The Summer of Jeff

Marginal ATP Rankings

Posted in tennis by Jeff on January 22, 2011

ATP rankings are frustrating: They are a decent approximation for player skill, but there are so many obvious flaws.  Some of those flaws derive from the problem of needing one number–there’s no accounting for surface, for instance.

The one that frustrates me the most is how much luck is allowed to creep into a player’s ranking.  When a player is awarded points for his performance in a certain tournament, there is no consideration of the skill level of the players he defeated.  So two players who lose in the second round get the same number of points, even if one defeated a 16-year-old wild card in the first round and the other defeated Rafael Nadal in the first round.

There are plenty of arguments in favor of the present way of doing things.

  • First, there’s the circular problem of finding a starting point–if ranking points aren’t an adequate measure of skill, how do you give numerical credit based on the skill of opponents?
  • Second, players don’t display consistent levels of skill; if Milos Raonic is in the fourth round of the Australian Open, he is probably playing better than he was four months ago when he lost in the first round of the U.S. Open.  Perhaps the person who defeats him in Melbourne deserves more points than the guys who beat him in qualifiers and challengers last fall.  Players also display different levels of skill depending on surface; beating Juan Carlos Ferrero is more impressive on clay than on grass, and you’re more likely to do so in a later round on clay.
  • Third, you could say that it all comes out in the wash.  Pros play a lot of tournaments, and while you might only get 20 points for beating a top-10 player in the first round, you might get an additional 90 points for beating an unseeded player three rounds later.

We could settle for the status quo, or we could experiment with a different approach and test it.  Testing these things is an enormous task, so for today I’m just presenting the experiment itself.

Opponent-based point awards

I looked at all ATP-level main draw and qualifying draw matches, along with Challenger-level main draw matches.  I figured out the marginal points awarded to the winner of each match (e.g., by winning in the third round in the Aussie Open, you get 180 points instead of 90 points, for 90 marginal points) and the ranking points of the loser at the time of the match.

For instance, when Nadal beat Federer in the Madrid final, Nadal was awarded 400 marginal points, and Federer had 10,690 ranking points.  Add up those two types of points, and it turns out that the total marginal points awarded in these matches are approximately 4.5% of the ranking points of the losers.

Thus, if we use a simple linear model, instead of giving Nadal 400 marginal points for winning that match, we give him 4.5% of 10,690, or 463 points.  In this case, not a big difference.  But when top players are upset in early rounds, the adjustment is huge.

To take a very different example: In Miami last year, Olivier Rochus beat Novak Djokovic in the round of 64.  For advancing to the round of 32, Rochus earned 20 marginal points.  Djokovic’s ranking point total at that point was 8,220, so if we give Rochus 4.5% of that, he gets 365 points.  As we’ll see, that single adjustment rockets him up the rankings.

Pros and Cons

Compared to the present ATP ranking system, this approach gives more credit to the players who are capable of a top-10 performance, even if they play at that level very rarely.  As we’ll see, a single major upset can make a huge difference, so perhaps it too heavily weighs a single match.  If Rochus happened to play Djokovic on a day when Djokovic had the flu, does he really deserve 365 points?

Another potential problem is that this model doesn’t consider the level of the opponents that a player loses to.  Nikolay Davydenko is known for his ability to beat Federer or Nadal, but in consecutive weeks in October, he lost to Pablo Cuevas and Mischa Zverev.  Should we rank someone based on their ability to defeat “better” players, or their inability to defeat “lesser” players?  As always the standard ATP ranking system appears to be a decent compromise.

For my purposes, what matters is how well a ranking system predicts future results.  I hope that soon I’ll be able to report on how this one performs.

In the meantime, here are the 2010 year-end top 100, using the opponent-based model I’ve described.  I’ve also included each player’s actual 2010 year-end ranking and the difference between their placement in the two systems.

