This article was downloaded by: [New York University] On: 04 November 2014, At: 22:43 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Sports Biomechanics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/rspb20 Association between body height and serve speed in elite tennis players Frantisek Vaverka a & Miroslav Cernosek b a Human Motion Diagnostic Center, University of Ostrava , Ostrava , Czech Republic b TK Plus , Prostejov , Czech Republic Published online: 20 Apr 2012. To cite this article: Frantisek Vaverka & Miroslav Cernosek (2013) Association between body height and serve speed in elite tennis players, Sports Biomechanics, 12:1, 30-37, DOI: 10.1080/14763141.2012.670664 To link to this article: http://dx.doi.org/10.1080/14763141.2012.670664 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions http://www.tandfonline.com/loi/rspb20 http://www.tandfonline.com/action/showCitFormats?doi=10.1080/14763141.2012.670664 http://dx.doi.org/10.1080/14763141.2012.670664 http://www.tandfonline.com/page/terms-and-conditions http://www.tandfonline.com/page/terms-and-conditions Association between body height and serve speed in elite tennis players FRANTISEK VAVERKA1 & MIROSLAV CERNOSEK2 1Human Motion Diagnostic Center, University of Ostrava, Ostrava, Czech Republic, and 2TK Plus, Prostejov, Czech Republic (Received 30 June 2011; accepted 27 January 2012) Abstract The purpose of this study was to determine the association between the body height (BH) of elite tennis players and their serve speeds: SF (fastest serve in a match), S1 (average speed of the first serve in a match), and S2 (average speed of the second serve in a match). Data were collected from the world’s best tennis players who participated in all four Grand Slam tournaments in 2008 (men, n ¼ 78–84, BH ¼ 1.85 ^ 0.07m; women, n ¼ 70–78, BH ¼ 1.73 ^ 0.07m). Statistically significant correlations (r) between BH and serve speed were found in all 24 statistical analyses ( p , 0.01). The correlation coefficients were similar in men and women. The correlation coefficients of BH with SF and S1 ranged 0.48–0.64 for men and 0.48–0.59 for women. The correlations between BH and S2 were weaker and more variable (r ¼ 0.20–0.50 for men and 0.24–0.42 for women). The BH of the men explained 27%, 30%, and 14% of the variance of SF, S1, and S2, respectively, with corresponding values for female players of 27%, 27%, and 12%. Keywords: Grand Slam tournaments, statistical analysis, correlation Introduction The serve is a key element of a tennis match, with the player having the opportunity to markedly influence the subsequent strokes in that point. It is generally considered that the speed of the first serve is the most important attribute of its performance, with players generally trying to maximize their serve speeds without sacrificing accuracy. Most research studies into the tennis serve have focused on the biomechanical aspects of the player’s movement and the analysis of various factors that could influence serve speed (e.g. Elliott, 1983, 1988; Elliott & Wood, 1983; Elliott et al., 1986; Brody, 1987; Elliott et al., 1988; Bahamonde, 1989, 1991, 1997; Kleinöder, 1990; Elliott et al., 1999; Bahamonde & Knudson, 2000; Chow et al., 2003; Elliott et al., 2003; Fleisig et al., 2003; Gordon & Dapena, 2006; Knudson, 2006). The relationship between body height (BH) and serve speed strongly influences the likelihood of a successful serve, defined as the ball landing in the service box. The height to which the ball is tossed also affects the accuracy and success of the serve (Reid et al., 2011), as do the initial direction of motion of the ball and the subsequent trajectory, which is q 2013 Taylor & Francis Correspondence: Frantisek Vaverka, Human Motion Diagnostic Centre, University of Ostrava, Varenska 40a, 702 00 Ostrava, Czech Republic, E-mail:
[email protected] Sports Biomechanics, 2013 Vol. 12, No. 1, 30–37, http://dx.doi.org/10.1080/14763141.2012.670664 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 influenced by the forces of gravity, lift, and drag (Brody, 1987). If the effects of gravity and fluid force on the ball are neglected and ball velocity approaches infinity, a ball must be hit at a minimum height of 2.74m for it to land in the service box (Trabert & Hook, 1984; Brody, 1987; Chow et al., 2003; Vaverka & Cernosek, 2007). Increasing the height at which the ball is hit in 10-cm increments from 2.7 to 3.0m moves the landing position of the ball in the service box by 25–30 cm from the service line (Vaverka & Cernosek, 2007). Hitting