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Predicting Lower Body Power from Vertical Jump Prediction Equations for Loaded Jump Squats at Different Intensities in Men and Women

Wright, Glenn A1; Pustina, Andrew A1; Mikat, Richard P1; Kernozek, Thomas W2

Author Information
Journal of Strength and Conditioning Research: March 2012 - Volume 26 - Issue 3 - p 648-655
doi: 10.1519/JSC.0b013e3182443125
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An essential role of the strength and conditioning (S & C) professional is to monitor the progress of an athlete's training. Monitoring progress allows the professional to evaluate the training program and adjust training progressions when needed. The ability to produce high amounts of force over a short period of time is a major factor determining optimal performance in many sports (2,9,10,22,23,26). As such, the development of power is given a high priority in conditioning programs (11). Optimization of power development requires not only a sound understanding of the training principles and programing to develop muscular power but also valid and reliable tests and measures to assess this component of athletic performance.

Many S & C professionals have used various types of vertical jump-based movements to develop and measure lower body power (6,7,13,24,27). Recently, lower body power has been assessed using maximal jump squats, countermovement jumps (CMJs) performed with a loaded barbell across the shoulders (2,3,19,21). The jump squat is considered to be a versatile exercise that can be used to assess lower body power production and as a training tool to develop lower body power.

Researchers have recommended assessing power for high velocity and low load sports, such as volleyball, with jump squats (5). Loaded jump squats may also be used to assess lower body power in those sports in which heavy protective equipment is used or where lower body power is important in contact sports when players must drive or tackle an opponent, such as American football or rugby. Loaded jump squat testing will also offer kinetic information about power production across the load-velocity relationship.

Various methodologies have been used to assess the lower body power produced during a jump squat, including the use of a force plate and different types of portable measurement systems, such as linear position transducers. Historically, the force plate has been used to measure ground reaction force to determine power (15,20,24) and force platforms are regarded by many as the “gold standard” for the assessment of power in a vertical jump (6). However, force plates are expensive and produce large quantities of complex data that may be difficult to analyze and interpret—especially in the field. Further, force plates appear to be sensitive to external vibrations that are produced from dropping weights in strength training facilities (6). In recent years, portable measurement systems, such as linear position transducers, have been used by S & C professionals to monitor power production during training sessions (14). Although linear position transducers are more cost effective than force plates, the cost may still be prohibitive for many high school and small college S & C budgets.

Maximal lower body power production has been estimated by the use of prediction equations using the body mass of an individual and the height of his or her maximal vertical jump (13,24). Because these prediction equations were created using body mass, it is not known whether they will accurately estimate maximal lower body power when body mass is replaced with system mass (mass of body + applied load) during a loaded jump squat. Therefore, the purpose of this investigation was to determine the reliability and validity of these prediction equations to determine peak power (PP) when the system mass is substituted for body mass.


Experimental Approach to the Problem

This study was designed to assess the reliability and validity of 3 common prediction equations for estimating lower body PP during a loaded jump squat. We hypothesized that the reliability of PP estimated by the prediction equations when substituting system mass for body mass will be high. In addition, we hypothesize that the error in the estimation of PP by these prediction equations will be no greater than the error when PP is estimated when using a vertical jump test with body mass used in the equation. Intraclass reliability of the prediction equations was assessed by comparing test to retest values within the same test session. Validity in estimating PP (13,24) was established by comparing predicted values with criterion values from a force plate (PPFP). To assess the utility of the different equations using varying applied loads, jump squats were performed under 3 load conditions (20, 40, and 60% of body mass). Both men and women were tested to determine if gender influenced the validity of the prediction equations.


A heterogeneous group of 30 female (body mass = 64.8 ± 7.5 kg; height = 164.1 ± 6.5 cm) and 30 male (body mass = 88.4 ± 16.1 kg; height = 179.9 ± 8.3 cm) physically active college students were recruited from a university weight training facility to be participants in this study. All the subjects were currently strength training regularly at least twice per week and were performing squats at least once per week during most weeks of their training programs for at least 1 year before being enrolled. The majority of subjects had performed loaded jump squats in their training programs previously but not on a regular basis. Current jump training was not a requirement for participation in this study. The testing protocol was approved by the University Institutional Review Board for the Protection of Human Subjects before data collection, and all the subjects signed an informed consent form before participation.


