WTA Head-to-Head Effects
If you thought Serena vs Maria was a lopsided head-to-head, you are right. But it isn’t the biggest head-to-head effect in recent WTA history.
Last week I looked at a mixed model approach for estimating unusual head-to-head results. I used the model to see which matchup results in the men’s game went the most against what each player’s overall ability on each surface would have predicted at the time of each match.
In this post, I apply the same model to the women’s game, focusing on matches played from 2010 to the present and events at the $125K level or higher. The 100 most surprising head-to-head results during this period are charted below. The player listed first in each label is the player who benefits from the head-to-head effect and the point sizes reflect the precision of the estimate (the bigger the point, the more certain we are that the effect is real).
The 2nd matchup from the top stands out immediately. This goes to Serena Williams now notorious dominance over Maria Sharapova, a rivalry that has gotten so lopsided that required a drug ban and a sensational memoir to revive interest in it. The two have faced each other 21 times and Williams has won 19 of those meetings. Between 2010 and their last completed match in 2016, they have played 14 times and Serena has never lost.
These stats may compel some readers to ask how the Serena-Maria head-to-head doesn’t get the No. 1 spot?
The reason goes back to what makes a head-to-head surprising. Is it simply the win-loss record? No. If that were enough we might be misled to conclude that no one saw Federer’s 13-1 record over Ivo Karlovic coming.
No, a surprise has to account for our expectations going into the match. And, to land on the list of most surprising head-to-heads, we have to see results repeatedly go against our expectations.
This makes Serena and Maria’s head-to-head an interesting one because, at least in terms of a surface-adjusted Elo rating, Serena was expected to win every one of their last 14 matches (from 2010 on). Across those, For most of those, her chances were between 55 and 75%. Serena’s least surprising win over Maria since 2010 was her semifinal victory at the 2015 Wimbledon Championships, while her most surprising wins were her back-to-back Madrid victories over Maria in 2012 and 2013.
Summing up all of Serena’s chances over these 14 matches tells us that winning 9 would have been entirely consistent with her odds. But, by winning all 14, Serena’s sheer dominance makes our already sunny forecasts back then look too pessimistic.
The number 1 spot on the list is probably not one that even avid tennis fans would have come up with. This is the head-to-head of Dominika Cibulkova and Svetlana Kuznetsova. Between 2010 and 2016, they met 6 times, each time Sveta had was the favourite, by a lot in their 2010 and 2011 meetings. Nonetheless, Cibulkova found a way to win every time. Because the standard ratings got this one wrong every time, it would seem a particularly strong case for some kind of style clash.
It is interesting to see several players appear multiple times among the 10 biggest matchup effects. Sveta is in the 3rd spot as well, with her head-to-head over Aga Radwanska, and this time the results were in Kuznetsova’s favour. Sam Stosur, Julia Georges, Ana Ivanovic, and Caroline Wozniacki all feature twice among the top 10 head-to-head effects, with Georges the only one to be favoured in both cases.
Looking across all of the top 100, there are several players who seem to be candidates for clashes of game style with their competitors. Agnieszka Radwanska is the most notable as she lands in 14 separate head-to-heads in this list. Now retired, Radwanska was known for her variety of shots and that versatility seems to have made her results much harder to pin down using standard ratings.
Although no other players approach the frequency of Radwanska among the head-to-heads, several do occur a large number of times. Sam Stosur and Ekaterina Makarova features in 8 of the matchups, Anastasia Pavlyuchenkova in 7 and Petra Kvitova in 6.
As was true for the men, adjusting for the head-to-head effects has no impact on performance of match predictions for a total season. The reason for this is two-fold. First, matchups of players with a considerable head-to-head are rare. In 2018, only 1 of every 6 matches at the International level of higher involved players who played 2 or more times since 2010. The second reason is that most head-to-head results are in good agreement with the overall ability of both players. Of more than 4,000 head-to-head effects estimated in the WTA match sample, only 30% had a matchup effect that would suggest shifting the standard prediction by >10%.
Although the global impact of the head-to-head correction isn’t that impressive, it is interesting to look at specific players to see how the way they matchup with other competitors would impact expectations around their results. Taking 2018 as an example, we look at the improvement of the head-to-head adjustment for matches played during the season.
Using the head-to-head corrected predictions would have gotten the best results for Elina Svitolina, considering how much she played in 2018 and the matchup effects she came up against. Some of the biggest gains she would have gotten owing to head-to-head were matches against Caroline Wozniacki, Angelique Kerber, and Darya Kasatkina. The table below shows that, all together, those adjustments amount to nearly 7 more correct predictions compared to the standard, transitive model.
| Player | Improved Win Predictions in 2018 with Head-to-Head Correction |
|---|---|
| Elina Svitolina | 6.6 |
| Simona Halep | 6.1 |
| Lucie Safarova | 2.8 |
| Petra Kvitova | 2.8 |
| Sloane Stephens | 2.7 |
| Timea Babos | 1.9 |
| Kristina Mladenovic | 1.7 |
| Madison Keys | 1.3 |
| Shuai Zhang | 1.3 |
| Anastasija Sevastova | 1.1 |
Predictions for Simona Halep would have been expected to get a similar improvement overall. The gains in this case would come from adjustments upward in 2018 against opponents like Naomi Osaka, Angelique Kerber and Caroline Garcia. But also adjustments downward against Caroline Wozniacki and Elina Svitolina who Halep has matched up less well against historically.
The expected gains in prediction over a season diminish quite notably from there on. It reinforces the conclusion that we should be skeptical when people suggest that head-to-heads are the most indicative of how players will perform against each other. The reality is that a players history against players of similar strength is a much more reliable indicator. All but a handful of head-to-heads involve too few matches that are too widely dispersed over time to be of great help in pinning down the peculiarities of a specific player-opponent matchups.
