Who Won the Draw?

The United States Open tennis tournament uses much the same procedures for draws and seeding as the Western and Southern. There are substantial structural differences, of course, as the Open has a draw of 128 with no byes, as opposed to the Western and Southern’s draw of 56 with 8 byes.

So, who benefits from the particular results of this draw?

The chief procedural difference between the two tourneys is that the Open has a much more sensible way of handling late scratches. At the Western and Southern, four players (including three of the eight whose seeding entitled them to first-round byes) were replaced directly with “lucky losers”, with the result that three players who lost in the last round of the qualifying not only got to play in the main draw, but were seeded into byes. At the open, the late scratch by Andy Murray wasn’t replaced directly by Lukas Lacko, the “lucky loser”. Instead, number 5 Marin Cilic gets Murray’s line, number 17 Sam Querrey get’s Cilic’s line, formerly-unseeded Philipp Kohlschreiber gets Querrey’s line, and Lacko comes in on an unseeded line.

As with the Western and Southern, I’ve simulated the tournament two ways: with the actual draw, and with a hypothetical draw that’s as close to the aspiration of the actual draw as my simulator allows.

For both simulations, I use a player’s rank according to the consensus betting odds (this time from oddschecker.com) as the measure of skill rather than the ATP point counts used for the actual seeding. I’ve tweaked the parameters of the model first developed here. Because the field is so much larger, it stands to reason that they’ll be a wider distribution of skills, so I set the cutoff for the entrants at Z=1 rather than Z=2. I also found that nudging the luck factor down from 1.15 to unity seems to fit the punter’s predictions a bit better.

The biggest winners and losers, at least in terms of absolute dollar expectancies, are toward the top of the table, where the numbers are bigger anyway.

Both Federer and Nadal are big losers, chiefly I expect because they are put into the upper half of the draw, while the two best players in the bottom half, Alexander Zverev and Cilic, are the biggest winners, especially because they’re the only two from the top eight in the skill distribution in the bottom half – all of the rest are stuffed into the upper half with Federer and Nadal.

As at the Western and Southern, Kyrgios and Del Potro suffer from the fact that they’re ATP point totals suggest a seeding much lower than their actual skill as assessed by the punters, and also because they land in the same overloaded quarter of the draw as Federer. Thiem is fairly seeded, but has the misfortune to land in Federer’s quarter of death. Dimitrov is a little under-seeded, and he too suffers by being sent to the top half.

Down the table, the unseeded players fortunate enough to draw other unseeded players do well. For example, 107th ranked Santiago Giraldo has drawn 118th ranked Vincent Millot, Neither one would be likely to do well in a fully-seeded tournament, and their prospects are still iffy in the base case tournament, which is partially seeded through 32 places. But one or the other has to win the extra $36,000 one gets for advancing to the second round. To some, perhaps, such pairings are a flaw in the partial seeding system that tennis uses, but I find the existence of such matches part of the charm of the event. No such luck for Dusan Lajovic, the 120th best player, who drew Nadal, but at least he probably gets to play a match on one of the big show courts.

Here is the full list, with expectations from the actual draw, the base case that protects 32 players but does not randomize them within tiers, and the difference between the two:

