Italian translation at settesei.it
Update: The numbers in this post summarizing the effectiveness of sElo are much too high–a bug in my code led to calculating effectiveness with post-match ratings instead of pre-match ratings. The parts of the post that don’t have to do with sElo are unaffected and–I hope–remain of interest.
One of the talking points throughout the 2017 WTA season has been the unpredictability of the field. With the absence of Serena Williams, Victoria Azarenka, and until recently, Petra Kvitova and Maria Sharapova, there is a dearth of consistently dominant players. Many of the top remaining players have been unsteady as well, due to some combination of injury (Simona Halep), extreme surface preferences (Johanna Konta), and good old-fashioned regression to the mean (Angelique Kerber).
No top seed has yet won a title at the Premier level or above so far this year. Last week, Stephanie Kovalchik went into more detail, quantifying how seeds have failed to meet expectations and suggesting that the official WTA ranking system–the algorithm that determines which players get those seeds–has failed.
There are plenty of problems with the WTA ranking system, especially if you expect it to have predictive value–that is, if you want it to properly reflect the performance level of players right now. Kovalchik is correct that the rankings have done a particularly poor job this year identifying the best players. However, there’s something else going on: According to much more accurate algorithms, the WTA is more chaotic than it has been for decades.
Picking winners
Let’s start with a really basic measurement: picking winners. Through Rome, there had been more than 1100 completed WTA matches. The higher-ranked player won 62.4% of those. Since 1990, the ranking system has picked the winner of 67.9% of matches, and topped 70% during several years in the 1990s. It never fell below 66% until 2014, and this year’s 62.4% is the worst in the 28-year time frame under consideration.
Elo does a little better. It rates players by the quality of their opponents, meaning that draw luck is taken out of the equation, and does a better job of estimating the ability level of players like Serena and Sharapova, who for various reasons have missed long stretches of time. Since 1990, Elo has picked the winner of 68.6% of matches, falling to an all-time low of 63.1% so far in 2017.
For a big improvement, we need surface-specific Elo (sElo). An effective surface-based system isn’t as complicated as I expected it to be. By generating separate rankings for each surface (using only matches on that surface), sElo has correctly predicted the winner of 76.2% of matches since 1990, almost cracking 80% back in 1992. Even sElo is baffled by 2017, falling to it’s lowest point of 71.0% in 2017.
(sElo for all three major surfaces is now shown on the Tennis Abstract Elo ratings report.)
This graph shows how effectively the three algorithms picked winners. It’s clear that sElo is far better, and the graph also shows that some external factor is driving the predictability of results, affecting the accuracy of all three systems to a similar degree:
Brier scores
We see a similar effect if we use a more sophisticated method to rate the WTA ranking system against Elo and sElo. The Brier score of a collection of predictions measures not only how accurate they are, but also how well calibrated they are–that is, a player forecast to win a matchup 90% of the time really does win nine out of ten, not six out of ten, and vice versa. Brier scores average the square of the difference between each prediction and its corresponding result. Because it uses the square, very bad predictions (for instance, that a player has a 95% chance of winning a match she ended up losing) far outweigh more pedestrian ones (like a player with a 95% chance going on to win).
In 2017 so far, the official WTA ranking system has a Brier score of .237, compared to Elo of .226 and sElo of .187. Lower is better, since we want a system that minimizes the difference between predictions and actual outcomes. All three numbers are the highest of any season since 1990. The corresponding averages over that time span are .207 (WTA), .202 (Elo), and .164 (sElo).
As with the simpler method of counting correct predictions, we see that Elo is a bit better than the official ranking, and both of the surface-agnostic methods are crushed by sElo, even though the surface-specific method uses considerably less data. (For instance, the clay-specific Elo ignores hard and grass court results entirely.) And just like the results of picking winners, we see that the differences in Brier scores of the three methods are fairly consistent, meaning that some other factor is causing the year-to-year differences:
The takeaway
The WTA ranking system has plenty of issues, but its unusually bad performance this year isn’t due to any quirk in the algorithm. Elo and sElo are structured completely differently–the only thing they have in common with the official system is that they use WTA match results–and they show the same trends in both of the above metrics.
One factor affecting the last two years of forecasting accuracy is the absence of players like Serena, Sharapova, and Azarenka. If those three played full schedules and won at their usual clip, there would be quite a few more correct predictions for all three systems, and perhaps there would be fewer big upsets from the players who have tried to replace them at the top of the game.
But that isn’t the whole story. A bunch of no-brainer predictions don’t affect Brier score very much, and the presence of heavily-favored players also make it more likely that massively surprising results occur, such as Serena’s loss to Madison Brengle, or Sharapova’s ouster at the hands of Eugenie Bouchard. Many unexpected results are completely independent of the top ten, like Marketa Vondrousova’s recent title in Biel.
While some of the year-to-year differences in the graphs above are simply noise, the last several years looks much more like a meaningful trend. It could be that we are seeing a large-scale changing of a guard, with young players (and their low rankings) regularly upsetting established stars, while the biggest names in the sport are spending more time on the sidelines. Upsets may also be somewhat contagious: When one 19-year-old aspirant sees a peer beating top-tenners, she may be more confident that she can do the same.
Whatever influences have given us the WTA’s current state of unpredictability, we can see that it’s not just a mirage created by a flawed ranking system. Upsets are more common now than at any other point in recent memory, whichever algorithm you use to pick your favorites.