How do ATP players react in high stress situations?

It is almost impossible to follow tennis, particularly on social media, without seeing players being accused of choking. In just the last few days, over the course of the five sets of the US Open final between Dominic Thiem and Alexander Zverev, both players were accused of choking on the big stage. Indeed, if you believe social media, pretty much every time that a player loses serve or fails to break serve, they have 'choked'.

Obviously, that is nonsense, but the concept of choking in tennis is a very real phenomenon. An article by Karlene Sugarman, a sports psychology consultant describes it as stemming 'from your need for psychological safety. The more threatening a competitive event is to your psychological safety, the more stressful and disruptive the situation will seem'.

One would expect that different players react differently to stressful situations and potentially that the same players react differently to different types of stressful situation. Actually determining what is a stressful situation is not as easy as it sounds, but for the purposes of this, we will look at two different types of situation - serving to win a set and serving to stay in a set. Clearly, there are many other scenarios that could be looked at, but we need to start somewhere, so this is what I have settled on.

Methodology

The way that I will investigate how different players respond to these stressful situations is relatively simple. It is easy to get the percentage of occasions that a player successfully held serve when serving in these situation, so this gives us a starting point. However, simply looking at that percentage will not give us a clear indication of how they deal with pressure. Players like Isner and Raonic will always have a high hold percentage simply because of their serve, but that does not mean that they serve well under pressure. Similarly, if every time that you are serving for a set is against Novak Djokovic, you would expect to have a relatively low hold percentage as he is arguably the best returner in the history of tennis, so that does not really tell us anything.

To get a better indication, we need to calculate how likely a player is to win their service game in each situation. We can take the betting starting price to give us a good estimate of the chance of each player to hold serve at the start of the match. This is a good starting point, but it can be improved further. By the time that we get to one of our pressure situations, we have additional information as to how the two players are playing. If a player has held to love in every service game up to the point where they are serving for the set, we want to take this information into account. The predicted hold percentage for that player at the start of the match is almost certainly not the best estimate of his predicted hold percentage now - given his success on serve, we would want to increase this estimate. Similarly, if a player has been broken to love in every service game, we would probably want to decrease our current estimate.

I am not going to go into depth on how precisely we would update these estimates, but for each of our pressure situations, we can generate an estimate on how likely a player is to hold their serve given the progression of the match up until that stage.

Furthermore, at this stage, I am not going to distinguish between situations where players may have a double-break advantage or disadvantage. It is definitely something that is worth drilling down into in more detail at a later stage as having the additional cushion of an extra break certainly reduces the pressure on that particular game.

Serving for the set

Of our two stressful situations, this is probably the less stressful of the two. If you fail to serve out the set, you are still in the set and still have opportunities to win the set. However, we still see players often changing how they approach points in stressful situations. I have written in the past about how players often approach their first serve differently on break points, either serving more aggressively to try and increase their ace percentage or dialing back their serve to ensure that they have a better chance of landing their first serve.

Using data from the past 2 years on the ATP tour, we have a set of 79 players that have served for a set on at least 50 occasions. Unsurprisingly, Novak Djokovic is the player that has served for a set on the most occasions, followed by the new US Open champion Dominic Thiem, Daniil Medvedev, Stefanos Tsitsipas and Roger Federer. Now, let us have a quick look at which players hold their serve most often when serving for the set.

We can see that no player holds serve more regularly when serving for the set than Roger Federer, who holds serve a remarkable 97.4% of the time in this situation. The likes of Reilly Opelka, John Isner and Milos Raonic are also not surprising given they are three of the biggest servers in the game. So, this chart does not necessarily tell us that much. Now, let us look at which players have the biggest positive difference between their actual hold percentage and their expected hold percentage.

Once we control for expected hold, we can see some different names appear at the top of this list. Casper Ruud and Fabio Fognini are the two players that see the biggest increase in their serve hold percentage compared to expectation when serving for the match. Now let us look at the other end of the scale.

Here, we can see a number of players that have spent plenty of time near the top of the rankings that can struggle to successful serve out sets. Indeed, we saw Alexander Zverev unsuccessful attempt to serve for the US Open title in the 5th set on Sunday night, so maybe we should not be surprised that he was unsuccessful, given his clear under-performance in far less stressful scenarios. Similarly, I imagine few regular tennis watchers will be that surprised at the appearance of the French trio of Gilles Simon, Benoit Paire and Pierre-Hugues Herbert in this list.

Serving to stay in the set

Attempting to stay in a set is arguably a more stressful scenario than serving for the set given that you do not have a chance to rectify the situation in the set if you fail. Based on the hypothesis that players struggle more in higher pressure situations, we would expect to see more players under-performing expectations in this scenario.

However, let us first look at those players that actually seem to thrive under the pressure of serving to stay in the set.

Interestingly, none of the top 10 players in over-performance here appeared in the top 10 of over-performance when serving for the set. It raises some interesting questions about whether players are mentally strong or weak in general or whether the personalities and mental approach of players mean that they feel different types of pressure in different ways. Let us now look at the biggest under-performers in this situation.

As we hypothesized, the drop-off in actual hold percentages when serving to stay in the set are significantly larger than for serving for the set.

This does not make good reading for Kei Nishikori. When serving to stay in a set, he managed to hold serve just 57.4% of the time compared to an expected hold percentage of 80.0%. He also appeared toward the bottom of the serving for the set numbers, which suggests that he really does struggle with his serve when the pressure is on. Precisely how this manifests itself is potentially something to look at elsewhere - does he struggle to get his serves in or does he change how he plays in the rallies themselves?

Fabio Fognini is an interesting one having been one of the biggest over-performers when serving for the set. Clearly he reacts to the different types of stress in very different ways. Alexander Zverev and Benoit Paire also appear in the bottom 10 of both charts.

The final player to note in this chart is the world number one, Novak Djokovic. While he tends to serve to stay in sets on fewer occasions than most players due to his general quality, he does tend to under-perform in these situations.