skill rank seed  actual draw  base case  gain or (loss)
1 3 Roger Federer  $1,637,008  $1,823,752  $(186,744)
2 1 Rafael Nadal  $1,113,508  $1,216,593  $(103,085)
3 4 Alexander Zverev  $984,507  $918,152  $66,356
4 7 Grigor Dimitrov  $661,896  $718,687  $(56,791)
5 2 Marin Cilic  $785,143  $607,545  $177,597
6 14 Nick Kyrgios  $414,540  $545,300  $(130,760)
7 6 Dominic Thiem  $411,831  $470,768  $(58,937)
8 24 Juan Martin del Potro  $367,988  $391,627  $(23,639)
9 8 Jo-Wilfried Tsonga  $409,212  $356,365  $52,847
10 10 John Isner  $385,699  $352,273  $33,426
11 18 Gale Monfils  $291,799  $331,883  $(40,083)
12 15 Thomas Berdych  $232,094  $303,033  $(70,939)
13 5 Sam Querrey  $290,829  $280,408  $10,421
14 16 Lucas Pouille  $297,862  $263,280  $34,581
15 28 Kevin Anderson  $239,790  $240,038  $(248)
16 9 David Goffin  $228,942  $208,159  $20,783
17 13 Jack Sock  $236,280  $199,004  $37,275
18 21 David Ferrer  $250,046  $208,473  $41,572
19 Denis Shapovalov  $159,258  $207,632  $(48,374)
20 11 Roberto Bautista-Agut  $187,520  $200,700  $(13,180)
21 26 Richard Gasquet  $159,111  $196,065  $(36,954)
22 Steve Johnson  $200,469  $191,525  $8,944
23 19 Gilles Muller  $174,831  $182,446  $(7,615)
24 31 Feliciano Lopez  $122,402  $171,258  $(48,856)
25 Thanasi Kokkinakis  $173,817  $165,223  $8,594
26 25 Karen Khachanov  $219,552  $165,583  $53,969
27 12 Pablo Carreno Busta  $230,014  $160,770  $69,244
28 Danill Medvedev  $110,259  $154,359  $(44,100)
29 Alexandr Dolgopolov  $130,905  $147,296  $(16,391)
30 Ernests Gulbis  $122,049  $141,187  $(19,138)
31 Gilles Simon  $119,994  $131,698  $(11,704)
32 17 Philipp Kohlschreiber  $146,262  $120,338  $25,924
33 32 Robin Hasse  $123,406  $114,719  $8,687
34 Jared Donaldson  $136,352  $112,939  $23,412
35 22 Fabio Fognini  $139,315  $111,049  $28,266
36 20 Albert Ramon-Vinolas  $172,111  $109,646  $62,465
37 Benoit Paire  $145,927  $108,310  $37,617
38 Hyson Chung  $118,435  $106,511  $11,924
39 23 Mischa Zverev  $144,717  $105,407  $39,310
40 30 Adrian Mannarino  $128,669  $104,094  $24,575
41 Jordan Thompson  $103,393  $102,456  $936
42 Borna Coric  $91,862  $101,270  $(9,409)
43 Kyle Edmund  $98,806  $100,030  $(1,224)
44 29 Diego Schwartzman  $121,372  $98,979  $22,393
45 Bernard Tomic  $96,821  $97,990  $(1,169)
46 Andrey Kuznetsov  $83,188  $97,209  $(14,021)
47 Damir Dzumhur  $103,198  $95,635  $7,562
48 Ivo Karlovic  $108,731  $95,059  $13,672
49 27 Pablo Cuevas  $100,106  $94,194  $5,912
50 Ryan Harrison  $76,717  $93,224  $(16,507)
51 Viktor Troicki  $110,487  $92,417  $18,071
52 Adrian Menendez-Maceiras  $101,902  $91,594  $10,308
53 Pierre-Hugues Herbert  $78,130  $90,836  $(12,706)
54 Andrey Rubiev  $82,387  $90,014  $(7,627)
55 Aljaz Bedene  $81,784  $89,348  $(7,564)
56 Joao Sousa  $97,287  $88,677  $8,610
57 Taylor Fritz  $94,255  $87,876  $6,379
58 Yuichi Sugata  $90,219  $87,505  $2,713
59 Dudi Sela  $96,393  $86,775  $9,618
60 Donald Young  $93,524  $85,996  $7,528
61 Fernando Verdasco  $91,685  $85,647  $6,039
62 Florian Mayer  $92,738  $85,210  $7,529
