The standing vertical jump (SVJ) is 1 of the most popular ways to monitor the level of performance of both elite and recreationally active athletes (22,33) and to investigate the functional ability of the lower limbs under different conditions (1,23). The SVJ has been accepted as a valid evaluation of leg power (17,21,31), related to the force-velocity relationship of the muscle contractile mechanics (9) and therefore could be a useful index of the muscular ability to generate power (34). In fact, the ability to generate power is a key element of success, and estimation of the peak power is an essential element when evaluating the performance of athletes (8) in sports in which jumping and striking are important elements. In sports such as soccer, the movement sequence must often produce a high speed of release or impact; therefore, the capacity to produce explosive power can determine the level of performance that will strongly depend on the strength and speed of the movement (24).
Force platforms are used to monitor the SVJ by means of the ground reaction force (FGR), which allows measurement of the maximum height of the jump (hmax). The instantaneous power is calculated by means of the FGR, as reported by Harman et al. (11), and so yields the actual peak of the developed power (PPac). However, force platforms are quite expensive, because they need a protected environment such as a Movement Laboratory (19,34) because, for proper use, whenever they are moved they have to be repositioned on a level floor, and they also need to be calibrated before each acquisition session.
Different tools have been developed for making sports or other outdoor assessments, such as contact platforms (14,16) or accelerometers (26), which allow the values of Tf and hmax to be obtained (7). Previous studies have demonstrated that PPac is highly correlated with hmax (8,11,17), so several authors have presented regression equations serving to estimate PPac from hmax, the subject's body mass (BM) (5,11,12,17-19,28,29), and the subject's height (SH) (17). However, underestimations or overestimations of PPac, ranging from -76.7% (12) to 5.2% (28), have been obtained from the same regression equation when applied to groups with different features. Therefore, several authors have pointed out that each population may require its own regression equation to ensure an accurate estimation of PPac (8,12,19), because the accuracy of regression equations is related to the jump execution modalities (“jump and reach” test, countermovement jump [CMJ] or squat jump) (5,8,19,28); the experimental sample size (19); the gender (5,8,19); and the sport practiced (8,18).
Regression equations are now available for both physically active and sedentary higher education students (11,12,17,18,28) and volleyball players (12,18), but there are no models available yet for soccer, even if the CMJ has been widely adopted as a performance test to assess the PPac in this sport (13,14,32).
Moreover, in view of the fact that the development of motor skills is strongly dependent on growth (25), it can be hypothesized that the link between PPac and hmax may change, especially during the periods of greatest physical development of the individual. For this reason, it may be necessary to adopt equations specifically designed for homogeneous age groups, particularly for adolescents, to obtain accurate estimation (PPes) of PPac.
In this scenario, the purpose of the study was (a) to assess the accuracy of the regression equations available in the literature to estimate the PPac produced in CMJ executed by young male soccer players, (b) to develop new regression equations from this population, and (c) to verify whether regression equations obtained for age-based subgroups could increase the accuracy of PPes. The authors hypothesize that new regression equations, specifically developed from a population of young male soccer players, could provide better estimates of the PPac and that more accurate equations could be obtained from homogeneous age-based subgroups.
Experimental Approach to the Problem
To test the hypothesis, a sample of young male soccer players performed 5 maximal CMJs on a force platform. Following indications in the literature (17), PPac, hmax, BM, and SH were taken as independent variables to develop the regression equations, whereas PPes was the dependent variable.
The PPes values were estimated using 7 equations reported in the literature (5,11,12,17,19,28,29). After verifying the presence of statistically significant differences between PPac and PPes, new regression equations were obtained for the entire experimental sample. To see whether PPes could be improved by using more homogeneous age groups, the sample group was subdivided into 3 subgroups, according to Tanner's stages (4).
The study sample (G1) consisted of 117 young male soccer players (age, 13.6 ± 2.4 years; BM, 53.5 ± 14.1 kg; and height, 161.5 ± 12.9 cm), randomly chosen among subjects presenting at the local Sports Medicine Institute to undergo the annual medical visit, legally required to obtain the necessary medical certificate of health to do competitive sport. Players had 5.5 ± 3.0 years of experience in soccer training and competitions and were taking part in national championships in the year of the investigation. Players trained 5 times a week (about 90 minutes per session) and had competitive matches during the weekend. Training sessions consisted mainly of technical and tactical skill development. Physical conditioning was aimed toward anaerobic and aerobic performance development. Anaerobic training consisted of plyometrics and sprint training drills (2). Aerobic fitness was developed using small-sided games (27) and short or long intervals of running (15). Testing procedures were performed before the start of the competition season.
