Holding Serve: Sole Recipe for Success?
Evaluating the importance of winning service games from a statistical perspective
Most tennis players, at some stage of their tennis career, have been told that “winning matches boils down to holding your serve”. For the non-tennis folks, all points in a tennis match begin with a serve- it is the only way that a game of tennis starts. In general, serving in tennis offers plenty of advantages and having a good serve is crucial for winning tennis matches, especially at professional level. From a physical perspective, being tall is beneficial when it comes to serving; however, with the modern game of tennis evolving, holding serve is not as easy as it used to be. That is where the mental fortitude of a player comes in; winning a game from being 40–0 up may not be the most challenging obstacle, but what separates grand slam champions from the rest of the pack is the ability to be mentally strong and win a game from being 0–30 down. This article analyzes point-by-point data to calculate the statistical likelihood of winning a service game from the various stages/scores within a game.
Raw data for the mens’ US Open and Wimbledon grand slams was collected from Github (https://github.com/JeffSackmann/tennis_slam_pointbypoint). This includes a list of all matches played in the two slams between 2016–2019, as well as point-by-point data. Unfortunately, similar data with such granularity was unavailable for the other two slams, the Australian Open and Roland Garros- this may introduce a slight bias when examining specific players, since players like Rafael Nadal aka the “King of Clay”, have a game style that suits the Parisian clay. Despite missing data from those two slams, the eight tournaments in total (two slams for four years) comprise almost 200,000 points in total. Table 1 displays the top 10 players from a points played perspective- no surprises that the “Big 3” lead the way.
The Service Matrix
Prior to focusing on specific players or splitting the data by year or tournament, it makes sense to begin by looking at the aggregate picture i.e. calculating the probability of holding serve from the various stages in a game for all the matches played. The stages are simply the different score-lines within a tennis game, hence this article aims to determine the likelihood of winning a game from all these different score-lines. Since serving is an advantage in tennis, intuitively one would expect that the probability of holding serve from 40–0 would be greater than from 15–0. Given the current score, one can calculate the probability of winning a game without any additional information from the past. For the statistical nerds, this is analogous to the Markov property, thus one can picture winning a tennis game as a Markov process. Each score-line within a game is a transition state and winning a game is the ultimate goal, hence the absorbing state (a state from which it is impossible to leave).
Figure 1 portrays these probabilities visually in the form of an interactive matrix, with the server’s score on the y-axis and the receiver’s score on the x-axis. One can notice that at 0–0, the server is a clear favourite to win the game; on average, the server is expected to win close to 81% of tennis games before even making contact with the ball. This validates the claim that serving is a clear advantage in professional men’s tennis and on average before a game is commenced the receiver is likely to break serve once in five attempts. However, one can see that the likelihood of winning a game is significantly dependent on the current score. Another intriguing observation is the importance of winning the first point of the game: from a server’s perspective, going 15–0 up increases the odds of holding serve by approximately 9%. On the other hand, if the receiver wins the first point (probability of 19%), his odds of breaking serve from 0–0 almost double to around 36%. A similar comment can be made when the score is at deuce (40–40); at deuce, the server has approximately a 73% chance of holding serve- if the server wins the next point, his chances of holding serve improve to 90%, but if the receiver wins the next point his chances rise from 27% to 56%. Intuitively, this does make sense because at 40-AD (ad-out) the receiver is only one point away from breaking, while at 0–15, the receiver still needs to win at least three more points to win the game. Needless to say, the probabilities in the plot indicate that the receiver is the under-dog in a tennis game and every point won against serve is a mini-achievement of some sort (maybe not at 40–0 down).
Wimbledon vs US Open
There has been much debate between fans and players regarding the speed comparison between the hard courts in New York and the grass courts in London. Thus, it is fascinating to see how the chances of holding serve varied over time and between the two slams. Court speed is dependent on factors such as topspin, bounce, court elevation, external conditions, friction and the type of tennis balls used. Many experts have concluded that the court speeds at Wimbledon are slower than in the 1990s, but remains the fastest surface in the majors.
Figure 2 depicts the probability of holding serve from various positions in a game. Probabilities from a winning (losing) position are computed as the weighted average of all score-lines when the server is ahead (behind) of the receiver and the probability of holding serve from a neutral position is the weighted average of the following probabilities: love-all, 15-all, 30-all and deuce. From figure 2, one can clearly infer that the likelihood of holding serve is higher at Wimbledon than at the US Open, regardless of position in the game and year. This alongside the fact that Wimbledon is the slam with the highest aces per match does suggest that the grass courts at the All England Lawn Tennis Club are the fastest, at least from a serving perspective.
The Height Factor
Similar to basketball, height plays a significant factor in tennis; the wider wingspan allows taller tennis players to have a more powerful and effective serve than their shorter counterparts. As of today, the joint-tallest players are Ivo Karlovic and Reilly Opelka. Both are 6 feet and 11 inches tall, however Karlovic is 41 years old, while Opelka is only 22 years of age.
