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Evaluation of Power Prediction Equations: Peak Vertical Jumping Power in Women


Medicine & Science in Sports & Exercise: September 2004 - Volume 36 - Issue 9 - p 1589-1593
doi: 10.1249/01.MSS.0000139802.96395.AC

CANAVAN, P. K., and J. D. VESCOVI. Evaluation of Power Prediction Equations: Peak Vertical Jumping Power in Women. Med. Sci. Sports Exerc., Vol. 36, No. 9, pp. 1589–1593, 2004.

Purpose: The purpose of this investigation was to: 1) compare actual peak power (PPactual) to estimated values (PPest) derived from three different prediction equations (Sayers and Harman), 2) determine the ability of the prediction formulas to monitor change following 6 wk of plyometric training, and 3) generate a new regression model.

Methods colon; Twenty college females (age = 20.1 ± 1.6 yr; body mass = 65.9 ± 8.9 kg) were randomly assigned to a control or intervention group. Pre- and posttest countermovement jump (CMJ) height and PPactual were determined simultaneously on a force platform. Body mass and maximal CMJ height were used to predict peak power.

Results colon; All three PPest were significantly correlated 0.84–0.99) and post (r = 372.4 W) was significantly less to PPactual and to each other on pre (r = 0.88–0.99) tests. PPactual (2425.4 ± 2920.8 ± 482.6 W; CMJ = 2925.1 ± 409.7 than PPest (Sayers: SJ = 473.0 W) but was not different from PPest (Harman: 2585.0 ± 409.7 W). Posttests revealed similar differences between PPactual and PPest for the intervention group, however no significant differences were observed for the control group. Mean differences from pre and posttests did not differ within or between PPest. Regression analysis determind the formula: ppest = 65.1 × (jump height) + 25.8 × (body mass) − 1413.1 (R2 = 0.92; SEE = 120.8), which slightly determined (0.77%) peak power is compared with PPactual in our cross-validation sample (n = 7)

Conclusions colon; Changes in peak power is accurate using any of the regression equations; however, the new prediction formula and that of Harman seem to more precisely estimate peak power. Strict jumping technique along with simultaneous measurement of power and jump height should be used as the standard for comparison.

1 School of Allied Health, Northeastern University, Boston, MA; and 2 Human Performance Laboratory, Department of Kinesiology, University of Connecticut, Storrs, CT

Address for correspondence: Paul K. Canavan, Department of Physical Therapy, Northeastern University, 6 Robinson Hall, Boston, MA 02115; Email:

Submitted for publication October 2003.

Accepted for publication April 2004.

Power is considered an essential element for successful athletic performance (14,15,18), as well as for carrying out daily activities and occupational tasks (14). The assessment of power can be used to track performance improvements or decrements over time and subsequently determine the efficacy of a training program (13). Whereas a force platform is ideal for directly and precisely measuring power, this method is expensive and not easily accessible outside the laboratory setting. The use of vertical jump height has been widely used by sports performance professionals as an alternative to direct assessment of power (7,9,17). Typically prediction equations have been used to estimate peak and average power from jump height. The Lewis formula (7) was commonly used but deemed inaccurate by Harman et al. (9), who reported the formula did not measure the peak power from jumping but rather estimated it indirectly based on calculation of the average power gravity exerts on the falling body. Consequently, Harman et al. (9) determined a regression equation from a sample of college men (N = 17) that was later cross-validated by Sayers et al. (17) in a larger sample of men and women. The equations generated from each study are listed in Table 1; however, examination of these formulas is needed due to several limitations.



First, both studies used separate tests to determine vertical jump height and peak power instead of pairing these two variables from the same jump. Power output was measured on a force plate, whereas jump height was determined from a jump and reach test. Performing the jump and reach test against a wall may impede jumping technique and therefore effect jumping ability compared with jumping on a force plate. Second, the cross-validation study by Sayers et al. (17) included an extremely heterogeneous group of men and women as well as a combination of athletes and nonathletes. It could be argued differences in vertical jump technique and/or coordination may exist between genders and between athletes and nonathletes (5,10). Lastly, specificity would commonly dictate the use of a countermovement jump (CMJ) compared with a static squat jump (SJ) when assessing athletes. A squat jump begins from a paused crouched position before jumping vertically, whereas CMJ begins from an erect position and uses a quick crouching action followed immediately by a vertical jump. Harman et al. (9) used squat jump height in their regression model, whereas Sayers et al. (17) reported the prediction equation derived from SJ was more accurate than the formula from CMJ. These factors may add to the variability of their regression models, which would subsequently affect the accuracy of peak power prediction.

