# Peak Vertical Jump Power Estimations in Youths and Young Adults

Amonette, WE, Brown, LE, De Witt, JK, Dupler, TL, Tran, TT, Tufano, JJ, and Spiering, BA. Peak vertical jump power estimations in youths and young adults. *J Strength Cond Res* 26(7): 1749–1755, 2012—The purpose of this study was to develop and validate a regression equation to estimate peak power (PP) using a large sample of athletic youths and young adults. Anthropometric and vertical jump ground reaction forces were collected from 460 male volunteers (age: 12–24 years). Of these 460 volunteers, a stratified random sample of 45 subjects representing 3 different age groups (12–15 years [*n* = 15], 16–18 years [*n* = 15], and 19–24 years [*n* = 15]) was selected as a validation sample. Data from the remaining 415 subjects were used to develop a new equation (“Novel”) to estimate PP using age, body mass (BM), and vertical jump height (VJH) via backward stepwise regression. Independently, age (*r* = 0.57), BM (*r* = 0.83), and VJ (*r* = 0.65) were significantly (*p* < 0.05) correlated with PP. However, age did not significantly (*p* = 0.53) contribute to the final prediction equation (*Novel*): PP (watts) = 63.6 × VJH (centimeters) + 42.7 × BM (kilograms) − 1,846.5 (*r* = 0.96; standard error of the estimate= 250.7 W). For each age group, there were no differences between actual PP (overall group mean ± *SD*: 3,244 ± 991 W) and PP estimated using *Novel* (3,253 ± 1,037 W). Conversely, other previously published equations produced PP estimates that were significantly different than actual PP. The large sample size used in this study (*n* = 415) likely explains the greater accuracy of the reported *Novel* equation compared with previously developed equations (*n* = 17–161). Although this *Novel* equation can accurately estimate PP values for a group of subjects, between-subject comparisons estimating PP using *Novel* or any other previously published equations should be interpreted with caution because of large intersubject error (± >600 W) associated with predictions.

^{1}Human Performance Laboratory, Fitness and Human Performance Program, University of Houston-Clear Lake, Houston, Texas

^{2}Department of Kinesiology, Center for Sport Performance, California State University, Fullerton, California

Address correspondence to William E. Amonette, amonette@uhcl.edu.

## Introduction

Power, as it relates to human performance, is defined as the ability of skeletal muscle to rapidly generate force (i.e., power equals force multiplied by velocity). Peak power (PP) capabilities correlate with performance for many athletic (^{14}), occupational (^{7}), and functional (^{10}) tasks. Accordingly, testing batteries designed to comprehensively quantify human performance routinely include a test of PP. Directly measuring PP requires laboratory equipment (i.e., a force platform and/or position transducer) (^{3,6}). Because purchasing this equipment can be prohibitively expensive, some human performance practitioners instead use a vertical jump test as a surrogate assessment of PP capabilities. However, estimating PP based on vertical jump height (VJH) alone is imprecise. Heavier individuals must generate a greater absolute power compared with a lighter individual to propel their body mass (BM) to a given height. Similarly, if the subject's BM increases or decreases over the course of a training intervention (which is quite common), changes in VJH will not adequately reflect changes in PP capabilities. Therefore, a simple method of accurately assessing actual PP (PP_{act}) is important for practitioners.

To address difficulties in assessing PP_{act}, several prediction equations using VJH and BM have been developed to estimate PP (PP_{est}) (^{2,5,8,11–13}). However, significant estimation error is expected when using a given equation, depending on the age, gender, activity level, etc., of the population and the type of jump used to measure VJH (e.g., the use of a countermovement and/or arm swing) (^{2,5,8,11–13}) (Table 1). Most of the existing equations to obtain PP_{est} (^{2,5,8,12,13}) were derived from small to moderately large samples (*n* = 17–161) of young adults (Table 1). Estimating PP using these equations (^{2,5,8,12,13}) may not accurately estimate PP in other populations (e.g., youth athletes). Therefore, the purposes of this study were to (a) develop a regression equation to estimate PP using a large sample (*n* = 415) of athletic youths and young men (age = 12–24 years); (b) determine if the accuracy of PP_{est} can be enhanced by generating age-specific equations; and (c) compare the accuracy of the “Novel” equation to previously published equations (^{2,5,8,11–13}).