The subjects completed an experimental session 48–72 hours after an identical familiarization session. Both sessions took place at approximately the same hour of the day to avoid differences in body rhythms. The subjects were requested to report to the laboratory within 3–4 hours of their last meal, not have exercised in the last 24 hours, and had at least 6 restful hours of sleep the night before both the familiarization and experimental testing sessions. Height and body mass were determined before the familiarization session. During each session, the subjects warmed up for 3–5 minutes on a stationary bike at a low to moderate self-selected intensity followed by a set of 3 unloaded submaximal CMJs. After 5 minutes of passive rest, 3 repetitions of maximal jump squat were performed at each load condition (20, 40, and 60% of body mass). Percentage of body mass was used as recommended by Dugan et al. (7) to reduce error in using relative intensity of subjects because of a lack of standardization of determination of 1-repetition maximum for squat performance. To control for fatigue, order effect, and practice-related changes in loaded jump squat technique, each load condition was presented in a randomized order. The subjects were given 60 seconds of rest between repetitions and 3 minutes of rest between load changes (16). The best jump squat from each load condition determined from the PP measurement on the force plate (PPFP) was used in the analysis. Test-retest interclass reliability measures between the familiarization and the experimental session was high (intraclass correlation coefficient [ICC] = 0.97) for PPFP using the 3 different load conditions, suggesting that a single familiarization trial was sufficient for this study.

All jump squat testing was performed in the confinement of a Plyometric Power System (PPS; Norsearch, Lismore, Australia). This device restricted barbell movement to the vertical plane, similar to a Smith Machine. On this machine, linear bearings were attached to each end of the barbell. These bearings allowed the barbell to slide along 2 hardened steel shafts with minimal friction. To perform the jump squat, the subjects were instructed to stand motionless in an upright position with the loaded bar held tightly across their shoulders and then to perform a countermovement to a self-selected depth, immediately followed by a jump for maximal height. Other than these instructions, no other verbal motivation was given. If the barbell moved off the subject's shoulders during the jump, the trial was repeated.


Flight time and vertical ground reaction force (VGRF) data were recorded simultaneously via a contact mat and a force plate, respectively, for all the subjects and with all applied loads. The entire mass of the system (subject's body + loaded bar mass) was used to determine power output using each method (19).

Force Plate

A force plate (Quattro Jump, Type 9290AD, Kistler, Switzerland) with a sampling rate of 500 Hz was used to measure VGRF during the performance of a jump squat. Velocity and power were calculated from vertical ground reaction force data using the impulse-momentum theorem (7,20). A change in the momentum of the body or the system during the jump squat is relative to the impulse produced. This method involves collecting vertical ground reaction force data, beginning when the subject is standing stationary with the load across their shoulders and ending when the subject leaves contact with the force plate. Force-time data were used to calculate velocity and power for the entire duration of each repetition. When the system mass does not change during the time that force is applied: VGRF × time = mass × ΔV and ΔV = force × time/mass, where ΔV is the change in vertical velocity. Absolute V was determined by adding ΔV to the previous time interval, starting at zero at the beginning of the jump. Instantaneous power was determined by the product of VGRF measured by the force plate and the calculated V (13). The PP was the highest value measured during each repetition of the jump squat and the repetition with the highest PP on the force plate at each load was used for statistical purposes.