The participants (Table 1) were then subdivided into 3 age-based groups: G2 (prepubertal; age range: 11-12 years; Tanner stages I and II); G3 (peripubertal; age range: 13-14 years; Tanner stages III and IV) and G4 (postpubertal; age range: 15-20 years; Tanner stage V).
After providing oral and written explanations of the experimental design and potential risks of the study, written informed consent to take part was received from all players, and informed parental consent was obtained for minors. The local Institutional Review Board approved the study. All players were made familiar with the testing procedures used in this study through preinvestigation familiarization sessions.
The method of jump execution was standardized to obtain a more homogeneous jump technique and to decrease the intersubject variability. The CMJ was preferred to the squat jump because it is considered a more specific means of evaluating peak power (18).
The CMJ allows assessment of leg power under a slow stretch-shorten cycle and low stress load conditions; starting from an upright standing position, the jumper makes a preliminary downward movement by flexing at the knees and hips, lowering his or her center of mass, and then immediately extends the hips and knees again to jump up vertically off the ground through a “stretch-shorten movement” (20).
The jump technique was demonstrated to each participant and was followed by a standard warm-up routine, consisting of moderate jumping and stretching. Each participant performed a series of 5 maximal CMJs, each followed by 1 minute's rest. All jumps were performed barefoot, and subjects were asked to keep their hands on their hips throughout the jump performance.
A Kistler 9286A piezoelectric force plate (Kistler Instrumente AG Winterthur, Switzerland), connected to an Elite system (BTS S.p.A. Milan, Italy), was used to acquire FGR components. The vertical component of the FGR was sampled at 1,000 Hz for 4 seconds. All calculations were made using custom software in MatLab® R14 (The Mathworks Inc., Natick, MA, USA).
The hmax was obtained by means of the ballistic motion equation (hmax = g/8 × Tf2) where Tf is the flight time, directly obtained from the vertical component of FGR as the time interval in which the FGR was equal to zero.
The vertical velocity of movement of the subject's center of mass (vCM) was calculated (11) by subtracting the body weight from the FGR, dividing by the BM, and integrating with respect to time, using the trapezoidal rule for numerical integration (7). Power output was calculated from the product of the instantaneous values of FGR and vCM, thus easily identifying PPac.
To estimate PPac, the regression equations most commonly used in the literature were applied (Table 2). Because they had been obtained for different experimental samples in terms of number, gender, sport practiced and level of physical activity, we hypothesized that the equation providing the most accurate estimate of PPac would be the one obtained in the experimental sample with the most similar characteristics to the one under study.
Then, the new regression equation was developed from a training set (TS), which included two-thirds of the experimental sample jumps (344 jumps by 77 subjects), and crossvalidated in a validation set (VS) consisting of the remaining 186 jumps by 40 subjects.
Stepwise multiple regression analysis was adopted to obtain the best prediction results with the smallest number of variables (17), assuming hmax as the fixed variable.
Three criteria were used to form the database from which the regression equation was derived, to see which was able to provide the best estimation of PPac. These criteria were (a) the best-performance jump; (b) the mean values per subject of hmax and PPac; (c) all the jumps executed.
Finally, a TS and a VS were assessed for each age group, adopting the same criteria as for the entire experimental sample.
All statistical analyses were carried out using Minitab14 (Inc, State College, PA, USA). A normal data distribution was firstly ascertained using the Kolmogorov-Smirnov normality test so as to choose whether to apply parametric or nonparametric methods. The homogeneity of variances was checked using Levene's test. The results were considered statistically significant at a value of p ≤ 0.05.
The standard error of estimate (SEE) was adopted to evaluate the precision of the regression model (6), and the coefficient of determination (R2) was used as a measure of the proportion of total data variation accounted for by the regression model (3).
The values of hmax showed a normal distribution and homogeneity of variances, but the PPac values did not (p = 0.02), so nonparametric methods were adopted. The correlation coefficient (Spearman) between PPac and hmax ranged from 0.38 to 0.66 in the different samples.
