Quantifying luck of the draw in tennis

Matthew Stockman

The biggest influence of luck in tennis happens before the matches even start. Here's how to quantify it, and why it's important.

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.

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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