Introduction
Vertical jump (VJ) ability is important for successful performance in a number of sports (7,37,38). Jumping ability has also been associated with specific physical capabilities, including sprint running (35), running agility (3), and weightlifting (6). Given the established importance of VJ for athletic performance, the identification of related variables may provide insight into possible ways a person's aptitude for jumping and/or their individual shortcomings requiring remediation. Previous work has examined the relationship between VJ and trainable variables, such as muscular strength, muscular power, joint flexibility, and body composition (1,10,27). For example, VJ is positively related to both total lean mass percentage (r2 = 0.73) and lower extremity lean mass percentage (r2 = 0.77) in individuals aged 18–35 years (32). Likewise, body fat percentage (BF%) and VJ displacement are inversely related (1,10,13), with BF% explaining 56% of the variability in VJ performance (13). Despite this, the specific variables explaining VJ performance have yet to be fully identified, and structural variables have been given little consideration for this purpose.
The proportions of the lower body (feet, thigh, and legs), including the length of associated moment arms contribute to the mechanical leverage by which force is generated, may affect subsequent VJ performance. In recent work, sprinters have been shown to have longer toes than nonsprinters (24). Similarly, leg length has been reported to explain 69% of the variability in VJ displacement in elite male performers (2), with individuals with longer legs having comparatively higher VJ displacement than those with shorter legs (2). Likewise, quadriceps angle (Q-angle) may also explain variance in VJ. The Q-angle is formed at the knee and reflects the orientation of the line of pull of the quadriceps femoris muscles to the longitudinal axis of the tibia. Theoretically, a large Q-angle may result in lateral displacement of the patella when the quadriceps femoris muscles contract (16). Given that the knee joint and quadriceps femoris muscles are key elements involved in jumping (8,17,25,28), an excessive Q-angle may result in the loss of mechanical efficiency in forces created by the quadriceps muscles at the knee, and consequently influence VJ (13).
The contributions of structural variables to VJ performance have been given little attention. Such knowledge may provide insight into individual characteristics that may be changed through systematic training, assist talent identification, and offer useful additions to what is already known. Therefore, the objective of this study was to further establish the variables explaining VJ performance by examining the relationship of lower-body dimensions and body composition to VJ displacement.
Methods
Experimental Approach to the Problem
This study was designed to examine the association of lower-body dimensions and body composition with VJ in young adults. However, because several of the protocols for obtaining the dimensional measures were unique and all were based on surface landmarks, stability, reliability, and precision were concurrently examined using a repeated-measures design. This information is reported in detail in an associated piece of research (5). Reliable and precise measures were included in a bivariate correlation matrix, with those having at least moderate correlations with VJ displacement subsequently considered for forced multiple regression. The sample size of this study (n = 50) provided reasonable precision for estimates of reliability (15), and consequently allowed appropriate regression analysis.
Subjects
Twenty-five men (22.6 ± 4.1 years, body weight 79.7 ± 14.5 kg, and height 177.4 ± 8.6 cm) and 25 women (21.6 ± 2.6 years, body weight 59.9 ± 7.1 kg, and height 163.9 ± 7.0 cm), participated in this research to determine the relationship of VJ to lower-body dimensions and body composition. Participants were recruited from a university campus population, had been involved in at least 6 months of systematic lower-body resistance training, and were capable of performing technically competent countermovement VJs as assessed by the investigators. Participants were also free from current or recent lower-body injury that may have predisposed them to injury during the investigation and were sufficiently lean so that relevant anatomic landmarks could be easily identified. The study received ethical approval from the local institutional review board and was conducted in accordance with the Declaration of Helsinki. After written and verbal information about the study and its procedures had been provided, written informed consent was obtained from all subjects.
Procedures
Participants took part in a total of 2 testing sessions separated by either 48 or 72 hours. All participants were instructed to refrain from other exercise at least the day before the first session and for the duration of the study. For both testing sessions, participants wore the same shoes and dressed in a manner that enabled the investigator to have easy access to anatomic landmarks and allowed participants to perform unencumbered jumps. Data were collected by the same investigator for both testing sessions, with testing taking place at a parallel time of the day to control for possible diurnal fluctuations. Hydration status, nutritional intake and sleep the night before testing were not controlled in this investigation. Testing sequence involved the investigator initially measuring lower-body dimensions bilaterally, followed by body composition, and then countermovement VJ.