Although the values of PPes, obtained by applying the regression equations reported in the literature to the entire sample showed a high correlation coefficient with PPac (Table 3), the estimated values were much lower than the actual values (Table 4 and Figure 1), showing highly significant statistical differences (Mann-Whitney, p < 0.00005). The Lewis equation, which presented the highest correlation coefficient, was also the equation that produced the highest estimation error (a difference of −77.6% with respect to the median PPac value), whereas the best estimate was obtained with the Lara equation, which yielded a −21.0% difference between the median values of PPes and PPac.
The results obtained applying the same equations to the 3 age-based subgroups: G2, G3, and G4 are reported in Table 4; also in these cases, the values of PPes were invariably lower than those of PPac, showing highly significant statistical differences (Mann-Whitney p < 0.00005), and the correlation among these was always lower than for the sample as a whole (Table 3). Therefore, the finding of highly significant differences between the PPes and the PPac showed the need to calculate new regression equations.
The values of the correlation coefficients between PPac and the independent variables (hmax, BM, and SH) in the 3 groups were all highly significant (p < 0.0005), ranging from 0.623 to 0.895.
Following the stepwise multiple regression analysis, the use of 3 variables (hmax, BM, and SH) instead of 2 (hmax and BM) did not yield a significant improvement in the adjusted R2 (0.882-0.893 according to the criterion adopted) or SEE (from 330 to 347 W). For this reason, SH was concluded not to be a significant predictor variable and was not included in the regression equation calculation.
As regards the assessment of the 3 criteria for calculating the regression equations, it was found that criterion C did not verify the hypothesis of independence of the residuals (Durbin-Watson test, p < 0.005); therefore, the calculation of PPes on the basis of all the jumps performed would have required a Generalized Least Squares regression approach (10,30). The adoption of a new model to develop the regression equations would have complicated the issue and so was considered outside the scope of this work. For this reason, the analysis proceeded using only criteria A and B.
The most accurate estimate (Table 5a) was obtained using the equation adopting criterion B (equation 1B). Instead, the criterion based on the best jump (criterion A), adopted by other authors, produced the worst results. The Bland-Altman plots (Figure 2) also showed that the agreement between PPac and PPes was better for criterion B.
To verify the efficacy of subdividing the experimental sample into homogeneous age groups, equation 1B was applied to G2, G3, and G4, and the results were compared to those of equation 2B applied to G2, equation 3B applied to G3, and equation 4B applied to G4 (Table 5b).
It was found that equations 2B, 3B, and 4B improve the SEE (15.5% in G2, 5.6% in G3, and 0.9% in G4), even if the differences between the medians of estimated peak power (PPes*) values and the corresponding PPes were never >0.3%.
The first purpose of the present work was to see whether the application of the regression equations reported in the literature to estimate the PPac of CMJs performed by young, male soccer players could yield accurate results. This was not found to be so for any of the equations considered, because the PPes was invariably, and statistically significantly lower than the PPac, despite the high correlation coefficient values. These findings are concordant with those reported by other authors (8,11,18,19,28) and justify the need to develop estimation equations that reflect the characteristics of a population, like gender, sport practiced, and age.
At this stage, we proceeded to check whether a new equation based on the specific study sample could yield more reliable PPes values. To calculate the regression equation, 3 different possibilities were compared, based on the use of the best performance achieved by each subject; the mean value of all the CMJs executed by each subject; the values for all the jumps. This last approach, based on within subjects measures, makes it possible to increase the sample size but yields correlated data points and so requires the application of a Generalized Least Squares method instead of the typical Least Squares Regression (10,30). The introduction of a new regression model that would be more complex than the one used up to now to calculate PPes was considered to be outside the scope of this study and was postponed to later works.
The adoption of the mean values of hmax and PPac for each subject yielded the most accurate results. It reduced the influence of chance factors that are the likely cause of the intraindividual performance variability and provided a SEE value of 302.9 W that is markedly lower than the values reported by Sayers et al. (28) and Johnson and Bahamonde (17), ranging between 379.2 and 561.5 W. Our results thus seem to confirm the suggestions in the literature that estimation equations specifically modeled on the population under study are needed to obtain reliable results.
The last of the purposes listed in the study aims was to obtain more accurate estimates by developing specific regression equations from specific age-based groups. Moreover, the fact that the most accurate results, among the regression equation reported in the literature, were obtained with the Lara equation, developed from a similar age group to our own, further supported the importance of assessing homogeneous age groups.
