By: Rosie Chen and Stella Koh
Intro
The first thing you need when playing tennis is the racquet. And while the racquet may seem to be merely a tool to ricochet a ball back and forth the court, it can be–and is–a customizable tool. Differences in length, size, weight, and stiffness amongst others of tennis racquet specifications can lead to varying levels of power and comfort. In this article, we aim to isolate and identify the effects of changing racquet specifications on power potential levels. We will also compare the known racquet specs of professional ATP players to our findings in corroboration of their playing styles.
Data
Data was sourced from Tennis Warehouse University. The first dataset included 1403 racquets sold to the general public from 27 different brands ranging from Babolat and Head to Dunlop and Wilson. Information on the racquets included specs such as weight, head size, sweet zone size, flex, balance, and vibration. This dataset was used for the main analysis of racquet performance.
A second dataset, also sourced from Tennis Warehouse University, contained data of verified racquet specifications of 130 professional ATP players. This dataset was used in conjunction with the first to infer racket specification preferences of the pros.
Results
To preface, some racquet dimensions are static, measured in racquet stillness, while others are dynamic and measured by swinging the racquet. Examples of static specs include weight, head size, balance, and beam width. Dynamic specs include swingweight, twistweight, recoil weight, and power potential.
Effect of Racquet Head Size
One of all racquet specs, the most visible dimension would be the head size. The head size measures the total surface area of the racquet where the strings are. This measurement is highly correlated with the size of the sweetzone, an area defined by Tennis Warehouse University as having a power potential over 30%. This indeed makes sense: a larger racquet size gives more string contact for a larger sweet zone.
Noticeably, however, increases in head size do not see significant increases in power. We do not see a strong horizontal pattern in colors. Rather, increases in sweet zone size appear to have a strong positive relationship with power. The stark color contrast along the vertical profile makes this clear. Why does this happen despite the strong correlation between head and sweet zone size?
Because head size affects more than just the sweet zone. Increasing the size of the racquet affects the weight, balance, and distribution of mass of the racquet as well–all of which play a role in determining power. We will analyze this in greater detail below.
Effect of Racquet Weight
Generally, as the weight of the racquet increases, power also increases. This positive correlation is significant with a p-value less than 0.05, but extremely small and explains very little of the variation in the data. A better understanding is achieved when weight is broken down into specific dynamic components: swing, twist, and recoil.
Swingweight is the measurement of resistance to racquet acceleration in a circular motion along a lengthwise axis. Twistweight is the measurement of resistance to a racquet twisting along a perpendicular axis. Recoil weight is a measurement of inertia along its point of contact. All three can be interpreted as measures of stability in units of kg*cm2.
In the first row of the graph, it is clear that increases in all three types of weights correspondingly increases their power potential. Of these effects, swingweight appears to have the largest marginal effect on power compared to both recoil and twist. This makes sense. A heavier recoil weight would mean that the racquet absorbs more of the recoil impact than the arm, retaining more power. A heavier twistweight means that an off center hit would wobble to the sides less, enabling a stronger hit. And last but not least, a heavier swing weight means more mass at the point of impact for a larger transfer of energy.
But these weights are dynamically measured. What static specs are useful in determining recoil, twist, and swing weights? Intuitively, these weights depend on the mass of the racquet. More mass, more stability–less twisting and recoiling but more swing. We would thus expect heavier racquets to have higher recoil, twist, and swing weights. And while this does appear to be the case for recoil and swing weights, plotted in the second row of the graph above, twist weight shows a surprising negative correlation. Why? Because the distribution of mass is equally as important as the mass of the racquet itself.
To better characterize the relationships between these weights and static specs, we need to account for balance as well as head size. Balance, per its namesake, measures the point along the racquet edge where it will balance. It is highly suggestive of where most of the weight is in the racquet, generally defined into 2 categories: head-light (blue) and head-heavy (red).