Foot Dimensions
To facilitate measurement acquisition, the foot in question was elevated 40 cm by resting the plantar surface on a small platform. Surface landmarks were identified and then marked on the skin using a wax-based marking instrument. Participants assumed a seated position with their hip and knee joints at 90 degrees of flexion. Using a 12-inch sliding digital caliper (General Tools, New York, NY, USA), the investigator measured the following distances:
- the most postero-superior aspect of the calcaneus to the most anterior point of the first distal hallux,
- the most postero-superior aspect of the calcaneus to the most medially prominent aspect of the first metatarsal head,
- the most prominent aspect of the medial malleolus to the most medially prominent aspect of the first metatarsal head,
- the most postero-superior aspect of the calcaneus to the most laterally prominent aspect of the fifth metatarsal head,
- the most prominent aspect of the lateral malleolus to the most laterally prominent aspect of the fifth metatarsal head (5,34).
Additional measurements were calculated from the distances above. Furthermore, medial and lateral foot measures were averaged to represent singular axes at both the talocrural and metatarsophalangeal joints. Because loading might affect individual longitudinal foot dimensions and their relationship to VJ performance, foot measures were obtained with participants seated, bilaterally standing, and unilaterally standing. When participants were in a bilateral or unilateral position, they steadied themselves by placing one hand continuously on an adjacent wall (5,34).
Thigh, Leg, and Lower-Limb Lengths
Participants were asked to assume a relaxed standing position with one hand continuously on an adjacent wall. The investigator was situated at the side of the participant at a level to minimize parallax error. Using a large broad-blade caliper (Mediform, Beaverton, OR, USA), thigh length was measured as the distance between the most prominent aspect of the greater trochanter of the femur and the most prominent aspect of the lateral condyle of tibia. Leg length was measured as the distance between the most prominent aspect of the lateral condyle of tibia and the most prominent aspect of the lateral malleolus of the ankle. Unilateral measures were completed on both sides of the body. A measure of lower-limb length was then calculated post hoc by adding together leg length and thigh length (5).
Hip and Pelvic Width
Participants were asked to assume a relaxed standing position with one hand continuously on an adjacent wall. Using a large broad-blade caliper (Mediform), the investigator standing in front of the participant measured hip width as the bilateral distance between the most prominent aspects of the left and right greater trochanter, and measured pelvic width as bilateral distance between the most prominent aspects of the left and right anterior superior iliac spine (19).
Quadriceps Angle
Quadriceps angle was measured by establishing lines from the anterior superior iliac spine of the pelvis to the center of the patella and from the center of the patella to the middle of the anterior tibial tuberosity. The angle superior to where these 2 lines met was operationally defined as the Q-angle. With the participant in a supine position and the medial border of their feet together, the investigator positioned the axis of an extendable-arm goniometer (Lafayette Instruments, Lafayette, IN, USA) over the center of the patella. One arm of the goniometer was then placed directly on the anterior superior iliac spine of the pelvis and the opposing arm of the goniometer directly on the center of the tibial tuberosity (33). The participant was then instructed to perform a near-maximal voluntary isometric contraction of the quadriceps femoris muscles, before the goniometer was repositioned as needed and Q-angle measured (33). For all measures of Q-angle, knee angle through the sagittal plane was standardized to 0 degrees. This was achieved by placing a small pad under the measured knee before goniometer measurement.
Body Weight and Height
An electronic platform scale (Sterling, Southfield, MI, USA) was used to obtain body weight without shoes. Height was measured without shoes using a stadiometer. Participants were required to stand with their feet together, with their head placed in the Frankfort horizontal plane. From this position, measurement was taken at the end of a deep inward breath.
