.0% | 0.0% |
Andrea Hlavackova | 2.3% | 0.3% | 0.0% | 0.0% | 0.0% | 0.0% |
Mathilde Johansson | 4.5% | 0.8% | 0.1% | 0.0% | 0.0% | 0.0% |
Olga Puchkova | 1.7% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Anna Tatishvili | 3.9% | 0.6% | 0.1% | 0.0% | 0.0% | 0.0% |
Donna Vekic | 2.5% | 0.4% | 0.0% | 0.0% | 0.0% | 0.0% |
Melanie Oudin | 1.7% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
Maria Joao Koehler | 0.7% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
Yulia Putintseva | 2.7% | 0.4% | 0.1% | 0.0% | 0.0% | 0.0% |
Sara Sorribes Tormo | 1.0% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% |
The difference between the specific draw forecast and the aggregated draw forecasts are a rough measure of how much each player’s chances of advancing to each round changed as a result of the draw.
Okay, that’s kind of a measure of luck, but an 88x7 matrix with a bunch of pluses and minuses doesn’t do a great job of providing a single number to hang our hat on and see how lucky or unlucky a draw was for someone. However, the existing payout structures of tennis tournaments give us a readily available way to convert the differential between those two grids into a single number.
Each finishing place in a tennis tournament awards two types of payouts: a cash prize and ranking points, with different amounts assigned to different finishing places. If we multiply the payout structure by the expected finishing places of each player from the specific forecast, we can calculate how much money and points each player is expected to earn. We can repeat the same procedure for the aggregated draw forecast, and just like before, subtract the two for each player. This gives us two hard numbers to measure the effect of luck of the draw: how much money and points the draw gave or took away for each player. Here are the changes in expected money and points for each of the players in Madrid as a result of the draw:
Player | Change in Expected Points | Change in Expected Money |
Svetlana Kuznetsova | +154.1 | +€ 53,276 |
Maria Sharapova | +94.8 | +€ 44,476 |
Ana Ivanovic | +75.9 | +€ 28,243 |
Angelique Kerber | +58.7 | +€ 19,314 |
Julia Goerges | +56.3 | +€ 16,043 |
Francesca Schiavone | +51.8 | +€ 15,153 |
Sara Errani | +44.1 | +€ 14,334 |
Sabine Lisicki | +43.8 | +€ 12,696 |
Silvia Soler-Espinosa | +31.2 | +€ 8,302 |
Alize Cornet | +23.0 | +€ 6,663 |
Kaia Kanepi | +22.9 | +€ 7,405 |
Sorana Cirstea | +22.8 | +€ 6,545 |
Magdalena Rybarikova | +22.2 | +€ 5,874 |
Sloane Stephens | +21.6 | +€ 6,051 |
Elena Vesnina | +21.5 | +€ 5,751 |
Jelena Jankovic | +21.2 | +€ 6,693 |
Kiki Bertens | 21.2 | +€ 6,039 |
Mona Barthel | 14.2 | +€ 3,567 |
Kristina Mladenovic | 10.0 | +€ 2,590 |
Daniela Hantuchova | +8.0 | +€ 2,088 |
Serena Williams | +6.2 | -€ 1,806 |
Dominika Cibulkova | +4.6 | +€ 1,073 |
Laura Robson | +3.7 | +€ 1,012 |
Bojana Jovanovski | +2.5 | +€ 681 |
Kirsten Flipkens | +2.3 | +€ 417 |
Ayumi Morita | +1.6 | +€ 602 |
Shuai Peng | +1.1 | +€ 96 |
Alexandra Dulgheru | +0.2 | +€ 51 |
Sara Sorribes Tormo | -0.1 | -€ 14 |
Maria Joao Koehler | -0.3 | -€ 72 |
Melanie Oudin | -0.4 | -€ 109 |
Sofia Arvidsson | -0.5 | -€ 189 |
Aravane Rezai | -0.6 | -€ 158 |
Annika Beck | -0.7 | -€ 218 |
Yulia Putintseva | -0.7 | -€ 206 |
Olga Puchkova | -0.9 | -€ 243 |
Marina Erakovic | -1.0 | -€ 264 |
Andrea Hlavackova | -1.2 | -€ 325 |
Donna Vekic | -1.3 | -€ 349 |
Anna Tatishvili | -1.6 | -€ 446 |
Karolina Pliskova | -1.7 | -€ 454 |
Lucie Hradecka | -2.0 | -€ 562 |
Mathilde Johansson | -2.1 | -€ 574 |
Chanelle Scheepers | -2.3 | -€ 662 |
Varvara Lepchenko | -2.7 | -€ 613 |
Johanna Larsson | -3.0 | -€ 848 |
Venus Williams | -3.8 | -€ 2,692 |
Lesya Tsurenko | -3.9 | -€ 1,059 |
Camila Giorgi | -4.0 | -€ 1,110 |
Klara Zakopalova | -4.1 | -€ 1,478 |
Lauren Davis | -5.0 | -€ 1,383 |
Christina McHale | -5.0 | -€ 1,382 |
Stefanie Voegele | -5.2 | -€ 1,481 |
Mallory Burdette | -5.3 | -€ 1,512 |
Olga Govortsova | -6.0 | -€ 1,615 |
Garbine Muguruza | -6.3 | -€ 1,782 |
Maria-Teresa Torro-Flor | -7.8 | -€ 2,215 |