Table 2 shows the top 10 servers- this is based on the statistical likelihood of holding serve from love-all. Unsurprisingly, the top two players on the list are two of the three tallest players on tour. John Isner has a prominent serve and wins around 94% of his service games, this is 13% above the tour average and this means that Isners’ opponents have a mere 6% chance of breaking his serve. Karlovic is second on the list and the high holding percent can be associated with the number of aces he serves; Karlovic has the highest number of career aces with a staggering 13,599 aces to his name and averages 23.5 aces per match on grass. To further underline the height factor, the correlation was calculated between the probability of holding serve and height- the Pearson correlation coefficient is 0.622, which also illustrates a statistically significant correlation between height and the odds of holding serve. It is extraordinary to see Roger Federer (6’1”) at 4th on the list. This high holding percent can be attributed to his serve accuracy which results in a high number of aces, him being a great serve-and-volley player and his tough mental strength.
Best vs the Rest
To further understand what makes Isner and Federer very productive servers, it is worth comparing their winning probability against the average player on tour from the various score-lines.
Figure 3 illustrates how much more likely Isner is to win a game from a particular score-line than the average player. For example, at love-all, Isner is 15.79% more likely to hold his serve, relative to the other ATP players. One noteworthy observation is the pattern of colour change from left to right. Isner is more likely to hold serve from all positions within a game, however, the ratio increases based on the game score; it is lowest when Isner is ahead in the game, slightly higher when the game is in the balance and the highest when he is in a losing position. One can see that when he is 15–40 down, he is 90% more likely to hold serve vs the average, which is mightily impressive. It is worth revealing that when Isner has gone 40–0 up, he has never been broken in these eight grand slams.
Likewise, figure 4 illustrates a plot for Federer vs the rest and the deductions are similar. One remark from figure 3 is the high ratio at 0–40, this suggests that Roger is much more likely to hold serve from 0–40 down than the rest; in fact, from the 11 times he has been down 0–40, he has come back to hold serve 6 of those times. While this is true, one must be cautious since the frequency of this event is rare, hence credibility is low.
From figures 3 and 4, it is evident that the highest ratios were observed when the server’s score was less or equal to the receiver’s score. This implied that winning from losing and neutral positions was a major discriminant between top servers and the rest. Going a step further, figure 5 displays the winning probabilities of the top ten servers from losing, neutral and winning positions and compares these probabilities to the tour average.
An obvious deduction from the plot is that the top ten servers are above average from all three positions, however, as observed previously, the largest absolute difference between the top server and the average server comes when the server is in a losing position. This suggests that when the top servers find themselves in tight spots, they respond much better than the average tennis player- this could mean they either serve themselves out of such trouble or execute a well-constructed point. Another intriguing note from the plot is the dominance of John Isner’s serve; not only is he the best server from a losing position on tour, but the odds of him holding serve from a neutral position are almost equivalent to an average players’ odds of holding serve from a winning stance- which is incredible.
Is Serving Everything?
Before concluding, it is essential to evaluate whether factors such as being tall, having a huge serve, putting up massive ace tallies and a holding serve at a high percent exclusively can result in a tennis player being the best in the world. Aware that holding serve is of paramount importance, is it enough to win tennis matches? Being tall does have significant advantages, but being tall may constraint one’s ability to move swiftly on the court; in addition, it may restrict their reach for lower shots. Therefore, combining a player’s potential to hold his serve and break his opponent’s serve would be a reasonable strategy to compare the best players on the ATP tour. Figure 6 displays the probabilities of holding and breaking serve for all players on tour.
The size of dot on the interactive plot illustrates the number of points played by the player and the colour depicts the weighted expectation of winning a tennis game from love-all. This plot provides a great visual as to why the “Big 3” (Djokovic, Nadal and Federer) are in a league of their own; no surprises that they have won six out of the eight slams analyzed in this article. Another inference from the plot is the top-notch serving from Isner and Anderson, but unfortunately their return game is no match to the “Big 3”, thus their overall winning probability is lower relative to the “Big 3”. The top five players from an overall winning likelihood (in decreasing order) are: Djokovic, Nadal, Murray, Federer and Cilic- however, Andy Murray played less than half the number of points played by Federer.
The Complete Tennis Player
When discussing top tennis players, one of the most important attributes is serving. Being a great server can be associated with one’s physical abilities- height and physique. In addition, mental toughness is equally valuable when it comes to holding serve and this separates the best servers from the rest. Winning service games is of utmost importance, however, one must remain cognizant of the fact that holding serve alone does not make you the best tennis player. After all, despite all the height benefits, there has never been a player taller than 6’4” at number one in the ATP rankings. Therefore, it is fair to conclude by saying that a complete tennis player is one who holds serve at a very high percentage and possesses a return game that can break serve at a high frequency.