A series of analysis of variances conducted by blocking on head-light and head-heavy racquets shows that weight, balance, and head size all affect swing, twist, and recoil weights at a significance level of 5%. In each run, the mean square of the blocking variable is much larger than the mean square error, implying that head-light and head-heavy racquets also had a significant effect on the response variables. Model assumptions are also satisfied, with residuals randomly scattered and roughly normally distributed. Knowing that the above mentioned factors are significant tell us little about their role in tennis performance. The magnitude and direction of these effects are better examined through regression equations below.
As swingweight is a measurement made at the center of the racquet, it is not unexpected that balance and head size have minimal effects on swingweight. On the other hand, balance and head size have opposite effects on recoil and twistweight. The further the balance is along the racquet, generally corresponding to head-heavy racquets, we tend to see a decrease in recoil weight and an increase in twistweight. The same effects are seen in racquet head size: as head size increases, we expect to see a decrease in recoil weight and an increase in twistweight.
Adding these effects in addition to the effect of weight better explains twistweight. When the mass of the racquet is distributed towards the head and further from the hand, the racquet tends to twist less on off-center shots. A bigger head size also means that the racquet is more forgiving on the same off-center shots. As such, the actual weight of the racquet matters less in determining twistweight than the wider distribution of mass towards the head.
Effect of Flex (Racquet Stiffness)
Flex is a measurement of racquet stiffness, defined as how much the racquet bends along a longitudinal axis. There is no significant correlation between flex and power potential, which is measured at the center of the racquet’s sweet zone. Instead, the effect of flex is much more noticeable in off-center shots better characterized through recoil and twist weights. We see that as the stiffness of the racquet increases, recoil weight diminishes. The racquet absorbs less of the energy from the ball in place of the arm. Lower recoil weights thus tend to put greater physical stress on the arm. Additionally, we see that greater stiffness increases twist weight, which makes sense as less flex leads to less twisting.
Now, as vibration is heavily dependent on flex–stiff racquets produce higher frequencies–the effects of flex on recoil and twist weight are closely mirrored with the effects of vibration. Higher vibration frequencies lower recoil weight and increase stress on the arm. As such, many players utilize vibration dampeners on their racquet to reduce the sensation of recoiling.
Pro Racquet Comparisons
All data analyzed above was made with store-bought racquets sold to the general public. How do professional ATP players fall within these specifications?
Simply plotting histograms of weight distributions amongst all store racquets and professional racquets, we can see a clear difference in specification preferences. These differences are all statistically significant, with all independent two-sample t-tests returning a p-value < 2.2e-16. Generally, pros use heavier racquets, which as we mentioned before are associated with higher swing and recoil weights. All aspects correlate to higher power potential and stability, despite being a little more demanding of physical exertion. Unfortunately, recoil weight was not included in the dataset of the pro players. However, we can likely infer with the heavier racquet weights that professional players tend to use racquets with lower twist weights. This means there is less stability for off-center shots, requiring a greater standard of accuracy.
There is no significant difference in the length of the racquets used by the pros and store-sold racquets, which is not unexpected due to the limited nature of this spec. However, pros do have significantly smaller balance measurements, indicative of a lower mass distribution generally associated with head-light racquets. They also use racquets with significantly smaller head sizes, which tend to have a smaller sweet zone area, heavier contact, less stability in twist, and more recoil effect. These racquets require more precision when contacting the ball, with less area to forgive off-center shots, but tend to be more stable and powerful otherwise.
In sum, pros generally stick to relatively heavier head-light racquets to optimize power. These racquet specs generally sacrifice additional room for error, requiring player consistency and technique, but boost performance overall.
Types of Playing Styles
One result of having so much variation in racquets is diverse types of playing styles. First is the “Big Server.” These players tend to have quick first serves, winning points within the first few shots. Another type of player is the “Serve and Volleyer,” who primarily takes advantage of their serves and volleys for points. Someone who comfortably uses an ability throughout the entire court is the “All Court Player.” A player who takes advantage of playing from the baseline are called the “Baseliner”. Last but not least, we have the “Counter Puncher,” a player who stands solid ground playing defense.
