On this week’s podcast, Carl, Jeff and I briefly discussed where Caroline Wozniacki ranks among Open-era greats. She’s among the top ten measured by weeks at the top of the rankings, but she has won only a single major. By Jeff’s Championship Shares metric, she’s barely in the top 30.
I posed the same question on Twitter, and the hive mind cautiously placed her outside the top 20:
It’s difficult to compare different sorts of accomplishments–such as weeks at number one, majors won, and other titles–even without trying to adjust for different eras. It’s also challenging to measure different types of careers against each other. For more than a decade, Wozniacki has been a consistent threat near the top of the game, while other players who won more slams did so in a much shorter burst of elite-level play.
Elo to the rescue
How good must a player be before she is considered “great?” I don’t expect everyone to agree on this question, and as we’ll see, a precise consensus isn’t necessary. If we take a look at the current Elo ratings, a very convenient round number presents itself. Seven players rate higher than 2000: Ashleigh Barty, Naomi Osaka, Bianca Andreescu, Simona Halep, Karolina Pliskova, Elina Svitolina, and Petra Kvitova. Aryna Sabalenka just misses.
Another 25 active players have reached an Elo rating of at least 2000 at their peak, from all-time greats such as Serena Williams and Venus Williams down to others who had brief, great-ish spells, such as Alize Cornet and Anastasia Pavlyuchenkova. Since 1977, 88 women finished at least one season with an Elo rating of 2000 or higher, and 60 of them did so at least twice.
(I’m using 1977 because of limitations in the data. I don’t have complete match results–or anything close!–for the early and mid 1970s. Unfortunately, that means we’ll underrate some players who began their careers before 1977, such as Chris Evert, and we’ll severely undervalue the greats of the prior decade, such as Billie Jean King and Margaret Court.)
The resulting list of 60 includes anyone you might consider an elite player from the last 45 years, along with the usual dose of surprises. (Remember Irina Spirlea?) I’ll trot out the full list in a bit.
Measuring magnitude
A year-end Elo rating of 2000 is an impressive achievement. But among greats, that number is a mere qualifying standard. Serena has had years above 2400, and Steffi Graf once cleared the 2500 mark. For each season, we’ll convert the year-end Elo into a “greatness quotient” that is simply the difference between the year-end Elo and our threshold of 2000. Barty finished her 2019 season with a rating of 2123, so her greatness quotient (GQ) is 123.
(Yes, I know it isn’t a quotient. “Greatness difference” doesn’t quite have the same ring.)
To measure a player’s greatness over the course of her career, we simply find the greatness quotient for each season which she finished above 2000, and add them together. For Serena, that means a whopping 20 single-season quotients. Wozniacki had nine such seasons, and so far, Barty has two. I’ll have more to say shortly about why I like this approach and what the numbers are telling us.
First, let’s look at the rankings. I’ve shown every player with at least two qualifying seasons. “Seasons” is the number of years with year-end Elos of 2000 or better, and “Peak” is the highest year-end Elo the player achieved:
Rank Player Seasons Peak GQ
1 Steffi Graf 14 2505 4784
2 Serena Williams 20 2448 4569
3 Martina Navratilova 17 2442 4285
4 Venus Williams 14 2394 2888
5 Chris Evert 14 2293 2878
6 Lindsay Davenport 12 2353 2744
7 Monica Seles 11 2462 2396
8 Maria Sharapova 13 2287 2280
9 Justine Henin 9 2411 2237
10 Martina Hingis 8 2366 1932
11 Kim Clijsters 9 2366 1754
12 Gabriela Sabatini 9 2271 1560
13 Arantxa Sanchez Vicario 12 2314 1556
14 Amelie Mauresmo 6 2279 1113
15 Victoria Azarenka 9 2261 1082
16 Jennifer Capriati 8 2214 929
17 Jana Novotna 9 2189 848
18 Conchita Martinez 11 2191 836
19 Caroline Wozniacki 9 2189 674
20 Tracy Austin 5 2214 647
Rank Player Seasons Peak GQ
21 Mary Pierce 8 2161 637
22 Elena Dementieva 9 2140 629
23 Simona Halep 7 2108 562
24 Svetlana Kuznetsova 6 2136 543
25 Hana Mandlikova 6 2160 516
26 Jelena Jankovic 4 2178 450
27 Pam Shriver 5 2160 431
28 Vera Zvonareva 5 2117 414
29 Agnieszka Radwanska 8 2106 399
30 Ana Ivanovic 5 2133 393
31 Petra Kvitova 6 2132 346
32 Na Li 4 2095 310
33 Anastasia Myskina 4 2164 290