Prediction Equations

The prediction equations used in this study are listed in Table 1. Normally, jump height and body mass are entered into the equations provided by Harman et al. (13) developed using a jump and reach from a crouched position and 2 by Sayers et al. (24); 1 using a CMJ and 1 using a squat jump (SJ). However, to validate these equations under loaded conditions, the system mass (kilograms) as measured by the force plate with the subject in starting position was substituted for body mass. A contact mat (Just Jump, Probotics, Huntsville, AL, USA) was used to determine jump height during testing. When the athletes jumped and their feet left the mat, a timer was activated. As they returned to the ground, their feet made contact with the mat, stopping the timer. The subjects were informed to not tuck their knees during flight. Flight time was displayed with precision of 0.01 seconds. The Just Jump system's computer calculates the displacement of the body's center of mass (COM) using the formula: jump height = (t2 × g)/8. Here g is the gravitational acceleration and t is the flight time (17). Jump height was displayed in inches (to the nearest 0.1 in.) on the Just Jump's screen and converted to centimeters (1 in. = 2.54 cm) for direct comparison. Once jump height (centimeters) and total mass of the system (kilograms) were determined, they were entered into the prediction equations to estimate PP. During data collection, the contact mat was placed directly on top of the force plate, and the force plate was zeroed with the contact mat in this position. This setup allowed simultaneous data collection for both methods (force plate and prediction equations) of determining PP.

Table 1:
Prediction equations used to estimate peak power.*†

Statistical Analyses

Dependent variables consisted of PP from the force plate (PPFP) and PP from the 3 prediction equations (PPest). Load condition (20, 40, and 60% body mass) and gender were used as independent variables. All statistics were performed using the Statistical Package for the Social Sciences (SPSS Version 17.0, SPSS Inc., Chicago, IL, USA).

The ICCs and coefficients of variation percentage (CV) were used to determine the relative and absolute reliabilities, respectively, of the force plate and prediction equations. Measurements from all 3 jumps at each load were used to determine the ICC and CV values. The CV was calculated (CV = SD/mean × 100) for each individual and then the mean CV was determined for the entire sample.

It was not the intent to compare jump squat power of men with that of women but to determine whether this method of predicting peak lower body power was equally effective for both sexes. Therefore, separate analyses to determine reliability and validity of the prediction equations were done for men and women subjects. A repeated measures 3 (applied load: 20, 40, and 60% body mass) × 4 (method: force plate, and 3 prediction equations) factorial analysis of variance was used to examine differences between PPactual and PPest from each equation. When appropriate, Tukey post hoc comparisons were used to identify differences within the methods and applied load conditions. Pearson correlations were used to determine the relationship between PPFP and PPest for each equation. Overall, statistical significance was set at α = 0.05, whereas statistical power for all tests was between 0.90 and 1.00.


Reliability values for the prediction equations and force plate measures of PP can be seen in Table 2. Men had prediction equation ICC values across the 3 applied loads ranging from 0.95 to 0.99 and CV values ranging from 1.0 to 3.3%. These were similar to the ICC values (0.98–0.99) and CV values (2.5–2.6%) observed in force plate data for men. For women, ICC values for the prediction equations ranged from 0.96 to 0.99 and CV values from 1.2 to 7.0%, whereas force plate ICC ranged from 0.93 to 0.98 and CV ranged from 3.4 to 4.5%. In general, the ICCs and CVs of PP for prediction equations were similar to those calculated from the force plate in men and women.

Table 2:
ICCs and CV for the force plate and prediction equations for each load (20, 40, 60%) relative to body mass.*

Peak power from the force plate and the estimated PP from the prediction equations for men and women can be seen in Figure 1. No significant method by load interaction effect was identified in men (p = 0.39) or in women (p = 0.08).

Figure 1:
Peak power (watts) from the prediction equations (8,19) and the force plate across the 3 loading conditions (20, 40, 60% body mass) for (A) men (n = 30) and (B) women (n = 30).

For men, a significant (p < 0.001) main effect by method was found. Post hoc analysis determined that there was no difference between PPFP and PPest determined by the Harman (p = 0.07) equation; however, significant differences were found between the PPFP and PPest from the Sayers CMJ equation (p < 0.001) and the PPFP and PPest by the Sayers SJ equation (p = 0.02) (Figure 2A). Similar results were found in women, with a significant main effect by method (p < 0.001) identified. Post hoc analysis for women determined that there was no difference between PPFP and PPest from the Harman equation (p = 1.00), whereas significant differences were identified between the PPFP and PPest by the Sayers CMJ equation (p < 0.01) and the PPFP and PPest by the Sayers SJ equation (p < 0.01) (Figure 2B).

Figure 2:
Main effects for peak power by method for (A) men and (B) women. * Indicates a significant difference between the prediction equation and the force plate.