the ball at a greater height gives the player a larger area of the service box into which the ball can be hit. Taller players can hit the ball at a greater height, theoretically allowing them to serve at a higher speed than smaller players with the same probability of a successful serve (Brody, 1987; Vaverka, Cernosek, Tesarova, & Elfmark, 2005). The height at which the ball is hit is determined by how far the entire body is lifted from the ground (d1 in Figure 1), the vertical height of the hitting shoulder (d2), the vertical component of the length of the upper limb (d3), the vertical component of the tennis racquet and the place of impact (d4). The most significant parameter is the player’s BH, followed by the vertical lift of the body as determined by the serving technique, which can influence the hitting height by 20–40 cm (Vaverka & Cernosek, 2007). The racquet length and the position where the ball is hit vary only slightly from player to player. However, a hitting position that is more forward (d5 in Figure 1) positively influences the point at which the ball lands in the service box (Brody, 1987). Moreover, the effect of the BH on the serve speed could be modulated by interactions between the segment lengths and their resulting moments of inertia. The aim of the study was to identify whether such a relationship exists in elite tennis players at professional tournaments. It was hypothesized that the player’s BH would be positively related to the serve speed. Figure 1. Factors influencing the height of ball impact. d, the height of ball impact; d1, vertical lift of the whole body from the surface; d2, vertical component of body up to the level of the shoulder; d3, vertical component of length of the upper limb; d4, vertical component of tennis racquet and the place of impact; d5, horizontal shift of the place of impact from the basic line towards the net. Serve of elite tennis players 31 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 Method Participants The subjects of the research were among the world’s best tennis players (both men and women), as deemed by their participation in all four Grand Slam tournaments in 2008. The number of tennis players whose serve speeds were measured and analysed statistically ranged between 78 and 84 for men and between 71 and 85 for women (Table I). The participants in the Grand Slam tournaments are players from the world top 100 complemented by several successful participants from the qualification tournaments. Measured variables The players’ BHs were included as an independent variable in the analysis. The players’ body dimensions were obtained from publicly available information listed in official yearbooks of the International Tennis Federation and were checked at the official web pages of the players. The mean BHs of all men and women in the Grand Slam tournaments were 1.85 ^ 0.07 (M ^ SD) and 1.73 ^ 0.07m, respectively. The dependent variable, serve speed, is routinely obtained at top tennis tournaments of the Association of Tennis Professionals and Women’s Tennis Association circuits using a standardized procedure of measurement by a radar gun. The measured speed includes a measurement error that depends on the cosine of the angle between the ball motion and the radar beam. The maximum measurement error is typically 2.6%, which occurs when the angle is about 138. Official statistics of the Grand Slam tournaments are provided on the Internet, including further statistical information about serve speed. Three parameters related to serve speed in Grand Slam tournaments were used in our research: 1. The fastest serve (SF): the fastest serve speed for a player in a given match. 2. The average speed of the first serve (S1): computed for an entire match. S1 is affected not only by the quality of technique, fatigue and other factors, but also by the player’s strategy. 