63 Horacio Zeballos  $81,564  $84,536  $(2,973)
64 Jiri Vesely  $73,179  $83,922  $(10,744)
65 Paolo Lorenzi  $87,970  $83,275  $4,695
66 Andreas Haider-Maurer  $91,424  $83,026  $8,399
67 Alessandro Giannessi  $72,820  $82,357  $(9,537)
68 Alex de Minaur  $66,612  $81,728  $(15,116)
69 Andreas Seppi  $76,497  $81,347  $(4,850)
70 Blaz Kavcic  $75,676  $80,990  $(5,314)
71 Bjorn Fratangelo  $84,230  $80,630  $3,600
72 Cameron Norrie  $97,447  $80,139  $17,309
73 Cedric-Marcel Stebe  $92,098  $79,437  $12,660
74 Christopher Eubanks  $82,690  $79,328  $3,362
75 Dmitri Tursunov  $94,787  $78,844  $15,942
76 Darian King  $57,493  $78,582  $(21,089)
77 Denis Istomin  $88,614  $78,215  $10,399
78 Dustin Brown  $90,037  $77,870  $12,167
79 Evgeny Donskoy  $82,078  $77,374  $4,704
80 Ernesto Escobedo  $97,302  $76,969  $20,333
81 Frances Tiafoe  $53,682  $76,667  $(22,985)
82 Guido Pella  $86,491  $76,237  $10,254
83 Geoffrey Blancaneaux  $75,454  $76,008  $(554)
84 Henri Laaksonen  $62,835  $75,877  $(13,042)
85 John Millman  $61,629  $75,462  $(13,832)
86 Jan-Lennard Struff  $67,941  $75,162  $(7,221)
87 Janko Tipsarevic  $69,920  $74,848  $(4,928)
88 Jeremy Chardy  $63,978  $74,578  $(10,600)
89 John-Patrick Smith  $85,578  $74,234  $11,344
90 Julien Benneteau  $67,239  $74,008  $(6,768)
91 Leonardo Mayer  $65,919  $73,817  $(7,897)
92 Likas Lacko  $74,023  $73,388  $635
93 Marius Copil  $59,193  $73,178  $(13,985)
94 Marton Fucsovics  $91,419  $72,838  $18,581
95 Malek Jaziri  $78,395  $72,568  $5,827
96 Marcos Baghdatis  $71,423  $72,319  $(896)
97 Maximillian Marterer  $72,464  $72,096  $368
98 Mikhail Kukushkin  $65,757  $71,869  $(6,112)
99 Mikhail Youzhny  $67,210  $71,629  $(4,418)
100 Norbert Gombos  $73,888  $71,540  $2,349
101 Nicolas Kicker  $77,003  $71,116  $5,887
102 Nicolas Almagro  $64,098  $70,836  $(6,738)
103 Nicholas Mahut  $85,805  $70,795  $15,010
104 Nikoloz Basilashvili  $66,188  $70,665  $(4,477)
105 Ruben Bemelmans  $61,597  $70,316  $(8,718)
106 Richardas Berankis  $70,207  $70,161  $46
107 Santiago Giraldo  $82,439  $69,798  $12,641
108 Stefano Travaglia  $69,080  $69,819  $(739)
109 Steve Darcis  $74,671  $69,553  $5,118
110 Taro Daniel  $71,757  $69,403  $2,353
111 Thomas Fabbiano  $75,756  $69,075  $6,681
112 Thai-son Kwiatkowski  $68,951  $69,016  $(65)
113 Thiago Monteiro  $72,525  $68,666  $3,859
114 Thomaz Bellucci  $73,464  $68,658  $4,806
115 Tim Smyczek  $68,304  $68,417  $(113)
116 Tommy Paul  $70,499  $68,217  $2,282
117 Vasek Pospisil  $68,287  $68,108  $180
118 Vincent Millot  $78,423  $68,008  $10,415
119 Yen-Hsun Lu  $66,692  $67,760  $(1,068)
120 Dusan Lajovic  $53,230  $67,646  $(14,416)
121 Patrick Kypson  $65,815  $67,484  $(1,669)
122 Tennys Sandgren  $55,500  $67,282  $(11,782)
123 Carlos Berlocq  $65,947  $67,160  $(1,213)
124 Evan King  $66,353  $66,901  $(548)
125 J.C. Aragone  $58,082  $66,760  $(8,678)
126 Radu Albot  $73,697  $66,523  $7,173
127 Rogerio Dutra Silva  $65,431  $66,503  $(1,072)
128 Vaclav Safranek  $53,908  $66,427  $(12,519)

 

 

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