Body Fat Percentage
Body fat percentage was estimated via a 3-site skinfold approach using the Jackson–Pollock formula (20,21), and an electronic skinfold caliper (Skyndex, Albuquerque, NM, USA). Skinfold measures were taken at the chest, abdomen, and thigh for men (20) and at the triceps, iliac crest, and thigh for women (21). Each skinfold site was located using the anatomical landmarks as detailed by the ISAK International Standards for Anthropometric Assessment (19).
Countermovement Vertical Jumps
To ensure participants were adequately prepared for VJ testing, a dynamic warm up was completed. This consisted of 5 minutes of stationary cycling, 10 bodyweight squats, and 5 jump squats. Participants were provided practice jump attempts to familiarize them with the countermovement VJ testing protocol. Countermovement VJs were performed with participants wearing shoes and positioned adjacent to a Vertec measurement device (Sports Imports, Hilliard, OH, USA). To eliminate the contribution of arm swing, participants were instructed to (a) place their nondominant hand at the level of the waistline behind their back, (b) flex their dominant shoulder to a vertical position overhead, while also (c) extending the elbow, wrist, and fingers. Initial reach height for the Vertec was established using a one-hand reach with maximal plantar flexion (12). Countermovement VJs were performed with participants initiating a downward countermovement to a self-selected depth, before immediately maximally jumping to touch the Vertec at the highest point of the jump. Participants performed 3 countermovement VJs with a minimum of 1-minute rest given between each jump trial. Displacement for each jump was calculated by subtracting the initial reach height from the jump height (1.27 cm resolution). The jump producing the greatest displacement was used for analysis.
Statistical Analyses
Summary data are presented as mean ± SD. Stability and reliability for each variable were determined using intraclass correlation coefficients (ICCs, 2-way random model), whereas precision was established using standard error of measurement. Reliable and precise variables were included in a bivariate correlation matrix (14,15,33) with variables having at least moderate correlations with VJ displacement subsequently considered for forced multiple regression. A maximum of 1 independent variable per 10 participants was considered for inclusion in any regression analysis. Several multiple linear regression models for men and women combined were estimated via forced entry. Combining men and women participants increased both sample size and variability in the dependent and independent variables, likely resulting in increased explained variance for the generated models. Variable selection for inclusion in regression models was based on the correlation matrix, statistical independence (minimal or no multicollinearity), and logic. The values of variables from only the first session of testing were used in the regression models. Multicollinearity between independent variables was evaluated using tolerance (TOL > 0.20) and variance inflation factor (VIF < 4.00) (4). In estimating the regression equations, statistical significance was set at p ≤ 0.05. SPSS statistical software package (Version 22) was used for these analyses (SPSS Inc., Chicago, IL, USA). After regression equations were identified, we investigated possible sampling bias in estimating the equations predicting VJ. Bootstrap sample replicates (11) were generated and resulting equations were estimated from those samples. We investigated the predictive ability of these equations using the method of cross-validation (29). SAS software (Version 9.3; SAS Institute Inc., Cary, NC, USA) was used for this analyses.
Results
For all participants (n = 50), countermovement VJ displacement averaged 33.7 ± 9.9 cm (Table 1). When sex was considered, countermovement VJ displacement averaged 41.5 ± 8.1 cm for men (n = 25) and 26.5 ± 4.9 cm for women (n = 25).
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Table 1.: Descriptive characteristics of men, women, and all participants combined.
Reliability and precision for all lower-body and body composition variables met the minimum criteria set a priori (ICC ≥ 0.72), with ICC values ranging from 0.72 to 1.00. The reliability and precision of VJ displacement were satisfactory, with an ICC of 0.98 and an SEM of 0.2 cm. The scatter of points around the respective trend lines for men and women combined were uniform, with separate SEMs for men and women similar. Bivariate correlations between the independent variables and countermovement VJ displacement (Table 2) revealed BF% to have the highest correlation with countermovement VJ displacement (r = –0.76, p < 0.001). Of the lower-body dimensions examined, right-side Q-angle displayed the strongest relationship with countermovement VJ displacement (r = –0.58, p < 0.001).