No significant main effects by load were found (p = 0.19) within men (Figure 3A). In contrast, a significant main effect by load was found (p < 0.01) for women. Post hoc analysis (Figure 3B) determined that there was a difference between 20 and 40% (p = 0.01) and 20 and 60% (p = 0.02) body mass but no difference between 40 and 60% load condition (p = 0.99). In addition, Pearson correlations in Table 3 indicated that the association between the PPest from the equations and PPFP was stronger for men (r = 0.84–0.94) than for women (r = 0.50–0.72).

Figure 3:
Main effects for peak power by load for (A) men and (B) women. * Indicates significant difference between loads.
Table 3:
Pearson correlation coefficients between the force plate and prediction equations (8,19) for men and women at each load (20, 40, 60%) relative to body mass.*


The purpose of this study was to determine the efficacy of using prediction equations to determine lower body PP under externally loaded conditions in the jump squat for men and women. The ICC >0.9 and a CV <10% typically is interpreted as highly reliable (1). This study showed that the Harman (13), Sayers CMJ (24), and Sayers SJ (24) prediction equations were highly reliable for determining PP during the jump squat from trial to trial for both men and women at all loads tested, and as a result, this supports our first hypothesis.

Peak power estimated by the Harman equation was not significantly different from PPFP for both men and women. In contrast, the Sayers SJ equation and the Sayers CMJ equation were found to be significantly different from the force plate estimates of PP in both men and women. Therefore, the Harman equation was the only equation examined in this study that was found to be both reliable and valid for predicting PP for both men and women.

Although no significant difference was found between the Harman equation and the force plate estimates of PP for men in this study, it should be noted that PP was underestimated by the Harman equation by 9, 8, and 4% as load increased from 20, 40, and 60% of body mass, respectively. Because this study is the first to analyze the clinical utility of established prediction equations for determining PP from loaded jump squats, our results can only be compared with those of studies that have investigated the validity of the current equations using unloaded CMJs. The results of our study are supported by those of other studies that demonstrated that the Harman equation underestimated PP of a CMJs by 7% in college athletes and physical education students (24) and by 6% in male basketball players (8). It seems that the use of the Harman equation to estimate PP from a loaded jump squat on a contact mat does not modify the magnitude of the error involved with using the Harman equation to determine PP from a vertical jump at body weight. Therefore, the lack of significant difference leads us to conclude that the Harman equation is useful for estimating PP of lower body with loaded jump squats in men, partially supporting our second hypothesis.

For women in this study, it was found that as the applied load increased from 20, 40, and 60% of body mass, the Harman equation underestimated PP by 2, 14, and <1%, respectively. The results from this study did not lead to any explanation as to why there was such a large difference between the force plate and the Harman equation estimates of PP during the jump squat using 40% body mass compared with the 20 and 60% trials. The results of Canavan and Vescovi (4) largely support the findings of this study when predicting PP in women using the Harman equation because they reported no difference between PPest from the Harman equation and PPFP. However, for their group of women, PP during a body weight CMJ was overestimated by 6% in college women, whereas the results of this study underestimated PP by 3% when collapsed across loads using a loaded jump squat.

In this study, a significant difference was found between PPest from both the Sayers CMJ (men, +14%; women, +20%) and SJ (men, +8%; women, +12%) prediction equations when comparing PPFP for both men and women. Both Sayers equations produced an overestimation of PP during the loaded jump squat. However, the Sayers SJ equation was a better predictor of PP during the loaded jump squat than the CMJ equation, indicated by the smaller error between the PPFP and the PPest observed in the Sayers SJ equation. This is interesting because the jump squat used in this study employed a counter movement before the concentric jump. Sayers et al. (24) also reported that the SJ equation yielded a more accurate prediction of PP than the CMJ equation during a CMJ; however, the results of this study demonstrated greater error with loaded SJ conditions than have been reported in previous studies with unloaded jumps (8,24) leading us to partially reject our second hypothesis for the Sayers CMJ and SJ equations. Although our results indicated that both Sayers equations overestimated PP, in contrast, Duncan et al. (8) reported the Sayers SJ and Sayers CMJ equations underestimated PP by 12 and 3%, respectively, during a CMJ, indicating that the Sayers CMJ equation was better at predicting PP for a CMJ than was the SJ equation. The differences between our results and those of Duncan et al.'s (8) besides the use of loading during the jump in our subjects is that Duncan et al. (8) used elite basketball players with more jumping experience than the subjects used in this study.