## Methods

### Experimental Approach to the Problem

A cross-sectional study design was used to develop and validate a new to estimate PP in youths and young adults. Four-hundred-sixty boys and men (age 12–24 years) completed a single testing session during which BM, VJH, and PP_{act} were assessed using a force platform. After testing, an independent random sample of 45 participants, stratified by age, was selected as a validation sample. The data from the remaining 415 participants were used to develop a new regression equation to estimate PP. Ultimately, 4 regression equations were developed: one using the entire sample (*n* = 415) and 1 for each of 3 different age groups (12–15, 16–18, and 19+ years). The independent validation sample was then used to crossvalidate and compare the accuracy of the new equation vs. previously published equations for estimating PP.

### Subjects

Four hundred and sixty male volunteers (15.7 ± 2.8 years; 65.1 ± 14.8 kg), ranging in age from12 to 24 years participated in this study. The subjects were recruited from local area sports teams and a university population. The sample included 295 soccer athletes, 115 American football athletes, and 50 recreational athletes who were kinesiology students. All the athletes were tested during the offseason phase of training. The subjects were divided into a primary group used to develop the regression equation and a stratified random sample used to validate the regression equation and compare with previously published equations. The primary group consisted of 415 subjects (15.4 ± 2.6 years; 65.2 ± 14.6 kg). The stratified validation sample consisted of 45 subjects, with 15 subjects in each of 3 different age groups: 12–15 years (*n* = 15; 13.3 ± 1.3 years; 52.3 ± 11.9 kg), 16–18 years (*n* = 15; 16.9 ± 0.7 years; 68.8 ± 14.5 kg), and 19+ years (*n* = 15; 22.5 ± 1.8 years; 71.1 ± 8.8 kg).

Before the testing session, the subjects were given a detailed explanation of the study in understandable terms and provided a written document describing the study protocol. Each participant or their legal guardian completed a health and medical history analysis and signed an informed consent form before testing. The participants under the age of 18 were required to obtain written permission from their legal guardian and to sign a child assent form. The testing procedures, study protocol, informed consent and child assent forms were approved by the Committees for the Protection of Human Subjects of the University of Houston—Clear Lake and California State University, Fullerton.

### Procedures

Before vertical jump testing, subjects performed a 3–5 minutes of general warm-up consisting of light continuous exercise (i.e., cycle ergometer or overground running) followed by dynamic stretching (^{4,9,15}). The total warm-up lasted approximately 15 minutes. Because data were collected at multiple universities, vertical jump kinetics and BM were determined using 2 different force platforms (Advanced Mechanical Technology, Inc., Watertown, MA, USA) calibrated to the manufactures specifications. Ground reaction force data were collected using Labview 7.1 (National Instruments Corporation, Austin, TX, USA) and Dartpower (Athletic Republic, Park City, UT, USA) software. Although both force platforms collected 3-dimensional data, only the vertical ground reaction forces (*Fz*) were analyzed. Before testing, the countermovement vertical jumping procedures were verbally explained to the subjects and then they were allowed 3–4 practice jumps of increasing intensity. They were instructed to jump as high as possible using their typical jumping mechanics. Therefore, the depth of the squat before the jump was self-selected. When familiar with the vertical jump procedures, the subjects stood in the center for the force platform securely holding a wooden dowel (3-cm diameter, 171-cm length, 0.70-kg weight) across their shoulders. They performed a single, maximal countermovement vertical jump. The subjects were allowed to repeat the jump if an error occurred in data acquisition or if it was obvious that the jump was performed incorrectly (e.g., landing off the force platform, stopping during acceleration phase of jump).

### Power Calculations

The VJH and PP were analyzed at 400 Hz using a custom script in MatLab software (MathWorks, Natick, MA, USA). The center-of-mass (COM) vertical acceleration was found by dividing the vertical ground reaction force by BM. The COM velocity was then determined by integrating the acceleration curve relative to time using the trapezoid rule. Subsequently, VJH was determined based on the take-off COM velocity using a projectile motion equation. Power was calculated as the product of the vertical ground reaction force and the COM velocity. The PP_{act} was found as the maximum instantaneous power measurement in the *z*-axis during the take-off maneuver.