Table 2.: Correlations between independent variables and countermovement VJ displacement.*
Countermovement VJ displacement was regressed for all participants. A regression model including BF% and sex (Table 3, model 1) explained 66% of the variance in countermovement VJ displacement (Figure 1). No problems existed with multicollinearity (TOL = 0.54, VIF = 1.87), with included variables considered independent of each other, whereas both BF% and sex had a significant unique influence on the model (p ≤ 0.05). Within this model, BF% had the greatest influence on countermovement VJ displacement (β = –0.48), followed by sex (β = 0.41).
Table 3.: Regression models predicting countermovement VJ displacement.*
Figure 1.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 1.
A second regression model included BF% and body weight (Table 3, model 2). This model also accounted for 66% of countermovement VJ displacement variability (Figure 2), without multicollinearity (TOL = 0.96, VIF = 1.04). Body fat percentage and body weight each had a significant unique influence on countermovement VJ displacement (p ≤ 0.05), with BF% having the greatest influence (β = –0.69), followed by body weight (β = 0.31).
Figure 2.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 2.
The third regression model reported included BF% and right-side Q-angle (Table 3, model 3). This model accounted for 61% of the variability in countermovement VJ displacement (Figure 3), without multicollinearity issues (TOL = 0.71, VIF = 1.39). Both BF% and right-side Q-angle had significant unique influences on countermovement VJ displacement (p ≤ 0.05). Body fat percentage had the greatest influence within this model (β = –0.62), followed by right-side Q-angle (β = –0.25). For models 1–3, the inclusion of a third lower-body dimension or body composition measure to the equation was not plausible. Doing so not only led to problems with multicollinearity but also failed to increase the amount of explained variance.
Figure 3.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 3.
Regression models including foot dimensions were also developed. The combination of BF% and left-side seated calcaneus-to-metatarsophalangeal joint length (Table 3, model 4) explained 61% of the variance in countermovement VJ displacement (Figure 4), without multicollinearity (TOL = 0.84, VIF = 1.18). Body fat percentage and left-side seated calcaneus-to-metatarsophalangeal joint length each had a significant unique influence on countermovement VJ displacement (p ≤ 0.05), with BF% having the greatest influence (β = –0.67), followed by left-side seated calcaneus-to-metatarsophalangeal joint length (β = 0.21).
Figure 4.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 4.
A regression model including BF% and right bilateral calcaneus-to-distal hallux length (Table 3, model 5) also explained 61% of the variance in countermovement VJ displacement (Figure 5). As no problems existed with multicollinearity (TOL = 0.82, VIF = 1.22), these variables were considered independent of each other, whereas both BF% and right-side bilateral calcaneus-to-distal hallux length each had a significant unique influence on the model (p ≤ 0.05). Within this model, BF% had the greatest influence on countermovement VJ displacement (β = –0.66), followed by right bilateral calcaneus-to-distal hallux length (β = 0.23).
Figure 5.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 5.
The final regression model reported included BF% and left unilateral calcaneus-to-distal hallux length (Table 3, model 6). Likewise, this model accounted for 61% of countermovement VJ displacement variability (Figure 6), without multicollinearity (TOL = 0.80, VIF = 1.24). Body fat percentage and left unilateral calcaneus-to-distal hallux length each had a significant unique influence on countermovement VJ displacement (p ≤ 0.05), with BF% having the greatest influence (β = –0.65), followed by left unilateral calcaneus-to-distal hallux length (β = 0.23).
Figure 6.: Scatterplot for observed vs. predicted countermovement VJ displacement for model 6.
For models 4–6, the inclusion of a third lower-body or body composition measure not only led to problems with multicollinearity but also failed to increase the amount of explained variance.
Discussion
This study examined the relationship of lower-body dimensions and body composition to VJ displacement. The main findings were that BF% explained more variability in countermovement VJ than any other single variable, whereas the addition of either body weight or sex explained the greatest amount of variability. The inclusion of selected lower-body dimensions with BF% also explained more than BF% by itself, but less than the addition of body weight or sex. Collectively, these results indicate that a substantial amount of variability in VJ performance may be explained by knowing BF% and either of 2 simply measured variables.