3. The average speed of the second serve (S2): computed for an entire match. S2 is normally lower than S1 because its key criterion is its successful execution. The number of players included in statistical analysis was smaller than the official number of participants in the tournaments (Table I), since some matches in the tournaments’ first rounds took place on courts without the facilities for serve speed measurements. Players who were eliminated in the first rounds of the tournaments and whose serve speeds were not measured were excluded from the study. The data file from particular Grand Slam tournaments includes serve speeds from the first measured match. Table I. Number of players included in the statistical analyses. Men Women Australian Open 2008 82 78 French Open 2008 83 85 British Open 2008 78 70 US Open 2008 84 71 F. Vaverka & M. Cernosek32 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 Statistics All of the data included in statistical analysis were normally distributed, as confirmed by the Kolmogorov–Smirnov test. Differences in mean serve speeds between Grand Slam tournaments were not the subject of this research, but they were computed in order to provide descriptive data on the players and match conditions (Table II). Correlation analysis of relationships between BH and serve speed was performed after verifying the presence of linear patterns in the scatter plots. In all cases their linear dependence was confirmed; this is demonstrated in twoexamplesof regressionanalysis fromtwo tournaments (Figure2).Pearson’s correlation coefficient rwas used to quantify correlations, while coefficient of determinationwas used toexplain thecommonvariancebetweenBHandserve speeds.Thecomputationof average correlation coefficients was based on the meta-analysis procedure of Hedges and Olkin (1985), which requires a transformation of each individual correlation coefficient r into Fisher’s Z; the program of Schwartzer (1989) was used in this process. All calculations were performed using Statistica v9, and statistical significance was accepted at p # 0.05. Results There were significant associations ( p , 0.01) between BH and all three serve speed parameters in all of theGrandSlam tournaments for bothmenandwomen (Tables III and IV). The statistical strengths of the associations were similar in men and women. The correlation coefficients between BH and serve speeds S1 and SF were similar for men (r ¼ 0.48–0.63; Table III). There was aminimal variation in the average correlation coefficients across all four Grand Slam tournaments (BH vs. SF: r ¼ 0.52; BH vs. S1: r ¼ 0.55). The correlation betweenBHandS2wasweaker (r ¼ 0.37), and the correlation coefficients variedmore across the tournaments (r ¼ 0.20–0.50). The average values of coefficient of determination were around 27% for SF, 30% for S1, and 14% for S2. The correlation coefficients for female players in each Grand Slam tournament were more consistent than those for male players (r ¼ 0.48–0.59 for SF and S1; Table IV). The average correlation coefficient from all four Grand Slam tournaments was r ¼ 0.52 for both SF and S1. The correlation coefficient between BH and S2 was weaker (average r ¼ 0.35) and more variable (r ¼ 0.24–0.42) for female players than for male players. The average percentages of coefficient of determination in women were around, at 27% for SF and S1, and 12% for S2. Discussion There could be a significant association between BH and serve speed for groups of players and real serves at tournaments in which the best players participate. The values of coefficient Table II. Average serve speed ranges (in km/h) in the Grand Slam tournaments in 2008. Men Women Serve Range %SF Range %SF SF 205.9–208.2 171.9–175.7 S1 181.7–189.9 90 154.9–160.7 74 S2 148.5–158.7 91 129.3–138.0 77 Notes: SF, fastest serve; S1, average speed of the first serve; S2, average speed of the second serve; %SF, percentages of SF. Serve of elite tennis players 33 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 of determination of the monitored serves were influenced more by BH for SF and S1 (men 25–40%, women 24–35%) than for S2 (men 4–25%, women 6–18%). This difference is attributable to serving tactics, with SF and S1 being related to maximal effort, while S2 requires a successful performance. S2 is less influenced by BH due to the ball spin and the associatedMagnus force that results in a curved flight trajectory and increases the probability of a successful serve. The association between BH and serve speed could be influenced by variations in the quality of serves during a match, a tournament, and the different periods of the season. Players will vary speed, spin, and placement of first serves to trick opponents, which will Figure 2. An example (2008 US Open) of linear regression dependency between BH and average first serve speed: (A) men (n ¼ 84) and (B) women (n ¼ 71). S1, average speed of the first serve; rBH vs. S1, correlation coefficient between BH and S1; D, coefficient of determination. F. Vaverka & M. Cernosek34 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 certainly vary the first serve speeds (and consequently S1 and SF) used in a match. Figure 3 provides an example of the intra-individual