Last year, I introduced a bare-bones model that predicts men’s grand slam results for the next five years. It takes a minimum of inputs: a player’s age, and his number of major semi-finals, finals, and titles in the last two years. Despite leaving out so much additional data, the model explains a lot of the variation among players, achieving most of what a more complex algorithm would, but with nothing more than basic arithmetic.
A bit further down, I’ll introduce a similar model for women’s grand slam results. First, let’s look at the revised numbers for the men. Keep in mind that these are not career slam forecasts, but only slams in the next five years. That’s good enough for the Big Three, but it probably doesn’t tell the whole story for, say, Stefanos Tsitsipas.
Player Projected Slams Novak Djokovic 2.5 Rafael Nadal 2.1 Dominic Thiem 2.0 Alexander Zverev 0.9 Stefanos Tsitsipas 0.6 Daniil Medvedev 0.6 Matteo Berrettini 0.3 Lucas Pouille 0.1 Diego Schwartzman 0.1
A few other players (notably Roger Federer) reached a semi-final in the last two years, but because of their age, the model forecasts zero slams. Also keep in mind that Wimbledon was not played this year, so there was a bit less data to work with.* The sum of the forecasts is a mere 9.2 slams, out of a possible 20. In some previous years, the model predicted as many as 15 titles for the players it took into consideration. Because today’s top players are so old, they aren’t expected to dominate much of the 2021-25 calendar, leaving room for new contenders to emerge.
* My original post describes the forecasting algorithm as counting results from “the last four slams” and “the previous four slams.” We could account for the three-slam 2020 season by following those steps literally, giving greater weights to the last four slams (the 2019 US Open plus the three 2020 slams), and giving lesser (but still non-zero) weights to the four slams before that. I rejected that approach because (a) it would give an awful lot of weight to the US Open, and (b) the relative lack of 2020 data reflects higher-than-usual uncertainty, which ought to show up in the forecasts, as well. Thus, only seven slams were taken into account for 2021-25 predictions, instead of the usual eight.
Interestingly, the 2020 season has barely budged the predicted career totals for the big three. Numbers I published immediately after last year’s US Open forecast Rafael Nadal for 22.5 career slams: his (then) 19 plus 3.5 more. Now he has 20, and the model pegs him for another 2.1. Novak Djokovic was slated for a career total of 19.5: 3.5 more on top his then-total of 16. He’s still penciled in for 19.5: 17 plus another 2.5 in the future. Federer didn’t have reason to expect much a year ago, and it’s no better now.
The women’s model
It turns out that a similar back-of-the-envelope approach gives good approximations of future slam totals for WTA stars, as well. The weights are a bit different, the average peak age is one year sooner, and the age adjustment is slightly smaller, but the idea is essentially the same.
Here’s how to calculate the number of expected major titles for your favorite player:
- Start with zero points
- Add 20 points for each slam semi-final reached in the last 12 months
- Add 20 points for each slam final reached in the last 12 months
- Add 80 points for each slam title won in the last 12 months
- Add 10 points for each slam semi-final reached in the previous 12 months
- Add 10 points for each slam final reached in the previous 12 months
- Add 40 points for each slam title won in the previous 12 months
- If the player is older than 26 (at the time of the next slam), subtract 7 points for each year she is older than 26
- If the player is younger than 26, add 7 points for each year she is younger than 26
- Divide the sum by 100
To take a simple example, consider Iga Swiatek. For her recent French Open title, she gets 20 points for the semi, 20 points for the final, and 80 points for the title. She will still be 19 when the Australian Open rolls around, so we add another 49 points: 7 years younger than 26, times 7 points per year. Her projected total is (20 + 20 + 80 + 49) / 100 = 1.69.
Here are the results for all of the women who reached a major semi-final in 2019 or 2020 and are projected to win more than zero slams between 2021 and 2025:
Player Projected Slams Naomi Osaka 2.0 Sofia Kenin 1.9 Iga Swiatek 1.7 Bianca Andreescu 1.0 Ashleigh Barty 0.9 Amanda Anisimova 0.6 Simona Halep 0.6 Marketa Vondrousova 0.6 Nadia Podoroska 0.4 Garbine Muguruza 0.3 Belinda Bencic 0.3 Jennifer Brady 0.3 Elina Svitolina 0.2 Petra Kvitova 0.1 Victoria Azarenka 0.1
These forecasts sum to 11.0 slams, more than the men’s total. That’s largely because so many of recent women’s champions are younger, giving the model more reason to be optimistic about them. It still leaves plenty of room for other players to earn some hardware in the next half-decade, which makes sense. The WTA has featured a non-stop succession of breakout young stars for the past few years, and with players like Aryna Sabalenka, Elena Rybakina, and Cori Gauff in the mix, there’s no shortage of talent to keep the carousel turning.
And then there’s Serena Williams. The model projects her for zero slams, despite her three semi-finals and two finals in the last two years. The reason is her age: The algorithm expects players to steadily decline from age 27 onwards, so the age penalty by age 39 is harsh. One one hand, that makes sense: we’re forecasting the results of events that will mostly take place when she’s in her 40s. On the other hand, a player who had so much success at age 37 is probably a good bet to break the mold at 39, as well. Were this a more fully-developed model, we’d probably be smart to tinker with the age adjustment to reflect the reality that Williams is a much better bet to win a major title than Nadia Podoroska.
We could go on all day. For every variable that these forecasts take into account, there are a dozen more than have some plausible claim to relevance. But this simple approach gets us surprisingly far in telling the future–a future in which the men’s all-time grand slam race keeps getting more complicated, and the women’s game continues to feature a wide array of promising young stars.