In agreement with previous studies (1,9,13), the present findings show a strong negative association between BF% and VJ. Body fat percentage alone explained 57% of VJ variability, and explained 66% of variability when combined with sex or body weight. This inverse relationship could be anticipated because of the nonforce-producing nature of fat tissue. Given this, lower BF% is desirable for superior VJ as it represents a lighter relative body mass to be moved, allowing higher segment velocities to be achieved. Because body weight was moderately associated with VJ (r = 0.44) and unrelated to BF% (r = –0.19), both were included together in a regression model. The combination of these 2 variables and the combination of BF% and sex explained the equal greatest variance reported (R2 = 0.66).
Our results show that foot dimensions explain some variance in VJ. Specifically, both the anterior–posterior distance between the calcaneus and distal hallux and the anterior–posterior distance between the calcaneus and metatarsophalangeal joint seem to have potential in combination with BF% in explaining VJ. These findings build upon earlier work showing foot length to be a predictor of VJ in men (9). Furthermore, foot length may be a stronger predictor of VJ than first purported. Although previous work has reported foot length to explain 8% of the variability in VJ (9), it explained 25–28% in the current study.
In the current investigation, the inclusion of lower limb length or leg length in regression models failed to increase the amount of explained variance, whereas thigh length failed to be correlated at all with VJ. Our findings are in agreement with earlier work also failing to report lower limb length as a predictor of VJ (9,13). In contrast, a recent investigation showed lower limb length to explain 69% of the variability observed in VJ (2), with VJ improving as lower limb length increased. This inconsistency between findings may be explained by the fact that the study reporting a strong association between lower limb length and VJ involved elite male volleyball players as participants (2). In volleyball, players who are blockers have been shown to be the tallest players (26). These players have also been identified as stronger than other position players (26). Consequently, taller athletes have been shown to exhibit a greater capacity to perform jumping tasks involved in volleyball (31). As a result, the observation of a strong relationship between lower limb length and VJ may be limited to this specific athletic population.
Q-angle seems to provide some insight concerning the pull of the patella by the quadriceps femoris muscles. Our results show that Q-angle was negatively related to VJ and that its addition to BF% explained further variability, thus indicating that a large Q-angle seems to be undesirable for optimal VJ performance. This is in contrast to a previous report in which Q-angle explained no additional variability in VJ and suffered multicollinearity issues with other performance variables (13). Protocols used to measure Q-angle vary and may result in different values, which could easily account for differences in the relationship with VJ. However, in the current and previous investigations (13), the protocols used were equivalent. It is important to note that Q-angle measured statically may not be reflective of Q-angle during a dynamic movement such as the VJ. Indeed, with movement, lower extremity alignment would be expected to vary and consequently produce a change in Q-angle. A dynamic measure of Q-angle exceeded the scope of the current investigation; however, further work may be warranted along those lines to more fully resolve the relationship of Q-angle to VJ.
It was foreseeable that sex would be a strong predictor of VJ. Women have been shown to generally exhibit a higher proportion of relative fat mass and a lower amount of relative lean body mass compared with their male counterparts (22,23,30). Similarly, we also report women having more body fat than their male counterparts in the current investigation. Given the aforementioned noncontractile nature of fat tissue, these sex differences in the proportion of subcutaneous fat tissue and lean body mass between sexes would be expected to contribute to concomitant disparities in VJ. That being said, when sex was considered in addition to BF%, both were found to be independent of each other, suggesting that the generally higher level of body fat found in our women was not the primary basis for the observed sex differences in jumping performance. A difference has also been reported among the sexes in regards to Q-angle (16). Specifically, higher Q-angles have been recorded in women (16,33,36), a finding corroborated herein as women's measures of Q-angle were 5.5 and 5.8 degrees greater than the men's right and left sides, respectively. This could be explained by the wide gynecoid pelvis seen in women creating a more lateral reference point for the measurement of Q-angle and subsequently imposing an increased valgus orientation of the knee during weight bearing (18,36).
Practical Applications
The findings of this study demonstrate that BF% has a relatively high inverse association with VJ. As BF% can be manipulated with training and/or diet, interventions designed to improve relative BF% would concurrently be expected to augment VJ performance.