variability of S1 for two of the world’s best players, Federer and Nadal, in all matches they played in the Grand Slam tournaments in 2008 and in the Australian Open in 2009. One of the important factors underlying variation in the serve speed is the probability of its successful execution. We can assume that each player intuitively corrects the speed of the serve based on his or her individual experience of success with its execution. It can be hypothesized that taller players have an advantage in being able to hit the ball at a greater height with a larger service area into which the ball can land. It is important to distinguish between the ability to reach the maximum serve speed without regard to its success and having an acceptable probability of its successful execution. Shorter players generally have a lower hitting height and will have a lower probability of a successful serve for a higher serve speed. For example, Benjamin Becker, with BH of only 1.78m, was able to achieve a very high serve speed (S1 ¼ 194 km/h) but with only 46% of his first serves being successful (Australian Open 2008). In contrast, the average percentages of successful first serves in all Grand Slam tournaments during the monitored period were from 59% to 61% for men and women, respectively. This research was subject to several limitations. First, the accuracy of radar-based serve measurements is influenced by the angle between the ball trajectory and the radar beam, with a typical measurement error of 2–3% in extreme cases. Second, the data on the Table III. Correlations and coefficients of determination of association between the BH and three serve speeds for men in 2008 Grand Slam tournaments. SF S1 S2 Tournament R D (%) r D (%) r D (%) Australian Open 0.48 23 0.50 25 0.20 4 French Open 0.59 35 0.55 30 0.36 13 British Open 0.50 25 0.52 27 0.41 17 US Open 0.51 26 0.63 40 0.50 25 M ^ SD 0.52 ^ 0.06 27.2 ^ 5.3 0.55 ^ 0.07 30.5 ^ 5.4 0.37 ^ 0.11 13.5 ^ 7.2 Notes: SF, fastest serve; S1, average speed of the first serve; S2, average speed of the second serve; D, coefficient of determination. Table IV. Correlations and coefficients of determination of association between the BH and three serve speeds for women in 2008 Grand Slam tournaments. SF S1 S2 Tournament r D (%) r D (%) r D (%) Australian Open 0.59 35 0.55 30 0.42 18 French Open 0.48 23 0.53 28 0.40 16 British Open 0.51 26 0.50 25 0.24 6 US Open 0.51 26 0.49 24 0.33 11 M ^ SD 0.52 ^ 0.06 27.4 ^ 5.2 0.52 ^ 0.03 26.8 ^ 1.9 0.35 ^ 0.08 12.2 ^ 4.6 Notes: SF, fastest serve; S1, average speed of the first serve; S2, average speed of the second serve; D, coefficient of determination. Serve of elite tennis players 35 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 players’ BHs taken from the official sources might be inaccurate, although the BH of an adult player is very stable and subjective statements differ only minimally. The main source of errors of BH could be due to the rapid growth of younger players. Third, a lack of homogeneity among the different groups of players who participate in each Grand Slam tournament could result in slight variations in the results of statistical analyses of the associations between BH and serve speed between Grand Slam tournaments. Fourth, variations in the playing and environmental conditions, such as different court surfaces and weather, wind, and light, could also influence the associations between the monitored variables. Despite these potential sources of (small) errors, the data were accurate enough to establish weak-to-moderate positive correlations between BH and serve speed in elite tennis players. Conclusions This study has demonstrated a significant association between the genetically determined BH and the fastest serve speed in a match, average speed of the first, and second serves in a match in elite tennis players. The strengths of the correlations of BH with the fastest and average speed of the first serve were similar in men and women, with correlation coefficients ranging from r ¼ 0.48 to 0.63. The correlation between BH and average speed of the second serve was weaker, and the correlation coefficients were more variable in particular Grand Slam tournaments (r ¼ 0.20–0.50). BH is an important factor influencing the execution of the tennis serve, with it explaining in average 27–30% of the overall variability in the fastest and average speed of the first serve, and 12–14% of that in average speed of the second serve. The BH of both men and women tennis players is an important factor influencing the serve