Additionally, we can categorize players in terms of power and precision, “Power Players” tend to hit with more power, corresponding to Baseliners. On the other hand, defense playing styles such as “Counter Puncher” tend to more highly value precision, which is correlated with higher flex and certain string patterns. Based on their playing styles, players tend to have racquets favoring one over the others. Let’s take a look at a few types of tennis players through example Pro players:
Below, we provide a table with numerical values converted into percentiles based on ATP Pro players, referenced in the descriptions. As analyzed in previous sections, variables such as weight, swing weight, and recoil weight are generally higher in professional specifications compared to those of the general public.
Precision Player (Ex. Federer)
A master of precision, Federer skillfully uses his racquet to perform a wide range of consistent shots to defeat his opponents. His racquet's specifications reveal a string pattern of 16 x 19, perfect for precision play. Additionally, the smaller head size and lower balance make his racquet extremely headlight, further enhancing accuracy. Swingweight and recoil weight are both in the 50th percentile, providing a balanced mix of power and control, essential for Federer’s technique of precise, varied shots as a Precision Player.
All Court Player (Ex. Djokovic)
On the other hand, Djokovic utilizes a mix of precision and power. Analyzing his racquet specs, we can see that he has a racquet with an extremely small head in size, giving him the advantage of precision. At the same time, even amongst other head sizes, his racquet head is considered extremely heavy, which, in addition to the high swingweight, gives him more power. As a great returner, naturally, his shots have lots of power. It makes sense for precision to be just as important, since more power implies the need for more control.
Serve-and-Volley Player (Ex. Mcenroe)
Serve-and-volley players often come up at the net for quick yet powerful moves. Thus, we expect a mix of need for control and power. We can see from Mcenroe’s specs that a higher weight 86th percentile correlates to greater power for the quick and powerful shots at the net. There are many variables at 50th percentile, which indicate a balance between control and power, as expected for a player like this.
Baseline, Power Player (Ex. Agassi)
Andre Agassi exemplifies the Baseline Player, standing out in his powerful groundstrokes at the baseline. His racquet specs include a lower recoil weight, which implies more instability in his off-center shots. However, the instability is compensated by the power generated from his racquet. Notably, his racquet features a very large head, placing it in the 99th percentile of all professionals in these specs. A larger head generally correlates to a higher weight, which results in greater power, as needed in the powerful groundstrokes as he is known for.
Big Server (Ex. Karlovic)
Big Server players have high winning rates through serving really quick shots. One instance is Karlovic, who holds the fastest serve in professional tennis. Having a lower balance and larger head size, his racquet is rather head-light, which allows for greater maneuverability as needed in serves. The larger head size allows for a greater sweet spot while still allowing for precision. A higher recoil weight, at approximately 98th percentile, allows for stability and control, especially on off-center shots, a necessity for consistent serves.
Counterpuncher (Ex. Hewitt)
Counter punchers focus on being defensive, and thus rely heavily on consistency. With a smaller head size, and a head-light balance, Hewitt can control his shots with high precision and easy maneuverability, in order to tailor his shots for opponents’ weaknesses. The heavier racquet and higher swing weight provide the necessary stability to absorb and redirect the opponent’s power effectively. This allows Hewitt to maintain consistency in his returns, even when facing aggressive shots. Furthermore, a high recoil weight ensures that the racquet remains stable, minimizing vibrations in order to have consistent shots. These consistent shots keep rallies going, wearing down opponents strategically.
Conclusion
While these different racquet specs may increase power depending on how they are adjusted, tennis performance is far more than just the racquet. Depending on string type, tension, player style, and additional accessories, each racquet may vary in performance.
Still, tennis racquets are useful in changing the feels of the racquet. Adjusting the specs can increase power or comfort and maneuverability. Beginners may opt for lighter and bigger racquets that tend to be more forgivable on off-center shots while pros prefer heavier and smaller racquets for control and power. Some may choose head-light racquets for an easier swingthrough or head-heavy racquets for more stability of the swing. The combinations can go on and on. As such, understanding the contribution of racquet specs to one's performance can hugely benefit a player’s success.