Author: Patrick Rhodes
David dances lightly from side to side, his small feet stirring up wisps of dust from the clay surface. Twirling his racket in anticipation, he peers intently at his colossal foe hoping to spot some clue where the first serve will go. Across the net is a giant of a man, glaring at David with a stone-faced scowl. The crowd, once rowdy, is now silent; all eyes are riveted on Goliath as he bounces the ball on the rust-colored surface. Known for his amazing strength and exceptional height, they eagerly await his first monster serve.

Tennis players are getting taller

The above scenario appears to play out quite often in men’s professional tennis today. It seems that whenever I see a tennis match on television, at least one of the players is of remarkable height. It makes me wonder if the game is dominated by these individuals and if so, do they have some sort of advantage over shorter players?

Depending on which account you believe, Goliath was either somewhere around 206 cm (6’9”) or perhaps nearly 297 cm (9’9”). For purposes of relatability, let’s go with the 206 cm version, which is quite tall. Unbelievably however, he would not be the tallest player on the professional circuit today. As of this writing, that honor would go to Croatia’s Ivo Karlović, who stands in at 208 cm (6’10”), obliging many NBA (National Basketball Association) players to look upwards to meet his gaze.

David, on the other hand, was around 160 cm (5’3”) – again, depending on which account you choose to adopt. In men’s professional tennis, David would be tied with a handful of other players around that height, so a match between these two historical opponents is not unreasonable.

So, back to my original question: Would Goliath hold an advantage over the David due to his height?

Grand slam tournaments are a good indicator of success in tennis, since the best players are selected for this events. If a trend could be spotted that the best players were getting taller, then it lends credence that there is some sort of advantage for them. Finding a bit of data [1] from the U.S. Open, the table below reveals some interesting facts regarding player heights:

The table shows that there is a larger percentage of players that are of extreme height, but the data is insufficient to indicate a trend. Using a deeper set of data [2] from professional male players (capturing their height the year each turned pro and taking the mean) over a 30 year span reveals the following (Figure 1):
Note: (the player list from this database while not complete, provides quite a large selection of men’s players from the last 30+ years)

Figure 1

We can see that on average, male tennis players are indeed taller now than 30 years ago, further lending credence to our argument. The least-squares trend line clearly indicates an upward progression. In fact, the players have grown a full 9 cm (3.5”) since 1980:

Of course, this trend cannot continue indefinitely, since humans tend to be limited in height by mechanical considerations. Further, if the trend line were extended backward, it would reveal that the players started out at a height of zero, also impossible. Therefore, what this really shows is that for a short period of time, we are witnessing a phenomenon that most likely will not be seen again (i.e. the trend line cannot continue upward endlessly).

Goliath tosses the ball into the air, arching backward while winding up his racket. With an incredibly loud ‘thwack!’, the ball is transformed into a tiny green blur streaking over the net towards his opponent. Grunting, David deftly lunges right, fully extending his racket out, praying to make contact with the bullet coming his way.

And hitting faster serves…

Popular belief tells us that taller players have an advantage on the tennis court because their serves are hit at a higher rate of speed, leaving less time to react for their opponent. This, in theory, would result in more aces or weak returns. Over the course of a match, this should result in more points won on serve for the taller player, thus giving him an advantage. These same dynamics would work against the shorter player [3].

If this is true, we should be seeing faster serves in men’s tennis. Using data [4] collected from the grand slam tournaments, the following is revealed (Figure 2):
Note: this data was painstakingly hand collected by physics professor Rod Cross, who provided invaluable assistance during the writing of this article.

Figure 2

In all tournaments except Wimbledon [5], there has been a marked increase in the mean serving speed since 1999. Using this data, it does indeed appear that serving speeds are on the rise. Having said that, is there a relationship between player height and service speed?
Note: Unfortunately, the data was unavailable for all years, so the graph reflects that. In real-world data journalism, getting perfectly contiguous data is often a problem.

Are service speed and height related?

Since we have incomplete data and we’re working with two different datasets, we can’t formally correlate height and service speed without understanding that whatever results from that exercise would be inconclusive. That being said, it is wise to go through with this exercise since it might provide “probable cause” for someone else to delve further into this topic. With that mentioned, a plot of the correlation between height (taken from the data used to produce Figure 1) and the fastest recorded tennis serves [6] results in the following (Figure 3):
Note: This data lists the top recorded serves in tennis. However, each player is only allowed one entry in that set (their highest speed), so it doesn’t show how often these serves are actually hit. For example, Andy Roddick has hit many serves that would be in this set, but only his fastest recorded serve is included, and then only once.

Figure 3

The above chart shows a weak relationship between player height and the fastest recorded serves from the past 30 years. In fact, the coefficient of determination (r2) sits at 0.19, indicating a rather shaky correlation between the two variables.
Note: More research in this area is warranted, since physics shows us that the taller a person is, the faster a serve can be hit with ‘no spin’ and still be in play [2].

Since height doesn’t appear to be the dominant factor in service speeds, there must be other variables at play. Indeed, there have been advances in training methodologies [7], racket technology [8]) as well as the strings used in the rackets which all have an impact on the speed of a serve (not to mention every other aspect of the game).

All things being equal (in terms of equipment and training), physics tells us that taller players have the ability to hit faster serves than shorter players [2]. Therefore, it appears that Goliath should be able to hold a slight advantage over David, winning a few more points on serve. However, that advantage isn’t enough that David should be too concerned; tennis, like many challenges in life, often comes down to desire.

The ball hits David’s outstretched racket, rebounding down the line. Goliath lumbers towards it, his feet skidding in the clay as he slides to a stop, twisting his large torso preparing to hit the ball. Suddenly he relaxes, smirking ever so slightly at David. The ball careens into the backdrop with a thud as the line judge yells “out!” While not faced with an impossible task, it certainly is going to be a long day for David.

References:

1. The Wall Street Journal, Men’s Tennis Reaches New Heights, (accessed March 1, 2013); available from http://online.wsj.com/article/SB10001424052970203440104574403182239738354.html  

2. ATP Tennis Navigator, Player List database, (accessed April 14, 2013); available from http://www.tennisnavigator.com.

3. The Tennis Server, Tennis Set: 9 Feet Tall For A No-Spin Serve?, (accessed March 22, 2013); available from http://www.tennisserver.com/set/set_03_07.html.

3. Rod Cross, University of Sydney, School of Physics, Five Ways to Win a Point, (accessed March 20, 2013); available from http://www.physics.usyd.edu.au/~cross/GrandSlamStatistics.htm.

4. The Tennis Server, Tennis Set: Grand Slam Statistics, (accessed March 18, 2013); available from http://www.tennisserver.com/set/set_05_05.html.

5. Wikipedia, Fastest recorded tennis serves, (accessed April 18, 2013); available from http://en.wikipedia.org/wiki/Fastest_recorded_tennis_serves.

6. Journal of STMS, Medicine and Science in Tennis, vol. 13, no. 2; available from http://strategicgames.com.au/servingstrategies.pdf.

7. Hann Earl Kim and Johannes M. Pennings, Innovation and Strategic Renewal in Mature Markets: A Study of the Tennis Racket Industry (Organization Science, 2009); available from http://www.management.wharton.upenn.edu/pennings/documents/Innovation-and-strategic-renewal.pdf

Bio: For more information on the author of this article, please visit http://rhodestales.com/