This study had limitations that may have impacted our results. The 3 prediction equations used in this study were derived using vertical jumps with full arm swing during the jump and reach test. Before this study, it was not known if performing a vertical jump without an arm swing on a contact mat with a load across the shoulders would influence the accuracy of these prediction equations. The Harman and Sayers equations rely on jump height obtained from a jump and reach test, whereas this study used a contact mat to estimate jump height based on flight time, which did not allow the use of an arm swing. Linthorne (20) reported that using a contact mat results in an overestimation of true jump height (0.5–2.0 cm), because the height of the jumper's COM at landing is lower at landing than at takeoff. As a result, jump height measured using the jump and reach test was found to be underestimated by approximately 10%. Additionally, it has been determined that the arm swing may contribute about 10% to the PP of a maximal vertical jump (12). Therefore, it appears that the added jump height measured by the contact mat may have been partially canceled out by the loss of power produced by arm swing when holding the bar to the shoulders during a jump squat. Further, Leard et al. (18) reported that the Just Jump system used in this study was more accurate than the Vertec when compared with measuring the displacement of a reflective marker on the sacrum measured by a 3-camera motion analysis system to determine jump height. Therefore, the use of a contact mat should not pose significant problems in the prediction of PP produced during a loaded jump squat.

Another possible limitation to this study was that the jump squat was performed in a Plyometric Power System, where the movement of the bar was limited to a vertical plane, whereas the prediction equations used in this study were derived from free jumps without such limitations. This may not be a significant limitation because Sheppard et al. (25) reported that the PP and other force-time measures recorded during a Smith machine jump squat and a free weight jump squat were similar except of average power. Therefore, the use of a Smith machine or similar device such as the PPS used in this study may not create significant differences between jump squat methods determining PP.

The association between actual and predicted PP production during a loaded jump squat was assessed using Pearson Product-Moment correlations. This study showed that the relationships between PPest and PPFP were much stronger for men (r = 0.84–0.94) than for women (r = 0.50–0.72). Additionally, for women, the relationship between PPest and PPFP for all the equations was observed to be lower as the load increased. As a result, when using these equations to assess PP in women, they should be used with caution. Conversely, it appears that PP during the jump squat can be monitored at regular intervals for men using the height of the jump measured by a contact mat and any of these equations with applied loads between 20 and 60% of body mass.

Practical Applications

Assessing power production over the course of a training period using various loads allows the S & C professional to determine the needs of an athlete. Using relatively heavy loads during a jump squat power test will provide information about the contribution of force production (strength) to the power formula (power = force × velocity), whereas using jump squats with light loads will assess the athlete's ability to produce force rapidly (velocity). Further, data gathered using this simple and inexpensive method can be used to track changes in power production over different phases of training that may indicate the rate of progress being made by the athlete.

Using jump height of a loaded jump squat measured by a contact mat to monitor changes in lower body power appears to be a valid alternative to more complex and costly methods because of the high test-retest repeatability and relatively small coefficient of variation of this assessment. The high association between the force plate and all of the prediction equations measured support this method of assessment of lower body power production. Although using prediction equations to estimate PP may be an inexpensive way of assessing power development using different loads, it may be more appropriate for men than women based on the stronger associations observed in men. In addition, although PPest measured by all prediction equations assessed had strong associations with the force plate, the Harman equation had the strongest correlation and was the only prediction equation tested that had similar PPest and PPFP for both men and women.


The authors would like to acknowledge the funding for this project from the Graduate Student Research, Service and Education Leadership Grant Program at the University of Wisconsin-La Crosse. The results of this study do not constitute endorsement of any of the products used in this investigation by the authors or the National Strength and Conditioning Association.


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triple extension; athlete monitoring; jump height; force plate

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