Raising your game when it matters
Are some tennis players consistently better when it matters most?
Two weeks ago, Serena Williams made her return to singles tennis at Wimbledon after a year out injured. It didn’t start well, she lost the first set 7-5 to Harmony Tan, ranked 115 in the world. But she brought it back 6-1 in the second and it went to a third. After a back-and-forth third set the match went to a deciding tiebreak. I thought the result was inevitable at this point, Serena would raise her level when it really matters. Collective wisdom amongst pundits suggests that the top players always play better when it matters most. But shockingly she didn’t, the huge outsider Harmony Tan came through. It raises the question of whether the top players actually do play better in the more important points.
I decided to explore whether the best female tennis players perform better in the most important points. I used point-level data from every Grand Slam between 2011 and 2021. I use a win probability model to define important points. As discussed in a previous blog, you can measure the importance of a point by how much winning/losing it changes your probability of winning the match. I class all points which change win probability by more than 8 percentage points as important.
This approach improves on cruder measures such as break points. It excludes unimportant break points e.g. at 5-0 in the first set and includes other points which are important e.g. 30-30 at 5-5 in the final set. 21% of all points are classed as important points, including 50% of break points and 94% of tiebreak points are classed as important.
The below chart shows the results for players who played more than 50 matches in slams between 2012 and 2021. The point shows the difference between a player’s estimated point win percentage in important points versus other points in the same match (accounting for whether the player was serving/returning). The bars either side of the point reflect the 95% confidence interval around the estimate (an indication of the uncertainty of the estimates).
There are a few interesting results. Firstly, many of these most experienced players do not actually seem to raise their level in important points. Sharapova for example has performed worse in important points. Other players have performed better in the most important points but not by much and given the wide confidence intervals, this could just reflect lucky run rather than skill.
This suggests that commentators might be exaggerating when they say that the best players raise their games when it matters most. The below chart provides more evidence for this view. I split out the data into two periods 2011-2015 and 2016-21. I then investigate whether the players who played better in the important points in 2011-2015 also did so in 2016-2021. There is almost no correlation between the two measures. This suggests that most players aren’t either chokers who always drop their level when it matters or clutch players who always raise their level. Most players win a similar share of important points to other points. (This may be because all players perform slightly worse in important points by a similar amount, previous work has shown that unforced errors are more common in important points.)
However, some players do seem to consistently raise their games when it matters. Petra Kvitova appears to be the best at raising her level when it matters. She has won almost 4 percent more of important points than her other points. Caroline Garcia is a surprise name. She doesn’t have a particularly high win percentage on all points, but she does seem to raise her game when it matters.
Serena also seems to be able to raise her game when it matters most. She performs 2.7 percentage points better in the points which matter most. For Serena her improvement in performance is particularly driven by how her performance improves over the period of the game. Points tend to get more important the longer the match goes, and Serena has tended to perform better in points toward the end of the match. Part of the reason that Serena raises her game relative to her opponents in the important points may be better fitness.
The other (fairly obvious) thing to remember with Serena: she is really good. She wins a higher percentage of all of her points than other players. This is her main advantage in the important points. The below chart shows how players perform in important points relative to all players’ performance on all points (accounting for whether serving or returning). It differs from the first chart as it uses the average of all players’ performance as the comparison rather than an average of the player’s own performance on less important points. More familiar names come close to the top, which reflects the fact that they are good players who tend to perform well on average even if they don’t raise their performance for the most important points.
Serena stands out, she wins 6.2 percent more of her important points than the average of all points. 2.7 percentage points of that is due to her raising her game specifically for that point, but the other 3.5 percentage points just reflects that she tends to win a higher percentage of all points than other players. Serena is one of the few players who wins more of her points when it matters most and her game is already very good. Serena’s powers may be starting to wane, but if I had to bet on one player when it matters most, I’d still go for her.
Thanks to Jeff Sackman at Tennis Abstract for compiling the data. Let me know what you think, I plan on repeating the analysis for men’s players.