### Statistical Analyses

All statistical analyses were completed using a commercial software program (SPSS 18.0; SPSS Inc., Chicago, IL, USA). Sample size analysis using the data of Sayers et al. (^{12}) indicated that 15 subjects per group was sufficient to detect between-group differences with a desired power of 0.80 and an alpha of 0.05. Therefore, a stratified random sample of 45 subjects (15 subjects from each of 3 different age groups: 12–15, 16–18, and 19+ years) were selected from the overall sample of 460 subjects. Data from the remaining 415 subjects were used to develop the new equation to estimate PP using age, BM, and VJH via backward stepwise regression. Age-specific regression equations were also developed for each of the 3 age groups. A Group × Equation analysis of variance (ANOVA) with repeated measures was used to compare the PP_{act} values to the PP_{est} values obtained using the *Novel* equations (Table 2) and the previously published equations (Table 1). If the *F*-ratio was significant, Fisher least significant difference post hoc tests were used to determine pairwise differences. To further analyze the validity of the prediction equations for estimating PP, Bland-Altman (^{1}) plots were generated using SigmaPlot 12.0 (Systat Inc., San Jose, CA, USA) to compare PP_{est} with PP_{act} values; subsequently, the mean bias and 95% limits of agreement were calculated. For all comparisons, alpha was set at *p* ≤ 0.05. Data are reported as mean ± *SD* unless otherwise noted.

## Results

Independently, Age (*r* = 0.57), BM (*r* = 0.84), and VJH (*r* = 0.65) were significantly (*p* < 0.05) correlated with PP_{act} (Figure 1). However, after backward elimination, age did not significantly (*p* = 0.53) contribute to the final multiple regression model. The newly developed regression equation, hereafter referred to as “*Novel,*” used BM and VJH to estimate PP_{act} (Table 2 and Figure 2).

Age-specific equations were developed for 3 different age groups (12–15, 16–18, and 19+ years) (Table 2). The ANOVA revealed no significant differences between PP_{est} using the overall equation (based on *n* = 415) and PP_{est} using an age-specific equation (Table 3). Comparisons of the absolute differences of the residual values (PP_{est} – PP_{act} for overall vs. age-specific equations) also revealed no difference in the accuracy between the overall equation and the age-specific equations. Therefore, we relied on the overall prediction equation (developed using *n* = 415) for the remainder of the analyses.

When comparing the accuracy of *Novel* to previously published equations (presented in Table 1), the Group × Equation ANOVA revealed a significant main effect for Group and for Equation, and a significant Group × Equation interaction. The pairwise comparisons within “Group” revealed that 16–18 years (3,697.0 ± 1,026.5 W) and 19+ years (3,708.2 ± 447.2 W) were significantly more powerful than 12–15 years (2,325.5 ± 680.2 W). Pairwise comparisons within “Equation” indicated that there was no significant difference between PP_{act} and PP_{est} using the Novel equation. However, all other equations produced PP_{est} values that were significantly different than PP_{act} (Figure 3). The Group × Equation interaction revealed the following findings: within 12–15 years, the equations developed by Harman et al. (^{5}), Sayers et al. (^{12}), Canavan and Vescovi (^{2}), Shetty (^{13}), and Quagliarella et al. (^{11}) produced PP_{est} values that were significantly different than PP_{act}; however, the Novel equation and the equation developed by Lara et al. (^{8}) produced PP_{est} values that were not different than PP_{act}. Within 16–18 years, the equations developed by Harman et al. (^{5}), Canavan and Vescovi (^{2}), Shetty (^{13}), Lara et al. (^{8}), and Quagliarella et al. (^{11}) produced PP_{est} values that were different than PP_{act}; however, the Novel equation and the 2 equations developed by Sayers et al. (^{12}) produced PP_{est} values that were not different from PP_{act}. Within 19+ years, the equations developed by Harman et al. (^{5}), Sayers et al. (^{12}), Canavan and Vescovi (^{2}), Shetty (^{13}), and Quagliarella et al. (^{11}) produced PP_{est} values that were significantly different than the PP_{act}; however, the Novel equation and the equation developed by Lara et al. (^{8}) produced PP_{est} values that were not different than PP_{act}.

To determine the validity of the prediction equations for estimating PP for individual subjects, data were plotted using the methods of Bland and Altman (^{1}) (Figure 4); subsequently, the systematic bias and 95% limits of agreement were calculated (Table 4). The results indicated that the Novel equation was able to accurately estimate PP for a group of subjects (systematic bias = 10 W); however, for an individual athlete, all of the prediction equations produced random error components in excess of ±600 W.

