Introducing Serve and Return Skill Ratings

At You Cannot Be serious Stats we make a lot of use of player ratings. Ratings are the most informative single summary of a player’s ability at any point in time. This is why they are our go-to for tracking the ups and downs in each player’s success on court.

Ratings are great summaries of a player’s ability to win but they don’t say anything about the how behind wins. Take, for instance, the two most fundamental skills in tennis: serving and returning. Two players can earn the same rating with very different serve and return strengths – think, John Isner and Diego Schwartzman.

In order to evaluate skills, we have to go beyond match win outcomes. We have to look within a match at the way a player racks up points relative to their opposition. How much more effective are they at holding serve? How much more likely are they to win a point when receiving serve?

Fortunately, with public match statistics and some tweaks to standard ratings, we can construct serve and return skill ratings to answer these questions for any possible pro matchup.

What are the tweaks? First, rather than rating players on match wins we instead rate them on their points won on serve (or, in the case of return ratings, their opponent’s points won on serve). For any given match, we predict a server’s percentage of points won on serve based on the difference in their serve rating and their opponent’s return rating. We also add an adjustment for the average serve advantage on the surface being played. This accounts for the fact that we expect an average server playing an average returner to still have an edge.

In more exact terms, if we have a server rated S and a returner rated R, we let the probability the server win’s a point P as,

\(P = (1 + 10^{-(\theta + (S - R)/d)})^{-1}\)

where d is a scaling parameter that we optimize to be most predictive of serve outcomes. Ratings are updated after each match according to the actual and predicted performance on serve, using the above prediction rule.

Let’s see the method in action!

Below are current serve and return ratings for ATP players in the Top 64 on at least one skill. The rating shown combines surface-specific skills using weights that best explain serve and return results on all surfaces, so these can be considered all-surface skill summaries. The skill scatterplot in Figure 1 is one of the more interesting ways of visualizing skill ratings. It not only shows us how each player’s skill compares to the field but also highlights how much of a gap there is between a player’s server and return ability. Players far above the diagonal line are stronger servers, players far below are stronger receivers, players at the diagonal are those with little gap in skills.

Figure 1. Current all-surface serve and return ratings for ATP players that are in the Top 64 for at least one skill.

The scatterplot confirms that Novak Djokovic is currently the most complete player on tour. Djokovic takes the No. 1 spot in both serve and return skills with more than 2100 rating points on both skills. Several other current players who follow the Djokovic pattern, with close to equal ability on serve and return, are Jiri Lehecka and Sebastian Korda. Both Lehecka and Korda are several 100 points behind Djokovic, but at 21 and 22 years old, respectively, to match the level of his game in the same way they already match his balance.

Many top players have a more lopsided skill set and a more obvious target for raising the overall level of their game. Stefanos Tsitsipas and Felix Auger-Aliassime both fall into ‘strong serve, weak return’ pattern. At 2061 points on his serve rating, Tsitsipas is currently the No. 2 in serving skill. However, he takes the No. 22 on return ability with a rating of just 1834. Felix also has a roughly 200-point gap in serve and return skill.

With Tsitsipas’s recent loss to Novak Djokovic at the Australian Open, it is interesting to consider how many points he left on the table due to his return game. Against Djokovic’s serve, Tsitsipas would have been at a 289 point disadvantage when receiving. On hard courts that would correspond to a serve win probability for Djokovic of 75% – as it happens, this was exactly what Djokovic won on serve in the AO final. If Tsitsipas’s return were equal to his serve, the gap would be down to 62 points, dropping Djokovic’s serve win expectation to 65%. Clearly, that kind of skill gap is costing Tsitsipas major titles.

On the other end of the skill spectrum are players like Andy Murray, Jenson Brooksby and Alex De Minaur. These are the ‘strong receiver, weak serve’ type of players. All of them are rated between 1900 to 2000 points on return but are in the 1700 to 1800 range on serve.

We can find the same mix of patterns on the women’s side (Figure 2). But, in contrast to the ATP, we see the top players on the WTA reaching higher ratings on serve than on return. This tells us that there is greater depth on return side of the game and more players finding their edge with their serve ability.

Figure 2. Current all-surface serve and return ratings for WTA players that are in the Top 64 for at least one skill.

When we consider the relative rankings on serve and return, we find the more complete players represented among the current most decorated on tour. Aryna Sabalenka, Elena Rybakina, and Ons Jabeur are all included in this group and have fewer than 10 ranking positions between their serve and return skill rankings. Iga Swiatek is more in the ‘stronger server’ mold, with a rating of 2200 on serve and 1944 on return. While players like Victoria Azarenka and Amanda Anisimova are in the ‘stronger receiver’ camp, each having more than a +150 point edge on their return rating.

What does a 100 or 200 point difference in serve and return rating mean? For the current WTA, the chance of winning a point on serve when playing on hard courts is 53%. A server with a 100-point edge over the receiver would raise that expectation to 57%, and with a 200-point advantage to 62%.

Although we think the skill ratings we have debuted here are a great addition to standard player ratings, we have to acknowledge that they are not true measures of serve or serve return ability. Because we are basing these ratings on points won on serve, there is more at play to these ratings than the serve shot itself. This is why we can have a player like John Isner with a lower serve skill rating than Novak Djokovic, because, while Isner may have a better serve, the other parts of his game still give him a lower chance of winning points on serve against the same opponent as Novak’s chances.

It is hard to say much about the skill of individual shots with tennis match stats as they are. But we can go a bit further in our skill ratings by separating first and second serve skills, which we plan to introduce in an upcoming post. That will provide a more complete suite of serve and return skills to continue to analyze over the course of this and future seasons.