Elo is a fantastic tool for its explicit purpose: estimating the skill level of players based on available information. For instance, my WTA ratings currently rank Ashleigh Barty second. That seems plausible enough–it may be correct to give her the edge in a head-to-head matchup with everyone on tour except for Naomi Osaka. But with women pursuing such different schedules this season, a rating is only so useful.
For all of Barty’s or Osaka’s skill, is it right to say either one of them has had a better 2021 season than Garbine Muguruza? Osaka won the Australian Open, so she has a valid claim. Barty’s argument is a lot more tenuous, based on only eight victories. The Spaniard’s case writes itself–only a handful of players are up to double digits in wins this year, and Muguruza already has 18. How could we decide? If Elo is the smart version of the official rankings, what’s the smart version of the official race?
Starting fresh
The Elo algorithm itself offers a solution. A big part of the reason Muguruza is rated 4th on my current Elo list–and not higher–is her career before 2021. We had hundreds of matches worth of data on Garbine before January 1st, and it would be silly to throw all that away. Her 18-4 start is fantastic, but it doesn’t supersede everything that came before. It just gives us reason to update our rating.
Here’s where the ranking/race analogy is useful. The official rankings use a time span of 52 weeks (or more). The race restarts on January 1st. We could do the exact same thing with Elo, throwing away all results from the previous year and starting over, but that would be wasteful–it wouldn’t allow us to take into account whether players had faced particularly easy or tough draws, for instance.
The solution is to set Elo ratings back to zero (or 1500, in Elo parlance) one player at a time.
Take Muguruza. Instead of starting the year with a rating of 1981 and a history of several hundred matches, we pretend to know nothing about her. We give her a newbie’s rating of 1500 and a history of zero matches. Then we run the Elo algorithm to update her rating over the course of her 22 matches. First she faces Kristina Mladenovic (with her actual rating at the time of 1817), and improves to 1605. Then she beats Aliaksandra Sasnovich (and her rating of 1805), and improves to 1692. Repeat for each of her 2021 results, and the end result is a rating of 2160–almost 100 points higher than her current “real Elo” rating and within shouting distance of Osaka’s 2189.
To compare players, work through the same steps for everybody else, calculating their current-season rating as if they played their first career match in January.
It’s worth taking a moment to think about exactly what we’re measuring. That outstanding 2160 rating is what you get if a complete unknown shows up with zero match experience, then goes on the 22-match run that has been Muguruza’s season so far. The difference between real-Garbine and fake-newbie-Garbine is that the real one has an extensive track record that tells us she’s always been good–but that she probably isn’t quite this good.
I call it … yElo
This approach is “Elo for seasons” or “year Elo”–yElo*. It doesn’t have to be limited to calendar years, as the same approach would be useful to comparing, say, 20-match segments. It allows us to take advantage of the Elo algorithm–and the well-informed ratings of other players–to measure partial careers.
* you can pronounce it like the color “yellow,” but I prefer to say it like Phil Dunphy from Modern Family answering the phone.
Muguruza’s 2160 rating sure looks good, so how does it stack up against the rest of the tour? Here’s the 2021 top 20, considering players with at least five match wins through the Dubai and Guadalajara finals last weekend:
Rank Player W-L yElo 1 Garbine Muguruza 18-4 2160 2 Naomi Osaka 10-0 2094 3 Jessica Pegula 15-5 2002 4 Serena Williams 8-1 1997 5 Elise Mertens 11-2 1971 6 Karolina Muchova 7-1 1953 7 Aryna Sabalenka 11-4 1943 8 Iga Swiatek 10-3 1941 9 Daria Kasatkina 10-4 1910 10 Barbora Krejcikova 10-5 1905 11 Shelby Rogers 9-4 1902 12 Jil Teichmann 9-5 1899 13 Anett Kontaveit 9-4 1897 14 Jennifer Brady 9-4 1892 15 Cori Gauff 11-5 1885 16 Danielle Collins 9-4 1883 17 Ashleigh Barty 8-2 1878 18 Sara Sorribes Tormo 9-2 1867 19 Ann Li 5-1 1864 20 Simona Halep 6-2 1854
Like any Race list in March, this isn’t really reflective of skill. But when we consider the small amount of data it has to work with for each player, it’s … pretty good?
Again, you can quibble over whether Osaka or Muguruza has had the better season, but this approach weighs the better winning percentage and stronger average opponent against the much higher absolute win count and gives us a credible answer. Muguruza’s additional evidence of good tennis playing puts her ahead of Osaka’s evidence of short-term unbeatability.
While yElo is basically just a toy–it certainly doesn’t have the same predictive value as regular Elo–this initial look makes me like it. The possibilities are endless, from more sophisticated race tracking, to ranking the greatest seasons of all time, to comparing a player’s current hot streak to what’s she’s done in the past. Stay tuned, as I’m sure I’ll have more yElo results to report in the future.