The subdivision of the sample into 3 homogeneous age subgroups was based on Tanner's stages, associated with the onset of puberty. In fact, puberty is accompanied by differences in the use of the contractile force and velocity during the push-off phase of the jump (19). Applying specific regression equations to each age-based subgroup did yield more accurate estimates, as demonstrated by the improved SEE values.
In conclusion, it can thus be considered that yet other factors could better reflect the subjects' physiological development, especially during the pubescent phase, but are not deducible from the anthropometric parameters. They may need to be considered to obtain a more general regression equation, also applicable to heterogeneous samples, that can yield improved estimates of PPac.
Explosive peak power is considered as a determinant of performance in sport activities such as soccer. Because direct measurement requires costly, complex instruments, regression equations have been introduced to avoid this requirement, based on approaches that are easier to apply on the field. Unfortunately, some problems are still to be solved because it is not possible to obtain accurate estimations using the regression equations reported in the literature, and so it is necessary to develop specific equations for the population under examination.
In addition, an increase in the accuracy of the estimation could be obtained using the mean value of hmax, obtained from different executions of the CMJ of the same subject. This is a novel approach as compared to reports in the literature up to now.
Finally, it must be stressed that it is better to avoid using the estimation of peak power to assess the performance of a single subject (when monitoring the power developed during training, for instance) because very high error values (>50% in some cases) may occur. The use of PPes, especially if based on large study samples, can be useful only to compare the performance of groups of subjects (e.g., improvements in the performance of a team over time).
This study did not receive funding from any source. We would like to thank D. Accettura for his assistance in data collection. The authors disclose professional relationships with companies or manufacturers who will benefit from the results of the present study. The results of the present study do not constitute endorsement of the product by the authors or the National Strength and Conditioning Association.
1. Achard de Leluardière, F, Hajri, LN, Lacouture, P, Duboy, J, Frelut, ML, and Peres, G. Validation and influence of anthropometric and kinematic models of obese teenagers in vertical jump performance and mechanical internal energy expenditure. Gait Post
23: 149-158, 2006.
2. Bangsbo, J. Fitness Training in Football—Scientific Approach
. Bagsværd, Denmark: HO+Storm, 1994.
3. Bewick, V, Cheek, L, and Ball, J. Statistics review 7: Correlation and regression. Crit Care
7: 451-459, 2003.
4. Bond, L, Clements, J, Bertalli, N, Evans-Whipp, T, McMorris, BJ, Patton, GC, Toumbourou, JW, and Catalano, RF. A comparison of self-reported puberty using the Pubertal Development Scale and the Sexual Maturation Scale in a school-based epidemiologic survey. J Adolesc
29: 709-720, 2006.
5. Canavan, PK and Vescovi, JD. Evaluation of power prediction equation: Peak vertical jumping power in women. Med Sci Sports Exerc
36: 1589-1593, 2004.
6. Crawford, JR and Howell, DC. Regression equations in clinical neuropsychology: An evaluation of statistical methods for comparing predicted and obtained scores. J Clin Exp Neuropsychol
20: 755-762, 1998.
7. Dowling, JJ and Vamos, L. Identification of kinetic and temporal factors related to vertical jump performance. J Appl Biomech
9: 95-110, 1993.
8. Duncan, MJ, Lyons, M, and Nevill, AM. Evaluation of peak power prediction equations in male basketball players. J Strength Cond Res
22: 1379-1381, 2008.
9. Faulkner, JA. Power output of the human diaphragm. Am Rev Respir Dis
134: 1081-1083, 1986.
10. Fox, J. Time Series Regression and Generalized Least Squares. Appendix to An R and S-PLUS Companion to Applied Regression
.California, CA: Sage Publications, 2002.
11. Harman, EA, Rosenstein, MT, Frykman, PN, and Rosenstein, RM. The effects of arms and countermovement on vertical jumping. Med Sci Sports Exerc
22: 825-833, 1990.
12. Hertog, C and Hue, O. Jump evaluation of elite volleyball players using two methods: Jump power equations and force platform. J Sports Med Phys Fitness
42: 300-303, 2002.
13. Hoffman, JR, Nusse, V, and Kang, J. The effect of an intercollegiate soccer game on maximal power performance. Can J Appl Physiol
28: 807-817, 2003.
14. Hunter, JR. Lower-limb explosive power and physical match performance in female collegiate soccer players. Master's thesis, Humboldt State University, Humbolt, 2008.