Su-Wei Hsieh | -8.6 | -€ 2,229 |
Mirjana Lucic | -9.0 | -€ 2,463 |
Jamie Hampton | -9.3 | -€ 2,650 |
Nadezda Petrova | -9.6 | -€ 2,388 |
Simona Halep | -10.6 | -€ 3,543 |
Lourdes Dominguez-Lino | -11.0 | -€ 3,477 |
Monica Niculescu | -11.2 | -€ 3,231 |
Maria Kirilenko | -12.3 | -€ 4,715 |
Yaroslava Shvedova | -12.6 | -€ 3,726 |
Jie Zheng | -13.6 | -€ 3,610 |
Petra Kvitova | -14.1 | -€ 6,567 |
Yanina Wickmayer | -14.3 | -€ 3,932 |
Flavia Pennetta | -15.0 | -€ 4,227 |
Tamira Paszek | -15.2 | -€ 4,031 |
Roberta Vinci | -18.0 | -€ 6,344 |
Marion Bartoli | -18.9 | -€ 5,504 |
Madison Keys | -19.5 | -€ 5,561 |
Tsvetana Pironkova | -20.1 | -€ 5,372 |
Urszula Radwanska | -20.1 | -€ 5,345 |
Lucie Safarova | -28.7 | -€ 9,251 |
Ekaterina Makarova | -31.1 | -€ 9,350 |
Anabel Medina Garrigues | -32.6 | -€ 9,381 |
Carla Suarez Navarro | -34.0 | -€ 9,613 |
Bethanie Mattek-Sands | -35.6 | -€ 10,591 |
Andrea Petkovic | -38.3 | -€ 11,649 |
Na Li | -43.4 | -€ 18,340 |
Anastasia Pavlyuchenkova | -43.5 | -€ 12,129 |
Victoria Azarenka | -44.4 | -€ 20,017 |
Samantha Stosur | -53.7 | -€ 17,103 |
Agnieszka Radwanska | -56.0 | -€ 22,669 |
Caroline Wozniacki | -57.5 | -€ 20,206 |
These are some pretty good quick and dirty numbers for assessing luck of the draw at a glance, and they hold up once you go through the actual bracket and see each player’s path. Svetlana Kuznetsova’s big rise in expected money comes mostly a cascading effect of a weak first-round clay opponent and a favorable range of third round opponents. Her most likely third rounder, Angelique Kerber, is the worst of the top 8 seeds on clay, so a quarterfinal/semifinal run isn’t nearly as doomed from the start as if she drew a potential third rounder against Serena or Sharapova. Conversely, Caroline Wozniacki’s bad luck comes mostly from a first round unlucky draw of Yaroslava Shvedova, a solid clay player, and a potential third rounder with Serena.
There’s plenty about the expected points/money chart that can be misleading, though. The higher ranked players will experience luck swings that are higher in order of magnitude, since they are the only ones realistically in play for finalist points and money, but luck of the draw can be proportionally more devastating to fringe players looking to break out into main draw entries from qualifiers and the Challenger Tour.
Case in point: the last qualifying draw in Madrid consisted of four players -- Madison Keys, Mirjana Lucic, Andrea Petkovic, and Bethanie Mattek-Sands -- fighting for one spot in the main draw. Three of those players are ranked in the AB Top 40, and the fourth is a solid clay player, so that is a veritable Group of Death for a qualifying section. Sure enough, all three of these AB top 40 players are in the unluckiest 15 by expected points, but those 20-40 points they’re expected to lose are much more important to their overall ranking than the names at the bottom of the list. Wozniacki’s “lost” 57.5 points is about 1.5% of her current total of 3760, but Mattek-Sands’ 35.6 points is 4% of her current total of 880; so Bethanie’s sensitivity to this particular luck of the draw is 267% higher than Caroline’s, even though she lost the most points from the draw.
As stated above, it’s inevitable that there will be winners and losers of every draw. So why bother quantifying who won and lost from luck? The same reason you calculate BABIP and fumble recovery rate: to use as a soft metric to understand whether a performance level is sustainable or due for regression to the mean. Tennis players often have their best tournament runs cited as an indicator of either how good they are or could be, but the difficulty of the draw in those tournaments is never used to qualify those runs and put them in proper context. At the minimum, introducing the acknowledgement of luck of the draw into the conversation would be a good start. That’s a lot easier to do when you can reasonably condense that concept into a single number.
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