How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci

Among the many good things that have happened to Flavia Pennetta and Roberta Vinci after reaching the final of this year’s US Open, both enjoyed huge leaps in Monday’s official WTA rankings. Pennetta rose from 26th to 8th, and Vinci jumped from 43rd to 19th.

Such large changes in rankings are always a little suspicious and expose the weakness of systems that award points based on round achieved. A lucky draw or one incredible outlier of a match doesn’t mean that a player is suddenly massively better than she was a couple of weeks ago.

To put it another way: As they are, the official rankings do a decent job of representing how a player has performed. What they don’t do so well is represent how well someone is playing, or the closely related issue of how well she will play.

For that, we can turn to Elo ratings, which Carl Bialik and Benjamin Morris used at the beginning of the US Open to compare Serena Williams to other all-time greats [1]. Elo awards points based on opponent quality, not the importance of the tournament or round. As such, the system provides a better estimate of the current skill level of each player than the official rankings do.

Sure enough, Elo agrees with my hypothesis, that Pennetta didn’t suddenly become the 8th best player in the world. Instead, she rose to 17th, just behind Garbine Muguruza (another Slam finalist overestimated by the rankings) and ahead of Elina Svitolina. Vinci didn’t really return to the top 20, either: Elo places her 34th, between Camila Giorgi and Barbora Strycova.

While her official ranking of 8th is Pennetta’s career high, Elo disagrees again. The system claims that Pennetta peaked during the US Open six years ago, after a strong summer that involved semifinal-or-better showings in four straight tournaments, plus a fourth-round win over Vera Zvonareva in New York. She’s more than 100 points below that career-high level, equivalent to the present gap between her and 7th-Elo-rated Angelique Kerber.

The current Elo rankings hold plenty of surprises like this, having little in common with the official rankings:

Rank  Player                 Elo  
1     Serena Williams       2460  
2     Maria Sharapova       2298  
3     Victoria Azarenka     2221  
4     Simona Halep          2204  
5     Petra Kvitova         2174  
6     Belinda Bencic        2144  
7     Angelique Kerber      2130  
8     Venus Williams        2126  
9     Caroline Wozniacki    2095  
10    Lucie Safarova        2084

Rank  Player                 Elo   
11    Ana Ivanovic          2078  
12    Carla Suarez Navarro  2062  
13    Agnieszka Radwanska   2054  
14    Timea Bacsinszky      2041  
15    Sloane Stephens       2031  
16    Garbine Muguruza      2031  
17    Flavia Pennetta       2030  
18    Elina Svitolina       2023  
19    Madison Keys          2019  
20    Jelena Jankovic       2016

While Victoria Azarenka is still nearly 200 points shy of her peak, Elo gives her credit for the extremely tough draws that have met her return from injury. Another player rated much higher here than in the WTA rankings is Belinda Bencic, whose defeat of Serena launched her into the top ten.

The oldest final

Pennetta and Vinci are both unusually old for Slam finalists, not to mention players who reached that milestone for the first time. Elo doesn’t consider them among the very best players active today, but next to other 32- and 33-year-olds in WTA history, they compare very well indeed.

Among players 33 or older, Pennetta’s current rating is sixth best in the last thirty-plus years [2]. As the all-time list shows, that puts her in extraordinarily good company:

Rank  Player                Age   Elo  
1     Martina Navratilova  33.4  2527  
2     Serena Williams      33.9  2480  
3     Chris Evert          33.4  2412  
4     Venus Williams       33.3  2175  
5     Nathalie Tauziat     33.9  2088  
6     Flavia Pennetta      33.5  2030  
7     Wendy Turnbull       33.1  2018  
8     Conchita Martinez    33.3  2014

In the 32-and-over category, Vinci stands out as well. Her lower rating, combined with the somewhat larger pool of players who remained competitive to that ago, means that she holds 24th place in this age group. For a player who has never cracked the top ten, 24th of all time is an impressive accomplishment.

Keep an eye out for more Elo-based analysis here. Soon, I’ll be able to post and update Elo ratings on Tennis Abstract and, once a few more kinks are worked out, use them to improve the WTA tournament forecasts on the site as well.


  1. My numbers don’t precisely match those from the FiveThirtyEight article, but they’re close. The code I used is closely adapted from this, and all of us are working from the same dataset.
  2. A simple Elo rating doesn’t penalize players for missing lots of time, or even retiring, so a player who returns after many years away from tour comes back with the same ranking they had when they left. So technically, Martina Hingis (in her Fed Cup singles comeback this year) and Kimiko Date-Krumm (at the beginning of her 2008 comeback) belong on this list, making Pennetta 8th. However, that doesn’t seem to be in the spirit of the ratings, so I’ve left them out. Also, I only have player ages back to the early 1980s, which probably leaves out some greats who excelled past 30 in the 1970s.

8 thoughts on “How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci”

  1. Jeff,

    Great post. How do the ELO ratings differ on the Men’s side differ from Jrank? Do you think one would be more predictive than the other?

    1. Haven’t compared elo with jrank yet; will post something with elo ATP ratings in the next few days when I’m able to add men’s US Open results to the system. Jrank is similar to elo in concept, but I got bogged down creating predictive (in theory) surface-specific ratings, so I overcomplicated things.

      1. I think you might be surprised just how well jrank predicts tennis matches across surfaces, even when compared to betting lines. I have been comparing the two since the French Open and jrank has had both a better binary prediction rate and higher r^2 when comparing predicted vs actual probabilities.

        1. i am suprised! i did a similar test for awhile last year and the results weren’t as positive. anyway, good to know–thanks!

  2. Great stuff Jeff. Elo rankings are so interesting. In soccer, baseball, tennis, whatever competition they’re applied to, they always seem to be more ‘correct’ than the official rankings/standings.

    I like how it lets you calculate expected results. By my reckoning only Sharapova has even a 25% win expectancy against Serena Williams based on their 162 point difference. It seems to me there can’t be too many instances where there’s only been one player with such a probability.

  3. Hi Jeff,

    Great input from Carl Bialik and Benjamin Morris to try the Elo rating on the top players. And quite interesting since the Elo system, if correctly used would be the best thing to happen to tennis ratings. However, the analysis is flawed since it relies on a distribution and at the high end of the curve, it needs to be adjusted. That is, given historical data if you wanted to input more information, this analysis actually falls apart. The simple Elo model would change for the top 2% of players. That is, the model given is almost definitely using an incorrect K-factor and initial distribution of ratings (e.g, what is your median?). Still, it is a nice, simplified comparison for a short-term analysis.

  4. Hi Jeff, would you consider developing a full prediction model, taking into account surface, specific tournament, handness, H2H, margin of score etc. ?
    i would be very glad participating in such a project!

Comments are closed.