34 Anke Huber 6 2072 277
35 Mary Joe Fernandez 4 2110 274
36 Nadia Petrova 6 2094 265
37 Dinara Safina 3 2132 240
38 Andrea Jaeger 4 2087 237
39 Angelique Kerber 4 2109 224
40 Nicole Vaidisova 3 2121 222
Rank Player Seasons Peak GQ
41 Manuela Maleeva Fragniere 6 2059 194
42 Anna Chakvetadze 2 2107 174
43 Ashleigh Barty 2 2123 162
44 Helena Sukova 3 2078 150
45 Jelena Dokic 2 2110 142
46 Iva Majoli 2 2067 119
47 Elina Svitolina 3 2052 108
48 Garbine Muguruza 2 2061 98
49 Zina Garrison 2 2065 96
50 Samantha Stosur 3 2061 92
51 Daniela Hantuchova 2 2050 80
52 Irina Spirlea 2 2064 76
53 Nathalie Tauziat 3 2041 73
54 Patty Schnyder 2 2057 70
55 Chanda Rubin 3 2034 68
56 Marion Bartoli 2 2033 66
57 Sandrine Testud 2 2041 62
58 Magdalena Maleeva 2 2024 41
59 Karolina Pliskova 2 2028 37
60 Dominika Cibulkova 2 2007 7
You’ll probably find fault with some of the ordering here. While it isn’t the exact list I’d construct, either, my first reaction is that this is an extremely solid result for such a simple algorithm. In general, the players with long peaks are near the top–but only because they were so good for much of that time. A long peak, like that of Conchita Martinez, isn’t an automatic ticket into the top ten.
From the opposite perspective, this method gives plenty of respect to women who were extremely good for shorter periods of time. Both Amelie Mauresmo and Tracy Austin crack the top 20 with six or fewer qualifying seasons, while others with as many years with an Elo of 2000 or higher, such as Manuela Maleeva Fragniere, find themselves much lower on the list.
Steffi, Serena, and the threshold
It’s worth thinking about what exactly the Elo rating threshold of 2000 means. At the simplest level, we’re drawing a line, below which we don’t consider a player at all. (Sorry, Aryna, your time will come!) Less obviously, we’re defining how great seasons compare to one another.
For instance, we’ve seen that Barty’s 2019 GQ was 123. Graf’s 1989 season, with a year-end Elo rating of 2505, gave her a GQ of 505. Our threshold choice of 2000 implies that Graf’s peak season has approximately four times the value of Barty’s. That’s not a natural law. If we changed the threshold to 1900, Barty’s GQ would be 223, compared to Graf’s best of 605. As a result, Steffi’s season is only worth about three times as much.
The lower the threshold, the more value we give to longevity and the less value we give to truly outstanding seasons. If we lower the threshold to 1950, Steffi and Serena swap places at the top of the list. (Either way, it’s close.) Even though Williams had one of the highest peaks in tennis history, it’s her longevity that truly sets her apart.
I don’t want to get hung up on whether Serena or Steffi should be at the top of this list–it’s not a precise measurement, so as far as I’m concerned, it’s basically a tie. (And that’s without even raising the issue of era differences.) I also don’t want to tweak the parameters just to get a result or two to look different.
Ranking Woz
I began this post with a question about Caroline Wozniacki. As we’ve seen, greatness quotient places her 19th among players since 1977–almost exactly halfway between her position on the weeks-at-number-one list and her standing on the title-oriented Championship Shares table.
If we had better data for the first decade of the Open era, Wozniacki and many others would see their rankings fall by at least a few spots. King, Court, and Evonne Goolagong Cawley would knock her into the 20s. Virginia Wade might claim a slot in the top 20 as well. We can quibble about the exact result, but we’ve nailed down a plausible range for the 2018 Australian Open champion.
One-number solutions like this aren’t perfect, in part because they depend on assumptions like the Elo threshold discussed above. Just because they give us authoritative-looking lists doesn’t mean they are the final word.
On the other hand, they offer an enormous benefit, allowing us to get around the unresolvable minor debates about the level of competition when she reached number one, the luck of the draw at grand slams she won and lost, the impact of her scheduling on ranking, and so on. By building a rating based on every opponent and match result, Elo incorporates all this data. When ranking all-time greats, many fans already rely too much on one single number: the career slam count. Greatness quotient is a whole lot better than that.