ANGELIQUE KERBER’s (pictured, left) reign at the top of the women’s tennis world rankings ended on July 10, when Spain’s Garbiñe Muguruza (right) knocked her out of Wimbledon in the fourth round. Although Ms. Kerber had yet to win a title in 2017, the numbers indicated that she was a slight favorite in the game: according to Elo, a statistical rating system that rates players based on their performance and the quality of their opponents, she was both the better player in general and he was better in particular on grass courts, the British grand slam surface. Predictions based on the model put Ms Kerber’s chances at 66.9%.
However, Bettors saw things differently. Going into the match, Ms Muguruza was the bookies’ favourite, priced at a probability of victory of around 62.5%. Ms. Kerber’s declining season certainly played a role in how the betting public valued her chances, but it cannot explain all of the difference: Ms. Muguruza’s season was only marginally better. A more likely explanation for the market’s preference for the low-level Spaniard was the history between the two players. In recent years, Ms Muguruza has clearly been better than Ms Kerber, winning each of their last four meetings dating back to the 2015 French Open.
Commentators often say that tennis is a game of matchups. On one level, the statement is a fact. But a proven indication of that claim is that some players, or individuals with a particular style of play, tend to do better or worse against certain opponents with whom they “match up” unusually well or poorly than they would when they were playing a generic competitor. of equal skill. If true, you could produce more accurate predictions for the results of these games by combining a standard comparison of the players’ overall abilities with a dose of their previous head-to-head record – or, in the end, discarding the first one altogether.
There is no shortage of anecdotal cases suggesting that “small data”—a fairly large sample of highly relevant observations, containing both players in the game you want to predict—may be more informative than rankings based on complete seasons or careers. Even though the latter come from much larger samples of games, they ask you to extrapolate the performance of players against a wide range of opponents to their specific games against a specific enemy. Ms. Kerber’s latest loss certainly seems to support the theory, as do several high-profile tournaments. Serena Williams has won an incredible 18 consecutive matches against Maria Sharapova, herself one of the all-time greats. Before Roger Federer reworked his backhand to better handle Rafael Nadal’s vicious spin, Mr. Nadal won 23 of 34 career meetings, usually the lesser of the two players.
In general, these two sources of information tend to point in the same direction. Over 9,000 women’s matches since 1990 in which the rivals have faced each other at least three times and one of the players has won a majority of the meetings, the head-to-head record pointed to the same side to the Elo rating of the players by two thirds. of the time. The subset of 3,000 matches in which the head-to-head and Elo ratings do not agree lends some credence to the “matchups” theory: the player came away with the edge in previous encounters but the Elo score showed lower effectively 60% of the time. . However, when we combine Elo rating and head-to-head records in a joint prediction, the former carries much more weight. The recipe that gives the best predictions puts the overall Elo score at around 50 after head-to-head matches. In theory, that means if two players had already faced off 100 times, the prediction would include two-thirds of their previous record against each other and one-third of pre- Elo rating. However, in practice, very few pairs of active players have faced each other even 10 times. As a result, Elo almost always makes up at least five-sixths of the mix, raising the question of whether it’s worth including head-to-head records at all.
But if the markets were wrong to put so much weight on Ms Kerber’s recent struggles against Ms Muguruza – Ms Kerber won the first three of her eight matches ‘ twin – why does she fall for the Spaniard? The first suspect is simple chance: even if Ms. Kerber had a 66.9% favorite in five consecutive matches, she would still have a 250 chance of losing the lottery. Such an appearance may seem thin at first. But with the large number of games that are played each year, it is very likely that at least one player would suffer a long loss against a certain, inferior opponent simply due to random variation.
However, just because a long streak of money will include long streaks of heads or tails precludes the possibility that Ms. Kerber will actually match to bad for Ms Muguruza. To examine such a hypothesis, we need a database larger than a handful of head-to-head matchups, but one that is still limited to players whose games are relatively similar to those of those opponents. . For example, Ms. Kerber is a tactical, defensive player, who succeeds largely by outplaying and outthinking her opponents. In contrast, Ms Muguruza is more aggressive, trying to end points quickly with her powerful serve and groundstrokes aimed at the corners. Such differences can be measured statistically: according to a metric called Aggressive Score (AS), which estimates how often a player tries to finish points, Ms. Kerber is around the 25th percentile on the women’s tour, but Ms. Muguruza is the wind. up near the 65th.
Sure enough, it’s opponents of Ms Muguruza’s type – the third quartile of AS, the group of players who are aggressive but not terrible – that have given Ms Kerber trouble. Since the start of last season, the German has feasted on his passive teammates, winning 65% of games against opponents in his own AS quarterback. She has also resisted hitting the other end, getting involved in 69% of her contests against the most aggressive opponents. However, against players in Ms Muguruza’s category, she only won 40%. Of the women currently in the top ten, Ms Kerber has the worst record against opponents in the third quarter. (This difference is not because players with Ms Muguruza’s approach tend to be better overall: the average Elo score is about the same for each of the four quarters, both for her ‘tour as a whole and especially among Ms Kerber’s opponents.)
This suggests that Ms Kerber’s poor results against her Spanish rival may be more than just a fluke. Rather, it appears to represent a tactical weakness, one that can be measured using statistics about playing style. Because this breed of tennis analysis relies on shot-level data, which is not available for most tour-level matches, it is still in its infancy. But as the modern stage progresses, it becomes easier to identify the stylistic features that tend to justify the cliché that tennis is a game of matchups. And for Ms Kerber, better analytics will pinpoint the gaps in her game that make her so vulnerable against a certain type of opponent – and perhaps even give her a chance to end the streak who lost five games against Ms Muguruza.