speed, with tall players possibly having a significant biomechanical advantage. Future research should confirm these results and further explore the mechanisms underlying this potential advantage. Figure 3. Intra-individual variability of S1 for two of the world’s best players (Federer and Nadal) in the Grand Slam tournaments in 2008 and in the Australian Open in 2009 (each data point represents S1 value for a givenmatch). S1, average speed of the first serve; CV, coefficient of variation. F. Vaverka & M. Cernosek36 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14 References Bahamonde, R. E. (1989). Kinetic analysis of the serving arm during the performance of the tennis serve. In R. J. Gregor, R. F. Zernicke, and W. C. Whiting (Eds.), XIIth International Society of Biomechanics (p. 9). Los Angeles, CA: University of California. Bahamonde, R. E. (1991). Stroboscopic analysis of the axis of rotation in the tennis serve. In W. Liemohn (Ed.), Abstracts of research papers (p. 196). Reston: AAHPERD. Bahamonde, R. E. (1997). Joint power production during the flat and slice servers. In J. D. Wilkerson, K. M. Ludwig, and W. J. Zimmerman (Eds.), Proceedings of the 15th international symposium on biomechanics in sports (pp. 489–494). Denton, TX: Texas Woman’s University. Bahamonde, R. E., & Knudson, D. (2000). Ground reaction forces of two types of stances and tennis serves. Medicine and Science in Sports and Exercise, 33, S102. Brody, H. (1987). Tennis science for tennis players. Philadelphia, PA: University of Pennsylvania. Chow, J. W., Carlton, L. G., Lim, Y. -T., Chae, S. -W., Shim, J. -H., Kuenster, A., & Kokubun, K. (2003). Comparing the pre- and post-impact ball and racquet kinematics of elite tennis players’ first and second serves: A preliminary study. Journal of Sports Sciences, 21, 529–537. Elliott, B. (1983). Spin and the power serve in tennis. Journal of Human Movement Studies, 9, 97–104. Elliott, B. (1988). Biomechanics of the serve in tennis: A biomedical perspective. Sports Medicine, 6, 285–294. Elliott, B., Baxter, K., & Besier, T. (1999). Internal rotation of the uppper-arm segment during a stretch-shorten cycle movement. Journal of Applied Biomechanics, 13, 182–196. Elliott, B., Fleisig, G., Nicholls, R., & Escamilla, R. (2003). Technique effects on upper limb loading in the tennis serve. Journal of Science and Medicine in Sport, 6, 76–87. Elliott, B., Marsh, T., & Blanksby, B. (1986). A three-dimensional analysis of the tennis serve. International Journal of Sport Biomechanics, 2, 260–271. Elliott, B., Overheu, P., & Marsh, A. (1988). The service line and net volley in tennis: A cinematographic analysis. The Australian Journal of Science and Medicine in Sport, 20, 10–18. Elliott, B., & Wood, G. (1983). The biomechanics of the foot-up and foot-back tennis serving techniques. The Australian Journal of Sport Sciences, 3, 3–6. Fleisig, G., Nicholls, R., Elliott, B., & Escamilla, R. (2003). Kinematics used by world class tennis players to produce high-velocity serves. Sports Biomechanics, 2, 51–71. Gordon, B. J., & Dapena, J. (2006). Contributions of joint rotations to racquet speed in the tennis serve. Journal of Sport Sciences, 24, 31–49. Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. New York, NY: Academic Press. Kleinöder, H. K. (1990). The effect of tennis specific power training towards an increase of service speed and speed of leg movements. Unpublished doctoral dissertation, The German Sports University, Cologne. Knudson, D. (2006). Biomechanical principles of tennis technique. Using science to improve your strokes. Vista, CA: Racquet Tech Publishing. Reid, M., Whiteside, D., & Elliott, B. (2011). Hitting to different spots on the court: The ball kinematics of the professional tennis service. Portuguese Journal of Sport Sciences, 11 (Suppl. 2), 373–376. Schwartzer, R. (1989). Program META for meta-analysis. Berlin: Freie Universität Berlin. Trabert, T., & Hook, J. (1984). The serve: Key to winning tennis. New York, NY: Dodd, Mead & Co. Vaverka, F., & Cernosek, M. (2007). Základnı́ tělesné rozměry a tenis [Basic body dimensions and tennis]. Olomouc: Palacky University. Vaverka, F., Cernosek, M., Tesarova, K., & Elmark, M. (2005). The influence of the body height on the serve in tennis. In Q. Wang (Ed.), Proceedings of XXIII international symposium on biomechanics in sports (Vol. 1, pp. 335–338). Beijing: The China Institute of Sport Sciences. Serve of elite tennis players 37 D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 2 2: 43 0 4 N ov em be r 20 14