## Discussion

The specific aim of this study was to develop and validate age-specific regression equations to predict PP from vertical jump using a large sample (*n* = 415) of athletic youths and young men (Table 2). Several conclusions can be drawn from these data: (a) age-specific regression equations did not improve the accuracy of the PP_{est} values (Table 3); (b) the Novel equation using the large sample provided PP_{est} values that were not significantly different than PP_{act} values (Figure 3); (c) the Novel equation provided PP_{est} values that were more accurate than previously published equations (Figure 3). However, it should be noted that neither the Novel equation nor any other previously published equations should be used to compare PP_{est} values obtained from different subjects or potentially within the same subject over time because the 95% limits of agreement are wide (± >600 W) (Table 4).

Equations to estimate PP using BM and VJH have been published previously; however, the equations were derived from relatively small sample populations. We hypothesized that our regression equation would be more accurate than previously published regression equations (^{2,5,8,11–13}) primarily because of the large sample size (*n* = 415) used in this investigation. In accord with our hypothesis, it was determined that the Novel regression equation produced PP_{est} values that were not significantly different than PP_{act} values, and that PP_{est} using Novel was more accurate than PP_{est} values obtained using previously published equations (Figure 3 and Table 4).

We found that generating age-specific regression equations did not significantly improve the accuracy of PP_{est} values compared with the equation developed using the overall sample. In contrast, Quagliarella et al. (^{11}) recently reported that age-specific regression equations did in fact improve the accuracy. Their conclusion (^{11}) was based on improvements in the standard error of the estimate (*SEE*) when the age-specific equations were used. We found only minimal improvements in the residuals scores for some, but not all, age groups when the age-specific equations were used. These slight differences were not statistically significant. Because the age-specific equations did not significantly improve the accuracy of the regression equation, and because the overall equation was developed using a larger sample size, we relied on the overall equation to estimate PP values.

In accord with the findings of Quagliarella et al. (^{11}), we conclude that the Novel equation can be used to estimate the PP values of a group of subjects; however, neither the Novel equation nor any other previously published equation can be used to compare PP_{est} values obtained from different individual subjects because the 95% limits of agreement are substantial (± >600 W). For coaches without access to laboratory equipment, the Novel equation can be used as a method of assessing the efficacy of a training intervention for a group of athletes. However, it should be noted that comparisons within an individual athlete or comparison of the same athlete over time should be interpreted with caution because of the large standard error of the measurement. Indeed, large measurement error is a limitation of all previously published equations using VJH and BM to estimate PP. It is not evident from these data what creates the high within subject measurement error for the estimated equations. Although the jumping methods in this study were rigorously controlled, slight variations in jumping technique between athletes may create error in the estimations.

Future research is required to determine if regression equations can be used to accurately track changes in PP after a training intervention within a given individual or within a group of individuals (i.e., determine if *changes* in PP_{est} agree with *changes* in PP_{act}). Moreover, research is needed to determine if the new equation accurately predicts power in groups of female athletes.

In conclusion, we developed a regression equation that accurately estimates PP values in a group of athletic youths and young adults. This equation more accurately estimated PP in an age-stratified sample than previously published equations. This equation can be used to estimate PP in youths and young adults and produces estimates that are similar to age-specific regression equations. Finally, although the Novel equation can accurately estimate PP values for a group of subjects, neither the Novel equation nor any other previously published equation should be used to compare PP_{est} values obtained from different individual subjects because the 95% limits of agreement are large (± >600 W).

## Practical Applications

Peak power is a critical component of physical fitness for most athletes and many occupations. However, directly measuring PP is problematic for most coaches because it requires access to expensive equipment. This study provides a regression equation that can accurately estimate PP within groups by simply using VJH and BM: PP (watts) = 63.6 × VJH (centimeters) + 42.7 × BM (kilograms) − 1,846.5. Crossvalidation of this newly derived equation in comparison with others previously published suggests that it might more precisely predict power in youths and young men. Therefore, the new equation can be used by human performance practitioners to accurately compare groups of male athletes before and after a training intervention, or to compare different groups of male athletes (i.e., athletes from different sports).

### Acknowledgments

The authors wish to thank Denham Brown and Junhai Xu for their assistance in collecting a portion of these data. The results of the study do not constitute endorsement by the National Strength and Conditioning Association. This study was supported, in part, by a faculty stipend from California State University, Fullerton.

## References

**Keywords:**

American football; kinetics; muscle; soccer; sport