Rk   Player                   Pts  Actual  Diff  
1    Rafael Nadal            4562       1     0  
2    Roger Federer           4529       2     0  
3    Robin Soderling         3905       5     2  
4    David Ferrer            3450       7     3  
5    Andy Murray             3347       4    -1  
6    Tomas Berdych           2891       6     0  
7    Jurgen Melzer           2772      11     4  
8    Novak Djokovic          2730       3    -5  
9    Fernando Verdasco       2697       9     0  
10   Andy Roddick            2331       8    -2  
11   Gael Monfils            2266      12     1  
12   Nikolay Davydenko       2070      22    10  
13   Mikhail Youzhny         2059      10    -3  
14   Ivan Ljubicic           1952      17     3  
15   Guillermo Garcia-Lopez  1948      33    18  
16   Nicolas Almagro         1908      15    -1  
17   Marcos Baghdatis        1859      20     3  
18   Marin Cilic             1843      14    -4  
19   Albert Montanes         1832      25     6  
20   Michael Llodra          1822      23     3  
21   Ernests Gulbis          1695      24     3  
22   Viktor Troicki          1654      28     6  
23   Mardy Fish              1646      16    -7  
24   Jo-Wilfried Tsonga      1577      13   -11  
25   Stanislas Wawrinka      1573      21    -4  
26   Richard Gasquet         1570      30     4  
27   Florian Mayer           1497      37    10  
28   John Isner              1473      19    -9  
29   Philipp Kohlschreiber   1456      34     5  
30   Feliciano Lopez         1396      32     2  
31   David Nalbandian        1395      27    -4  
32   Juan Monaco             1394      26    -6  
33   Samuel Querrey          1353      18   -15  
34   Xavier Malisse          1342      60    26  
35   Jeremy Chardy           1272      45    10  
36   Andrei Goloubev         1236      36     0  
37   Juan Carlos Ferrero     1227      29    -8  
38   Jarkko Nieminen         1214      39     1  
39   Gilles Simon            1180      41     2  
40   Janko Tipsarevic        1178      49     9  
41   Benjamin Becker         1145      53    12  
42   Michael Berrer          1144      58    16  
43   Thomaz Bellucci         1125      31   -12  
44   Alexander Dolgopolov    1058      48     4  
45   Denis Istomin           1058      40    -5  
46   Andreas Seppi           1047      52     6  
47   Thiemo de Bakker        1033      43    -4  
48   Potito Starace          1031      47    -1  
49   Daniel Gimeno            983      56     7  
50   Olivier Rochus           971     113    63  
51   Lleyton Hewitt           944      54     3  
52   Julien Benneteau         941      44    -8  
53   Marcel Granollers        937      42   -11  
54   Juan Ignacio Chela       872      38   -16  
55   Pablo Cuevas             868      63     8  
56   Tommy Robredo            851      50    -6  
57   Philipp Petzschner       817      57     0  
58   Sergey Stakhovsky        813      46   -12  
59   Dudi Sela                808      75    16  
60   Santiago Giraldo         805      64     4  
61   Michael Zverev           797      82    21  
62   Radek Stepanek           789      62     0  
63   Fabio Fognini            784      55    -8  
64   Mikhail Kukushkin        781      59    -5  
65   Yen-Hsun Lu              745      35   -30  
66   Igor Andreev             722      79    13  
67   Carlos Berlocq           719      66    -1  
68   Ryan Sweeting            716     116    48  
69   Teimuraz Gabashvili      714      80    11  
70   Arnaud Clement           703      78     8  
71   Lukas Lacko              691      89    18  
72   Tobias Kamke             652      67    -5  
73   Pere Riba                646      72    -1  
74   Rainer Schuettler        642      84    10  
75   Robin Haase              626      65   -10  
76   Florent Serra            625      69    -7  
77   Leonardo Mayer           622      94    17  
78   Rui Machado              618      93    15  
79   Kevin Anderson           596      61   -18  
80   Albert Ramos             595     123    43  
81   Ivo Karlovic             567      73    -8  
82   Frederico Gil            554     101    19  
83   Daniel Brands            546     104    21  
84   Alejandro Falla          544     105    21  
85   Simon Greul              534     130    45  
86   Simone Bolelli           521     107    21  
87   Filippo Volandri         509      91     4  
88   Ilia Marchenko           488      81    -7  
89   Marco Chiudinelli        486     117    28  
90   Filip Krajinovic         483     214   124  
91   Victor Hanescu           481      51   -40  
92   Bjorn Phau               479     102    10  
93   Ivan Dodig               478      88    -5  
94   Kei Nishikori            477      98     4  
95   Evgueni Korolev          468     140    45  
96   James Blake              467     135    39  
97   Ruben Ramirez-Hidalgo    466      77   -20  
98   Ricardo Mello            461      76   -22  
99   Grigor Dimitrov          460     106     7  
100  Brian Dabul              458      85   -15
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