5. Only as good as your second serve. Unless you want to be very, very good.

Tennis’s most relatable maxim might well be: you’re only as good as your second serve. As an enthusiastic tennis hacker, I have many times drilled my first serve into the net and then thought between serves how much easier the game would be if I had a reliable, useful second serve.

Its importance stems from the fact that everyone serves a second serve at some point. You can hide other parts of your game, for example not everyone needs to come to the net, so you can hide a bad volleying technique. But you can’t hide the second serve.

As for me, the hacker, so for the rarefied air of the men’s top 100. How important is the second serve? How important is serving in general? Or returning serve?

Commentary on a professional player’s serve is the subject of a large percentage of TV air time. Tennis commentators and analysts focus on a player’s serving statistics and tend to highlight what is impressive or otherwise: for example, if a player has a very high first serve percentage in a match or a particularly low percentage of second serve points won. Occasionally, a player’s season or career averages are used to help explain his current performance – but of course this is confined to one player.

What we haven’t had is statistical analysis of a large set of data to determine whether serving statistics have any empirical relationship with a player’s ATP ranking. Whether serving statistics are meaningful in the big picture. (Stevegtennis.com, a staggering source of information for both men’s and women’s tennis, has probably come closest to analysing serving statistics in this post from November 2012.)

This post is that analysis.

The research

So, for this post, I have analysed the ATP tour’s “match facts” to determine whether there is any correlation between a player’s ranking and his serving performance. The match facts essentially present each Top 200 player’s serving and return of serve statistics by surface and in aggregate. I have set out the methodology for this analysis in more detail at the bottom of this post.

Unless otherwise stated, the analysis is for the period 2009 to 2013 on hard courts, the surface on which the majority of tennis is played. In the results below the numbers in brackets (eg 0.5) are correlation coefficients that essentially enumerate the strength of the link between a player’s ranking and a serving statistic. See the methodology below for further information.

The results

  • To get into the top 100, you need to win your service games, the stronger the second serve the better.

Within the top 100, there is a significant correlation between a player’s ranking and both the percentage of service games they win (0.6) and the percentage of second serve points won (0.5). The correlation with the percentage of first serves won is slightly weaker, but the overall message is clear.

  • To get into the top 50, do the same as before, but better.

Within the top 50, percentage of second serve points won (0.6) and service games won (0.5) remain central to a player’s ranking. There is no strong correlation yet with the ability to return serve.

  • Top 11-30: correlation tumbleweed. Develop consistency and mental strength?

For those players ranked between 11 and 30, there is no correlation between their serving performance or return of serve performance and their ranking.  This area of the rankings is like a customs holding area before either being passed through to the top 10 or returned back to the top 50. Other factors may explain this area of the rankings better: for example a player’s consistency (or lack of) or his mental strength (as espoused by this blog’s Clutch Index). Areas for further research, no question.

  • If you want to make it within the top 20, learn to return serve. Period.

There is a strong correlation with points won returning first and second serve (0.5 each) and with return games won (also 0.5). Over the last 3 years, the correlation with returning first serve and return games won reach 0.6. There is no correlation with serving performance. This helps to explain why Isner, Raonic and Almagro can make it to the edges of the top 10 but have not yet broken through. The percentage of points won in 2013 returning first serve for the three are low, respectively 24%, 28% and 26%. Wawrinka, Gasquet and Berdych are higher ranked and have first serve return percentages of 32%, 30% and 32% respectively.

  • The top 10: raising the bar again.

In the last three years, a player’s position within the top 10 has been conditioned predominantly on their ability to return serve. The correlation coefficients go through the roof: returning first serve (0.8), returning second serve (0.7) and return games won (0.8)*. In the same period, there is also a logical correlation with the percentage of break points won (0.7). As noted in the Clutch Index, these players also win the highest percentage of tight matches. A rarefied atmosphere indeed.

Summary

The information presented above is a framework created from patterns within the data. It does not explain why one player went up in the rankings: it shows what is broadly correlative as players move up and down the rankings. As such this information is the spine of what might be termed the “anatomy” of a tennis player. To which we can also add the Clutch Index and other measures in due course.

Can Isner, Raonic, Almagro change their spots, return serve better and head up the rankings? As President Bartlet said in the TV series, the West Wing:

“A coach once told me that the hardest thing to do in sports is to walk into your Super Bowl locker room at half-time and change the strategy that got you there ’cause it’s no longer working.”

And as I hack my way on the local courts of Wandsworth, south west London, it is good to know what will make me a better. You mean I need to work on my return too?

Annex 1: Methodology

Core data

The ATP Tour publishes and updates “match facts” for the top 200 players each year. The information is presented by three surfaces (hard, grass, clay) and also in aggregate.

There are fourteen points of analysis for each player that essentially break down into three categories:

  • Serving statistics: percentage of first serves made, first and second serve points won, service games won, and break points saved.
  • Return of serve statistics: percentage of points won returning first and second serve, return games won and break points won.
  • The ephemera or inconsequential: number of matches won and lost, aces and double faults.

Surface-specific ranking

The data are presented on each of the surfaces in the same ATP ranking order, regardless of a player’s ability on each of the surfaces. Let’s take as an example, Fabio Fognini. Fognini owes his ranking (19) to his performance on clay (including two clay court tournament wins and a final over the course of the summer). However, he is probably neither the 19th best player on clay nor the 19th best player on a hard court.

Accordingly, I created a surface specific ranking for each player. To do this I took the ATP points the player earned on that surface that year and divided it by the number of matches they played on that surface. This resulted in an ATP points per match score for each player. I ranked the players by the ATP points per match score in order to run the ATP match facts correlation.

Djokovic

Nadal

ATP ranking

1

2

ATP points on hard court

4190

5000

Hard court matches

36

22

ATP points per hard court match

116

227

Adjusted hard court ranking

2

1

Correlation coefficients

A good explanation of correlation coefficients can be found here.

Essentially, the coefficient is any number between 0 and 1. The nearer the number is to 1 the better the correlation. 0 means an absence of correlation; 1 a perfect correlation. Anything above 0.5 is meaningful; anything around 0.75 is El Dorado.

* I removed John Isner from the Top 10 correlation calculation for 2012. His win in Indian Wells skewed the data towards less correlation, which, with him removed, was otherwise almost a perfect correlation. Taking out one player from ten was acceptable, particularly Isner whose serve makes him an outlier in many ways.

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