Estimation of Lower Body Muscle Power from Vertical Jump in Youth

Figures & data

Table 1. Descriptive statistics (M ± SD) for validation sample, cross-validation sample, and total sample.

	Validation sample		Cross-validation sample		Total sample
Variable	Females (n = 172)	Males (n = 182)	Females (n = 77)	Males (n = 98)	Females (n = 249)	Males (n = 280)
Age (years)	13.7 ± 2.3	13.8 ± 2.3	13.9 ± 2.2	13.7 ± 2.5	13.8 ± 2.3	13.8 ± 2.4
Height (cm)	154.6 ± 9.3	159.7 ± 13.1	156.4 ± 9.0	158.7 ± 14.2	155.1 ± 9.2	159.4 ± 13.5
Body mass (kg)	49.0 ± 9.6	51.6 ± 13.4	49.9 ± 11.2	51.1 ± 14.5	49.3 ± 10.1	51.4 ± 13.8
BMI (kg·m^−2)	20.4 ± 2.8	19.9 ± 3.0	20.2 ± 3.6	19.9 ± 3.2	20.3 ± 3.1	19.9 ± 3.0
VJ Height (cm)	33.0 ± 6.6	38.2 ± 9.1	33.5 ± 7.9	37.9 ± 9.6	33.2 ± 7.0	38.1 ± 9.3
Power (W)	1911 ± 481	2334 ± 913	1953 ± 495	2265 ± 887	1924 ± 485	2310 ± 903

Note: BMI = body mass index. VJ Height is vertical jump height from field test. Power is from mechanography.

Table 2. Zero-order correlations between measured peak vertical jump power (W) and predictor variables for validation sample, cross-validation sample, and total sample.

Variable	Validation sample (n = 354)	Cross-validation sample (n = 175)	Total sample (N = 529)
Age (years)	.72*	.73*	.72*
Sex (1 = male, 0 = female)	.28*	.21*	.25*
Body mass (kg)	.86*	.85*	.85*
VJ Height (cm)	.69*	.62*	.66*

* p < .01. VJ Height is vertical jump height.

Table 3. Zero-order correlations among predictor variables for total sample.

Variable	Age	Sex	Body mass
Age (years)	–
Sex (1 = male, 0 = female)	.01	–
Body mass (kg)	.67*	.09	–
VJ Height (cm)	.54*	.28*	.37*

Note: * p < .01. VJ Height is vertical jump height.

Figure 1. Scatterplot between measured vertical jump power and vertical jump height.

Figure 2. Scatterplot between measured vertical jump power and estimated vertical jump power for the recommended model for the total sample.

VJ Power (W) = −1354.820 + (VJ Height * 35.455) + (Body mass * 43.942). VJ Power is vertical jump power in watts, VJ Height is vertical jump height in cm, Body mass is in kg.

Table 4. Multiple regression models to estimate peak vertical jump power (W).

	Validation sample (n = 354)		Total sample (N = 529)
Variable	Recommended Model	Full Model	Recommended Model	Full Model
Intercept	−1441.216 (−1590.862, -1291.571)	−1603.041 (−1772.292, 1433.791)	−1354.820 (−1474.880, -1234.759)	−1537.495 (−1675.094, -1399.897)
VJ Height (cm)	36.435 (32.631, 40.238)	29.818 (25.487, 34.150)	35.455 (32.515, 38.395)	29.544 (26.257, 32.831)
Body mass (kg)	45.085 (42.378, 47.791)	41.754 (38.620, 44.888)	43.942 (41.863, 46.020)	40.389 (37.904, 42.874)
Age (years)		35.222 (17.232, 53.212)		35.668 (21.134, 50.203)
Sex (1 = male, 0 = female)		158.011 (98.707, 217.316)		154.932 (106.880, 202.984)
R	.93	.94	.93	.94
R^2	.87	.88	.87	.88
SEE (W)	276	263	275	262

Note: 95% CI of regression coefficients are shown within parentheses. VJ Height is vertical jump height. BMI is body mass index. SEE is standard error of estimate.

Table 5. Cross-validation analysis of regression models developed on validation sample on cross-validation sample.

Model	M ± SD	Equivalence Bound (p = .05)	RYY’	SEE	TE	MAPE (%)
						Mean	SD
Cross-validation Sample (n = 175)
Measured VJ Power (W)	2128 ± 755
Models from Validation Sample
Mahar et al. (current model)	2147 ± 759	± 1.01%	.93	271	276	1.3	14.0
Sayers et al.	2330 ± 903	± 9.64%	.93	279	398	8.8	18.3
Gomez-Bruton et al.	2166 ± 762	± 1.95%	.91	319	330	2.9	18.3
Duncan, Hankey, & Nevill	2142 ± 901	± 0.84%	.93	281	345	1.1	19.2

Model 1: Mahar et al. current model. VJ Power (W) = −1441.216 + (VJ Height * 36.435) + (Body mass * 45.085)

Model 2: Sayers et al. VJ Power (W) = 2007 + (VJ Height * 51.9) + (Body mass * 48.9)

Model 3: Gomez-Bruton et al. VJ Power (W) = 1520.4 + (VJ Height * 54.2) + (Body mass * 34.4)

Model 4: Duncan, Hankey, & Nevill. VJ Power (W) = 2732.5 + (VJ Height * 38.4) + (Body mass * 35.5) + (Gender [F = 0, M = 1] * 309.2) + (Age * 110.6)

VJ Power is vertical jump power in W, VJ Height is vertical jump height in cm, Body mass is in kg. Age is in years.

Equivalence Bound is percent of mean difference at which the two-one-sided-tests method returns a p-value = .05.

R_YY’ is the correlation between measured and estimated vertical jump power; SEE is standard error of estimate; TE is total error; MAPE is mean absolute percenterror.

Figure 3. Residual plots for regression models. a. Residual plot for model developed in current study from validation sample. b. Residual plot for Gomez-Bruton et al. (2019) model. c. Residual plot for Sayers et al. (1999) model. d. Residual plot for Duncan, Hankey, and Nevill (2013) model.

Gomez-Bruton, A., Gabel, L., Nettlefold, L., MacDonald, H., Race, D., & McKay, H. (2019). Estimation of peak muscle power from a countermovement vertical jump in children and adolescents. Journal of Strength and Conditioning Research, 33(2), 390–398. https://doi.org/10.1519/JSC.0000000000002002

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Sayers, S. P., Harackiewicz, D. V., Harman, E. A., Frykman, P. N., & Rosenstein, M. T. (1999). Cross-validation of three jump power equations. Medicine and Science in Sports and Exercise, 31(4), 572–577. https://doi.org/10.1097/00005768-199904000-00013

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Duncan, M. J., Hankey, J., & Nevill, A. M. (2013). Peak power estimation equations in 12- to 16-year-old children. Comparing linear with allometric models. Pediatric Exercise Science, 25(3), 385–393. https://doi.org/10.1123/pes.25.3.385

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