15. Impellizzeri, FM, Marcora, SM, Castagna, C, Reilly, T, Sassi, A, Iaia, FM, and Rampinini, E. Physiological and performance effects of generic versus specific aerobic training in soccer players. Int J Sport Med
27: 483-492, 2006.
16. Ispirlidis, I, Fatouros, IG, Jamurtas, AZ, Nikolaidis, MG, Michailidis, I, Douroudos, I, Margonis, K, Chatzinikolaou, A, Kalistratos, E, Katrabasas, I, Alexiou, V, and Taxildaris, K. Time-course of changes in inflammatory and performance responses following a soccer game. Clin J Sport Med
18: 423-431, 2008.
17. Johnson, DJ and Bahamonde, R. Power output estimate in University athletes. J Strength Cond Res
10: 161-166, 1996.
18. Lara, A, Abian, J, Alegre, LM, Jiménez, L, Ureña, A, and Aguado, X. The selection of a method for estimating power output from jump performance. J Hum Mov Stud
50: 399-410, 2006.
19. Lara, AJ, Abian, J, Alegre, LM, Jimenez, L, and Aguado, X. Assessment of power output in jump test for applicants to a sport sciences degree. J Sport Med Phys Fitness
46: 419-424, 2006.
20. Linthorne, NP. Analysis of standing vertical jumps using a force platform. Am J Phys
69: 1198-1204, 2001.
21. Markovic, G. Does plyometric training improve vertical jump height
? A meta-analytic review. Br J Sports Med
41: 349-355, 2007.
22. Maulder, P and Cronin, J. Horizontal and vertical jump assessment: Reliability, symmetry, discriminative and predictive ability. Phys Ther Sport
6: 74-82, 2006.
23. Moretti, B, Quagliarella, L, Sasanelli, N, Garofalo, R, Moretti, L, Patella, S, Belgiovine, G, and Patella, V. Functional analysis after Achilles tendon repair. G Ital Med Lav Ergon
29: 196-202, 2007.
24. Newton, RU and Kraemer, WJ. Developing explosive muscular power: Implications for a mixed methods training strategy. Strength Cond J
6: 20-31, 1994.
25. Pearson, DT, Naughton, GA, and Torode, M. Predictability of physiological testing and the role of maturation in talent identification for adolescent team sports. J Sci Med Sport
9: 277-287, 2006.
26. Quagliarella, L, Minervini, G, Sasanelli, N, and Fabbiano, L. Likelihood ratio approach for flying time evaluation in standing vertical jump. Gait Post
28: S29-S30, 2008.
27. Rampinini, E, Impellizzeri, FM, Castagna, C, Abt, G, Chamari, K, Sassi, A, and Marcora, SM. Factors influencing physiological responses to small-sided soccer games. J Sports Sci
25: 659-666, 2007.
28. Sayers, SP, Harackiewicz, DV, Harman, EA, Frykman, PN, and Rosenstein, MT. Cross-validation of three jump power equations. Med Sci Sports Exerc
31: 572-577, 1999.
29. Shetty, AB. Estimation of leg power: A two-variable model. Sports Biomech
1: 147-155, 2002.
30. Ugrinowitsch, C, Fellingham, GW, and Ricard, MD. Limitations of ordinary least squares models in analyzing repeated measures data. Med Sci Sports Exerc
36: 2144-2148, 2004.
31. Van Praagh, E and França, NM. Measuring maximal short-term power output during growth. In: Paediatric Anaerobic Performance
. Van Praagh, E, ed. Champaign, IL: Human Kinetics, 1998. pp. 155-189.
32. Vanderford, ML, Meyers, MC, Skelly, WA, Stewart, CC, and Hamilton, KL. Physiological and sport-specific skill response of Olympic youth soccer athletes. J Strength Cond Res
18: 334-342, 2004.
33. Vicente-Rodriguez, G, Jimenez-Ramirez, J, Ara, I, Serrano-Sanchez, JA, Dorado, C, and Calbet, JAL. Enhanced bone mass and physical fitness in prepubescent footballers. Bone
33: 853-859, 2003.
34. Welsh, TT, Alemany, JA, Montain, SJ, Frykman, PN, Tuckow, AP, Young, AJ, and Nindl, BC. Effects of intensified military field training on jumping performance. Int J Sports Med
29: 45-52, 2008.
Keywords:© 2011 National Strength and Conditioning Association
peak power estimation; jump height; body mass; age; linear regression