{"id":3842,"date":"2020-01-09T14:20:43","date_gmt":"2020-01-09T14:20:43","guid":{"rendered":"http:\/\/www.tennisabstract.com\/blog\/?p=3842"},"modified":"2020-01-09T14:20:43","modified_gmt":"2020-01-09T14:20:43","slug":"whos-the-goat-balancing-career-and-peak-greatness-with-elo-ratings","status":"publish","type":"post","link":"https:\/\/www.tennisabstract.com\/blog\/2020\/01\/09\/whos-the-goat-balancing-career-and-peak-greatness-with-elo-ratings\/","title":{"rendered":"Who’s the GOAT? Balancing Career and Peak Greatness With Elo Ratings"},"content":{"rendered":"\n

On this week’s podcast<\/a>, Carl, Jeff and I briefly discussed where Caroline Wozniacki<\/a> 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<\/a> metric, she’s barely in the top 30.<\/p>\n\n\n\n

I posed the same question on Twitter, and the hive mind cautiously placed her outside the top 20:<\/p>\n\n\n\n

\nhttps:\/\/twitter.com\/tennisabstract\/status\/1214491560026484737\n<\/div><\/figure>\n\n\n\n

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.<\/p>\n\n\n\n

Elo to the rescue<\/strong><\/p>\n\n\n\n

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>, a very convenient round number presents itself. Seven players rate higher than 2000: Ashleigh Barty<\/a>, Naomi Osaka<\/a>, Bianca Andreescu<\/a>, Simona Halep<\/a>, Karolina Pliskova<\/a>, Elina Svitolina<\/a>, and Petra Kvitova<\/a>. Aryna Sabalenka<\/a> just misses.<\/p>\n\n\n\n

Another 25 active players have reached an Elo rating of at least 2000 at their peak, from all-time greats such as Serena Williams<\/a> and Venus Williams<\/a> down to others who had brief, great-ish spells, such as Alize Cornet<\/a> and Anastasia Pavlyuchenkova<\/a>. 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.<\/p>\n\n\n\n

(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<\/a>, and we’ll severely undervalue the greats of the prior decade, such as Billie Jean King<\/a> and Margaret Court<\/a>.)<\/i><\/p>\n\n\n\n

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<\/a>?) I’ll trot out the full list in a bit.<\/p>\n\n\n\n

Measuring magnitude<\/strong><\/p>\n\n\n\n

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<\/a> 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.<\/p>\n\n\n\n

(Yes, I know it isn’t a quotient. “Greatness difference” doesn’t quite have the same ring.)<\/i><\/p>\n\n\n\n

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. <\/p>\n\n\n\n

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:<\/p>\n\n\n\n

Rank  Player                     Seasons  Peak    GQ  \n1     Steffi Graf                     14  2505  4784  \n2     Serena Williams                 20  2448  4569  \n3     Martina Navratilova             17  2442  4285  \n4     Venus Williams                  14  2394  2888  \n5     Chris Evert                     14  2293  2878  \n6     Lindsay Davenport               12  2353  2744  \n7     Monica Seles                    11  2462  2396  \n8     Maria Sharapova                 13  2287  2280  \n9     Justine Henin                    9  2411  2237  \n10    Martina Hingis                   8  2366  1932  \n11    Kim Clijsters                    9  2366  1754  \n12    Gabriela Sabatini                9  2271  1560  \n13    Arantxa Sanchez Vicario         12  2314  1556  \n14    Amelie Mauresmo                  6  2279  1113  \n15    Victoria Azarenka                9  2261  1082  \n16    Jennifer Capriati                8  2214   929  \n17    Jana Novotna                     9  2189   848  \n18    Conchita Martinez               11  2191   836  \n19    Caroline Wozniacki               9  2189   674  \n20    Tracy Austin                     5  2214   647  \n                                                      \nRank  Player                     Seasons  Peak    GQ  \n21    Mary Pierce                      8  2161   637  \n22    Elena Dementieva                 9  2140   629  \n23    Simona Halep                     7  2108   562  \n24    Svetlana Kuznetsova              6  2136   543  \n25    Hana Mandlikova                  6  2160   516  \n26    Jelena Jankovic                  4  2178   450  \n27    Pam Shriver                      5  2160   431  \n28    Vera Zvonareva                   5  2117   414  \n29    Agnieszka Radwanska              8  2106   399  \n30    Ana Ivanovic                     5  2133   393  \n31    Petra Kvitova                    6  2132   346  \n32    Na Li                            4  2095   310  \n33    Anastasia Myskina                4  2164   290  \n34    Anke Huber                       6  2072   277  \n35    Mary Joe Fernandez               4  2110   274  \n36    Nadia Petrova                    6  2094   265  \n37    Dinara Safina                    3  2132   240  \n38    Andrea Jaeger                    4  2087   237  \n39    Angelique Kerber                 4  2109   224  \n40    Nicole Vaidisova                 3  2121   222  \n                                                      \nRank  Player                     Seasons  Peak    GQ  \n41    Manuela Maleeva Fragniere        6  2059   194  \n42    Anna Chakvetadze                 2  2107   174  \n43    Ashleigh Barty                   2  2123   162  \n44    Helena Sukova                    3  2078   150  \n45    Jelena Dokic                     2  2110   142  \n46    Iva Majoli                       2  2067   119  \n47    Elina Svitolina                  3  2052   108  \n48    Garbine Muguruza                 2  2061    98  \n49    Zina Garrison                    2  2065    96  \n50    Samantha Stosur                  3  2061    92  \n51    Daniela Hantuchova               2  2050    80  \n52    Irina Spirlea                    2  2064    76  \n53    Nathalie Tauziat                 3  2041    73  \n54    Patty Schnyder                   2  2057    70  \n55    Chanda Rubin                     3  2034    68  \n56    Marion Bartoli                   2  2033    66  \n57    Sandrine Testud                  2  2041    62  \n58    Magdalena Maleeva                2  2024    41  \n59    Karolina Pliskova                2  2028    37  \n60    Dominika Cibulkova               2  2007     7<\/pre>\n\n\n\n
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<\/a>, isn’t an automatic ticket into the top ten.<\/p>\n\n\n\n
From the opposite perspective, this method gives plenty of respect to women who were extremely good for shorter periods of time. Both Amelie Mauresmo<\/a> and Tracy Austin<\/a> 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<\/a>, find themselves much lower on the list.<\/p>\n\n\n\n
Steffi, Serena, and the threshold<\/strong><\/p>\n\n\n\n
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<\/em>.<\/p>\n\n\n\n
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. <\/p>\n\n\n\n
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<\/em> in tennis history, it’s her longevity<\/em> that truly sets her apart.<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
Ranking Woz<\/strong><\/p>\n\n\n\n
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.<\/p>\n\n\n\n
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<\/a> would knock her into the 20s. Virginia Wade<\/a> 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.<\/p>\n\n\n\n
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.<\/p>\n\n\n\n
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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 … Continue reading Who’s the GOAT? Balancing Career and Peak Greatness With Elo Ratings<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[32,127],"tags":[],"class_list":["post-3842","post","type-post","status-publish","format-standard","hentry","category-elo-ratings","category-wta"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/3842","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/comments?post=3842"}],"version-history":[{"count":0,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/3842\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/media?parent=3842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/categories?post=3842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/tags?post=3842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}