That body weight displayed a positive association with VJ suggests that an increase in body weight would concomitantly lead to increases in VJ performance. Therefore, practitioners can implement interventions aimed at increasing body weight with the knowledge that such change will not hinder VJ performance. However, any increase in body weight should be balanced against parallel increases in BF%. Ideally, body weight should increase with limited concurrent growth in relative BF% (i.e., increase in lean muscle mass).
Lower-body dimensions such as Q-angle and the longitudinal measures of the feet can also augment the amount of variance in VJ accounted by BF%. Practitioners may use simple practical tests to obtain reliable and precise measures of structural characteristics in an effort to assist athletic talent identification.
Acknowledgments
The authors have no professional relationships with companies or manufacturers that might benefit from the results of the study. There is no financial support for this project and no funds were received for this study. The results of this study do not constitute endorsement of any product by the authors or the National Strength and Conditioning Association.
References
1. Abidin NZ, Adam MB. Prediction of vertical jump height from anthropometric factors in male and female martial arts athletes. Malays J Med Sci 20: 39–45, 2013.
2. Aouadi R, Jlid MC, Khalifa R, Hermassi S, Chelly MS, Van Den Tillaar R, Gabbett T. Association of anthropometric qualities with vertical jump performance in elite male volleyball players. J Sports Med Phys Fitness 52: 11–17, 2012.
3. Barnes JL, Schilling BK, Falvo MJ, Weiss LW, Creasy AK, Fry AC. Relationship of jumping and agility performance in female volleyball athletes. J Strength Cond Res 21: 1192–1196, 2007.
4. Barton B, Peat J. Medical Statistics: A Guide to SPSS, Data Analysis and Critical Appraisal. Hoboken, NJ: BMJ Books, 2014.
5. Caia J, Weiss LW, Chiu LZ, Schilling BK, Paquette MR. Consistency of lower-body dimensions using surface landmarks and simple measurement tools. J Strength Cond Res 2016 Jan 29. [Epub Ahead of Print].
6. Carlock JM, Smith SL, Hartman MJ, Morris RT, Ciroslan DA, Pierce KC, Newton RU, Harman EA, Sands WA, Stone MH. The relationship between vertical jump power estimates and weightlifting ability: A field-test approach. J Strength Cond Res 18: 534–539, 2004.
7. Castagna C, Castellini E. Vertical jump performance in Italian male and female national team soccer players. J Strength Cond Res 27: 1156–1161, 2013.
8. Chiu LZ, Salem GJ. Potentiation of vertical jump performance during a snatch pull exercise session. J Appl Biomech 28: 627–635, 2012.
9. Davis DS, Bosley EE, Gronell LC, Keeney SA, Rossetti AM, Mancinelli CA, Petronis JJ. The relationship of body segment length and vertical jump displacement in recreational athletes. J Strength Cond Res 20: 136–140, 2006.
10. Davis DS, Briscoe DA, Markowski CT, Saville SE, Taylor CJ. Physical characteristics that predict vertical jump performance in recreational male athletes. Phys Ther Sport 4: 167–174, 2003.
11. Efron B, Tibshirani RJ. An Introduction to the Bootstrap. New York, NY: Chapman & Hall, 1993.
12. Ferreira LC, Schilling BK, Weiss LW, Fry AC, Chiu LZ. Reach height and jump displacement: Implications for standardization of reach determination. J Strength Cond Res 24: 1596–1601, 2010.
13. Ferreira LC, Weiss LW, Hammond KG, Schilling BK. Structural and functional predictors of drop vertical jump. J Strength Cond Res 24: 2456–2467, 2010.
14. Hopkins WG. A new view of statistics. Available at:
http://www.sportsci.org/resource/stats/. Accessed March 12, 2015.
15. Hopkins WG. Measures of reliability in sports medicine and science. Sports Med 30: 1–15, 2000.
16. Horton MG, Hall TL. Quadriceps femoris muscle angle: Normal values and relationships with gender and selected skeletal measures. Phys Ther 69: 897–901, 1989.
17. Hubley CL, Wells RP. A work-energy approach to determine individual joint contributions to vertical jump performance. Eur J Appl Physiol Occup Physiol 50: 247–254, 1983.