Many females are participating in high-intensity sports (i.e., soccer, lacrosse, volleyball, tennis) and training protocols (i.e., resistance and plyometric training) that require high power output from the lower extremities. Monitoring changes in performance over time is standard practice for sports performance professionals. To date, no research has examined the ability of prediction equations to track alterations in performance. It would be beneficial to have a procedure to assess and monitor changes in lower-extremity power for female athletes that is time efficient, accurate, and reliable. Therefore, the purpose of this investigation was to compare actual peak power (PPactual) with estimated peak power (PPest) determined by the aforementioned formulas (9,17) with a sample of college females. A secondary purpose was to assess the prediction formulas’ ability to monitor changes after a 6-wk plyometric program. A cross-validated regression formula was developed, which may be more accurate and possibly gender specific.

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Experimental approach to the problem.

A longitudinal study design with a training intervention was used to assess the predictive ability and accuracy of power prediction formulas. Twenty college females volunteered to participate and were randomly assigned to either an intervention (plyometric training) or control group for 6 wk. Before and after the 6-wk intervention, PPactual and maximal CMJ height were assessed on a Quattro Jump Portable Force Plate System (Kistler, Amherst, NY). Trials were measured in triplicate with the best jump height and associated peak power used for analysis. Body mass (kg) and maximal CMJ height (cm) were used as the predictors and peak power as the criterion variable in the regression analysis.

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Twenty recreationally trained college women (age = 20.1 ± 1.6 yr; body mass = 65.9 ± 8.9 kg) volunteered to participate in this investigation. Subjects participated in regular exercise and intramural sports and had a minimum of 3 yr of organized basketball experience. Written informed consent was obtained before beginning the study in accordance with the university’s Institutional Review Board.

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Peak power assessment.

PPactual and maximal CMJ height was assessed using a Quattro Jump Portable Force Plate System (Kistler, Amherst, NY) at a sampling rate of 500 Hz. Subjects were instructed to begin from a standing position and perform a crouching action immediately followed by a jump for maximal height. Subject’s hands remained on the hips for the entire movement to eliminate any influence of arm swing (4). Jump technique was demonstrated to each subject, followed by two submaximal attempts. Three maximal jumps, separated by ample rest, were then completed. Test-retest reliability was high (r = 0.95–0.97) for vertical jump height.

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Plyometric training intervention.

Plyometric training was performed 3 d·wk−1 for 6 wk. Each session lasted approximately 45–60 min and included a standardized warm-up, followed by the jump exercises and concluded with a cool-down. A variety of exercises were used including, squat jumps, broad jumps, bounds, and lateral jumps. The intensity was increased over the 6-wk period by increasing the duration of exercise (e.g., 10–25 s) or the distance jumped (e.g., broad jumps). A detailed description of the entire program and progression is provided by Hewett et al. (11,12). All subjects completed an orientation session to become familiar with the different jumps before the initial training session but after pretesting.

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Statistical analysis.

Statistics were performed using SPSS Version 11.0 (SPSS Inc., Chicago, IL). Pearson product correlations were used to assess the relationship between PPest and PPactual. A repeated measures ANOVA was used to compare the pre- (entire sample) and posttest (separate groups) peak power values with subsequent Tukey’s post hoc analysis when appropriate. Paired t-tests were used to examine changes pre to post for the intervention and control groups. Multiple regression analysis was used to determine a new prediction equation and cross-validated using a 2/3 split of the sample. Values reported are means ± SD. Statistical significance was accepted at P < 0.05.

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Table 2 shows the correlation matrix between PPactual and PPest. All three prediction models (9,17) were highly correlated with PPactual for the pretest (r ≥ 0.84) and posttest (r ≥ 0.88) data (P < 0.01). There was also a high correlation between each of the regression equations from Harman and Sayers (r = 0.97–0.99, P < 0.01).



Multiple regression analysis was used to predict peak power output (W) from CMJ height (cm) and body mass (kg). Results indicated that the two predictor variables accounted for a significant amount of peak power variability, R2 = 0.92, F (2,10) = 61.35, P < 0.000. Furthermore, the regression model (PPest = 65.1 × (jump height) + 25.8 × (body mass) − 1413.1) showed minimal error, SEE = 120.8. CMJ height (t = 9.62, P< 0.000) and body mass (t = 5.94, P < 0.000) each contributed significantly to the model and uniquely accounted for approximately 70% and 27% of the variance in peak power, respectively.

Cross-validation (N = 7) of the current prediction equation indicated no significant difference (P > 0.05) between 229.1 W PPactual and PPest. The mean difference of 17.5 ± corresponds to an underestimation of 0.77% by the regression model.

PPactual and PPest for the pretest are displayed in Figure 1. Both equations from Sayers et al. (17) significantly overestimated PPactual by approximately 20%. On the other hand, the Harman et al. equation (9) overestimated PPactual by only 6% (NS).



