Italian translation at settesei.it
15-year-old sensation Cori Gauff holds a WTA ranking of No. 313. She has played only a limited number of events that are considered by the WTA’s system, so even before her impressive run began, we could’ve predicted that her ranking was an understatement. But by how much?
Gauff doesn’t show up yet on my Elo ratings list because, before Wimbledon qualies, she hadn’t played at least 20 matches at the ITF $50K level or higher in the last year. However, she still had a rating: 1,488, good for 194th place among those who had met the playing time minimum. A rating in that range translates to about a 3% chance of upsetting current top-ranked player Ashleigh Barty, and a 10% chance of beating someone around 20th, such as Donna Vekic. Given how little data we had to work with at that point, that seemed like a reasonable assessment.
Since she arrived in London, she has won six matches: Three in qualifying and three in the main draw, with wins over Venus Williams, Magdalena Rybarikova, and Polona Hercog. Not bad for a teenager who had previous won only one slam qualifying match and one tour-level main draw match in her young career!
194th place doesn’t seem like such a fair judgment anymore. Any player who comes through qualifying and reaches the fourth round at a major deserves some reassessment, and that’s even more applicable to a player about whom we knew so little two weeks ago. The tricky part is figuring out how much to adjust. Is Gauff now a top-100 player? Top 50? Top 20?
Revising with Elo
The Elo algorithm does a good job of approximating how humans make those reassessments: The more data we already have about a player, the less we will adjust her rating after a win or loss. The previous player to defeat Hercog was Simona Halep, at Eastbourne. We already have years’ worth of match results for Halep, and she was heavily favored to win the match. Thus, the fact that she recorded the victory alters our opinion of her by only a small amount. In Elo terms, it was an increase from 2,100 points to 2,102–basically nothing.
Gauff is a different story. Entering her third-round clash with Hercog, not only did we know very little about her skill level, it wasn’t even clear if she was the favorite. The result caused Elo to make a considerably larger adjustment, increasing her rating from 1,713 to 1,755, a rise 21 times greater than what Halep received after beating the same opponent. The 42-point jump caused her to leapfrog 16 players in the rankings.
Here is Gauff’s Elo progression, from the moment she arrived at Wimbledon to middle Sunday. After each match, I show her overall Elo (the numbers I’ve been discussing so far), her grass-specific Elo, and her grass-weighted Elo, a 50/50 blend of overall and grass-specific that is used for forecasting. For each of the three ratings, I also show her ranking among WTA players with at least 20 matches in the last 52 weeks.
Match Overall Rk Grass Rk Weighted Rk Pre-Wimbledon 1488 194 1350 163 1419 187 d. Bolsova 1540 171 1405 132 1473 155 d. Ivakhnenko 1566 157 1447 107 1507 131 d. Minnen 1614 132 1514 57 1564 95 d. Venus 1670 108 1578 40 1624 73 d. Rybarikova 1713 83 1650 21 1682 41 d. Hercog 1755 67 1686 17 1721 31
Over the course of only six matches, Gauff has jumped from 194th in the overall Elo rankings to 67th. For forecasting purposes, her grass court rating has soared from 187th to 31st. Her current weighted rating of 1,721 is better than that of three other women in the round of 16: Karolina Muchova, Carla Suarez Navarro, and Shuai Zhang. She trails another surviving player, Elise Mertens, by only 20 points.
So you’re telling me there’s a chance
Unfortunately, none of those relatively weak grass-court players are Gauff’s next opponent. Instead, the 15-year-old will face Halep, the third-best remaining player (behind Barty and Karolina Pliskova), and a three-time quarter-finalist at the All England Club. Halep’s weighted Elo rating is 229 points higher than Gauff’s, implying that the veteran has a 79% chance of winning on Monday. The betting market concurs, suggesting that the probability of a Halep victory is about 80%.
It doesn’t usually have much of an effect on forecasts to update Elo ratings throughout a tournament. While anyone reaching the 4th round has a higher rating than they did before the event, the differences are typically small. And since forecasts are based on the difference between the ratings of two players, the forecast isn’t affected if both players’ ratings have increased by roughly the same amount.
As a teenager with such limited match experience, Gauff breaks the mold. Her pre-Wimbledon 1,488 Elo rating is only two weeks old, and it is already completely unrepresentative of what we know of her skill level. She’ll have ample time to prove us right or wrong in the upcoming years, but for now, we have good reason to estimate that she belongs–even more than some of the older players who have reached the second week at Wimbledon.