18. Hvid I, Andersen LI, Schmidt H. Chondromalacia patellae. The relation to abnormal patellofemoral joint mechanics. Acta Orthop Scand 52: 661–666, 1981.
19. ISAK. International Standards for Anthropometric Assessment. Underdale, SA, Australia: International Society for the Advancement of Kinanthropomery, 2001.
20. Jackson AS, Pollock ML. Generalized equations for predicting body density of men. Br J Nutr 40: 497–504, 1978.
21. Jackson AS, Pollock ML, Ward A. Generalized equations for predicting body density of women. Med Sci Sports Exerc 12: 175–181, 1980.
22. Kirchengast S. Gender differences in body composition from childhood to old age: An evolutionary point of view. J Life Sci 2: 1–10, 2010.
23. Kyle UG, Genton L, Hans D, Karsegard L, Slosman DO, Pichard C. Age-related differences in fat-free mass, skeletal muscle, body cell mass and fat mass between 18 and 94 years. Eur J Clin Nutr 55: 663–672, 2001.
24. Lee SS, Piazza SJ. Built for speed: Musculoskeletal structure and sprinting ability. J Exp Biol 212: 3700–3707, 2009.
25. Luhtanen P, Komi RV. Segmental contribution to forces in vertical jump. Eur J Appl Physiol Occup Physiol 38: 181–188, 1978.
26. Marques MC, van den Tillaar R, Gabbett TJ, Reis VM, Gonzalez-Badillo JJ. Physical fitness qualities of professional volleyball players: Determination of positional differences. J Strength Cond Res 23: 1106–1111, 2009.
27. McBride JM, Kirby TJ, Haines TL, Skinner J. Relationship between relative net vertical impulse and jump height in jump squats performed to various squat depths and with various loads. Int J Sports Physiol Perform 5: 484–496, 2010.
28. Nagano A, Gerritsen KG. Effects of neuromuscular strength training on vertical jump performance—A computer simulation study. J Appl Biomech 17: 113–128, 2001.
29. Pedhazur EJ. Multiple Regression in Behavioral Research. Orlando, FL: Harcourt Brace, 1997.
30. Shen W, Punyanitya M, Silva AM, Chen J, Gallagher D, Sardinha LB, Allison DB, Heymsfield SB. Sexual dimorphism of adipose tissue distribution across the lifespan: A cross-sectional whole-body magnetic resonance imaging study. Nutr Metab (Lond) 6: 17, 2009.
31. Sheppard JM, Cronin JB, Gabbett TJ, McGuigan MR, Etxebarria N, Newton RU. Relative importance of strength, power, and anthropometric measures to jump performance of elite volleyball players. J Strength Cond Res 22: 758–765, 2008.
32. Stephenson ML, Smith DT, Heinbaugh EM, Moynes RC, Rockey SS, Thomas JJ, Dai B. Total and lower extremity lean mass percentage positively correlates with jump performance. J Strength Cond Res 29: 2167–2175, 2015.
33. Weiss L, DeForest B, Hammond K, Schilling B, Ferreira L. Reliability of goniometry-based Q-angle. PM R 5: 763–768, 2013.
34. Weiss LW, Caia J, Harry JR, Chiu LZ, Schilling BK, Paquette MR. Reliability and precision of anthropometric measures of the feet that influence moment arm length of reaction forces. J Strength Cond Res 28: S79–S80, 2014.
35. Wisloff U, Castagna C, Helgerud J, Jones R, Hoff J. Strong correlation of maximal squat strength with sprint performance and vertical jump height in elite soccer players. Br J Sports Med 38: 285–288, 2004.
36. Woodland LH, Francis RS. Parameters and comparisons of the
quadriceps angle of college-aged men and women in the supine and standing positions. Am J Sports Med 20: 208–211, 1992.
37. Ziv G, Lidor R. Vertical jump in female and male basketball players—a review of observational and experimental studies. J Sci Med Sport 13: 332–339, 2010.
38. Ziv G, Lidor R. Vertical jump in female and male volleyball players: A review of observational and experimental studies. Scand J Med Sci Sports 20: 556–567, 2010.