Figures 2A and 2B show the differences in peak power after the 6-wk training period for the intervention and control groups, respectively. No differences were observed between pre- and posttest scores for any of the prediction equations. Significant overestimations still existed between PPest (Sayers) and PPactual for the intervention group (P < 0.000) on the posttest scores; however, no differences were observed within the control group (P = 0.178).



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This investigation found significant differences between PPactual and PPest on the pretest (Fig. 1). Regardless of which Sayers formula was used (SJ or CMJ), there was a significant overestimation of peak power. There was also a non-significant overestimation of PPest by the Sayers formula (17) compared with Harman PPest of approximately 13%. Because Harman et al. (9) also used the SJ technique to determine their regression formula, it is surprising to have found this discrepancy. It is interesting because the subject characteristics are vastly different between the current investigation and Harman et al. (9), yet Sayers and colleagues (17) reported that investigating a larger more heterogeneous group would provide more accurate results. A plausible explanation for the overestimation of previously developed equations compared with the current study could be the use of the jump and reach test, whereby subjects place a mark on the wall with their fingers (e.g., chalk). An individual’s unique flexibility in shoulder elevation combined with side bending of the trunk may not precisely measure the change in height of the center of mass. Therefore, the test may inadvertently misrepresent true vertical jump height and consequently effect power estimates. Hertogh and Hue (10) reported no differences between PPactual, Sayers, and Harman peak power for sedentary individuals, but the two prediction equations significantly underestimated peak power compared to PPactual for volleyball players. Whereas these findings conflict with the current study, they do lend support to the notion of developing and using regression models within homogeneous samples.

The similarity between PPactual and PPest (Harman) was not only unexpected due to the different samples examined but also because of the difference in jump technique used. Jump height is typically greater when using a CMJ compared with an SJ because more work is generated during the preparatory countermovement (2); however, Harman et al. (9) provided no indication regarding the depth of squat performed or how long of a pause was required before jumping. In addition, neither Harman et al. (9) or Sayers et al. (17) reported what was considered a successful SJ attempt, whereby no preparatory countermovement was observed. Therefore, it becomes difficult to decipher whether the SJ in Harman et al. (9) could have been more similar to the CMJ used in the current study or if the SJ and CMJ performed in Sayers et al. (17) study had minimal technique differences.

All of the prediction formulas were able to track performance similarly to PPactual (Fig. 2). Whereas no significant differences were observed between pre and posttest values, peak power for the intervention and control groups tended to increase and decrease, respectively. This is the first study to examine the ability of prediction equations to assess performance over time. These findings indicate that peak power can be accurately monitored for the duration of a typical mesocycle regardless of the formula chosen.

The regression equation developed from the current sample of recreationally trained college women appears highly accurate. The SEE (120.8) is considerably less than the values reported by Sayers et al. (17) (range: 372.9–561.5). Sayers et al. (17) have suggested that the SJ provides a more standardized protocol due to large variations in CMJ technique. Anecdotal evidence from our laboratory indicates that performing a pure SJ from a static squat position is nearly impossible, even when the hands are placed on the hips. It appears necessary to perform some type of countermovement action with the legs or torso before jumping. Allowing arm swing to occur will also add to the variability and more closely link the SJ to CMJ performance. This would appear true from a closer examination of Sayers et al. (17) data and regression equations. Just as we found no difference (9.6 W) when inserting CMJ height in both Sayers equations, the results from their female subsample (Tables 6 and 7 from Sayers et al. (17)) indicated a difference of only 60.2 W (it was not reported whether this difference was significant). This would seem to indicate that either a great deal of cross talk occurred between the two jump techniques or there is an inability of the regression equations to distinguish between them. So, although we agree that using CMJ in either formula will produce similar results, we are in disagreement with the rationale provided by Sayers et al. (17).

Including plyometric drills into a training program has been shown to improve both power production (6,16) and jumping performance (1,3,6,8,20). Whereas Gehri et al. (8) used women as participants, they did not report gender differences because men and women were combined in their training groups. The current investigation showed no change in peak power after a 6-wk plyometric program (Fig. 2), which is in agreement with Young et al. (21). They also used a 6-wk training program with men and found no difference in jumping ability. Research examining longer durations of training (8–12 wk) have reported a 40% increase in peak power (6). Therefore, a minimum of 8 wk should be considered when designing a training program to improve peak power and/or jumping ability.

Using power (0.8) and effect size (0.92) to determine an appropriate sample size revealed the need for approximately 25 individuals (19); therefore, our sample of 20 should be considered a limitation to this study. Nevertheless, a new regression formula was developed that is highly accurate but needs to be cross-validated with larger and different samples (e.g., elite athletes). Whereas all of the equations examined track performance with a great deal of similarity, the use of either Sayers equation overestimated peak power by roughly 20% compared with PPactual. Future research should establish criteria that can distinguish between a reliable from an unreliable SJ.

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