The correlation matrix (Table 4) shows that all the studied variables are correlated, and so a PCA could be performed. This PCA revealed 2 principal components, characterized by a time component and a force component that accounted for 76.8% of the total variance. The commonalities, which measures the percent of variance in a given variable explained by all the factors jointly, ranged from 0.74 (R-ECC-RFD) to 0.97 (CON-VF) revealing a high reliability of the indicator and the model found as well.
The first principal component that was rotated, accounting for 53.8% of the total variance, was associated with time variables. The Eigenvalue corresponding to this component was 2.69. This component linked TIME to ECC-T with high and positive loading (0.960 and 0.957), respectively, indicating that a long contact time is associated to a long eccentric time.
The second rotated principal component accounted for 23% of the variance of the force data. The Eigenvalue of this second component was 1.14 and was associated with the force variables and ratio time. This force component linked together R-ECC-RFD, CON-VF, and ECC-T:T with loadings of 0.602, 0.480, and −0.944, respectively. The positive loading indicates that a high value of R-ECC-RFD was associated with a high value of maximum ground reaction force and a low value of ECC-T:T.
The second goal of the PCA analysis was to describe the force pattern strategy differences among different sport group samples. Four sport groups were tested and contrasted. Plotting the mean individual scores on the 2 principal components allowed this comparison (Figure 3). The x-axis of the right part of Figure 3 corresponds to the first principal component, namely the time component. Figure 3 can be separated into 4 parts. The right side of the figure indicates a high value of the time component, meaning a long contact and eccentric time, therefore a slow jumping profile. Volleyball players are characterized by this profile with component score ranging from −2 to 4.5. The ANOVA confirms this analysis by showing a large effect of TIME between volleyball players and the 3 other sport groups (p < 0.001). The left side corresponds to a negative value of the x-axis, i.e., a short time and eccentric time, revealing a fast jumping profile, as illustrated by several football and baseball players (score ranging between −4.5 and 3). The top of the Figure 3 corresponds to a positive value of the y-axis (force component) revealing a high value of R-ECC-RFD and CON-VF, i.e., an explosive jumping profile. Football and baseball players exhibited such a profile (scores ranging from −1.5 to 2.8), with higher values of R-ECC-RFD than volleyball and basketball players (p < 0.001), In comparison, the bottom of the figure corresponds to a negative value of the y-axis revealing weak values of R-ECC-RFD and CON-VF and a high ratio of eccentric time on total time. Basketball revealed such a profile with component scores ranging from 0 to −3.5. This plotting defines 4 different profiles of jumper (1: fast and explosive to 4: slow and weak).
The first goal of the present study was to assess the predictability of selected variables extracted from the F-T curve. All the recorded variables were significantly correlated with JH (p < 0.01). The time variables explain less than 10% of the total variance, whereas the force variables explain 27–32% of the variance.
The novelty of the present study is that with this alternative method of looking at average ECC-RFD, maximal JH in CMJ is shown to highly correlate with this variable when calculated as an absolute value (ECC-RFD, r = 0.52, p < 0.001) and additionally when normalized to body mass (R-ECC-RFD, r = 0.40, p < 0.001).
Several studies have failed to find such a strong link between ECC-RFD and vertical jumping performance (20,26,34,36,46). The difference in these results could be explained by 4 key differences in their methodological approach. First, the present study measured JH while simultaneously recording RFD during CMJ on a force-plate, contrary to previous studies. Second, the method to measure the vertical performance is more accurate in the present study (impulse method) than with the flight-time method, which is associated to high errors (19,26) due to the variation in the take-off and the landing position. Third, the choice of recording the average eccentric RFD rather than peak eccentric RFD which is more conventionally used, identifies what happens throughout the entire eccentric loading phase, as opposed to just the highlight that peak measurements tend to give us. This point will be discussed further. Finally, several studies did not use arm swing (20,46), which is a more natural and functional approach that allows an increase in jumping performance (17,22,31,44). In all the studies where arm swing was not used (20,21,27), results did not find correlations between RFD and JH.
Only 1 study to date (McLellan et al. (37)) has found a positive and significant correlation between the maximum value of the rate of force and the JH (r = 0.68), and that study proposed a similar protocol than the one used in the present study (using 3 of the 4 aspects discussed above).
The present study is the first one that demonstrates that ECC-RFD is a stronger and more accurate predictor of JH than peak concentric RFD because it summarizes the capacity of the muscle-tendon unit structure to stretch quickly before attaining the peak of force. Only 2 studies have used ECC-RFD as a predictive tool. Earp et al. (14) studied the effect of muscle-tendons architecture on the rate of force development calculated during the very beginning of the jump (eccentric phase). They found that the gastrocnemius fascicle length had an intensity-dependent relationship with RFD, serving to positively predict RFD during early CMJs. In another study, Jensen and Ebben (24) recorded the eccentric RFD during different plyometric jumping tasks, but without investigating a link with the JH. They show that ECC-RFD is different among the jumps and the plyometric constraints as well. The method used to measure ECC-RFD in the latter article (between the first peak of GRF divided by the time from onset of landing force to the first peak of GRF) is quite different than in the present one (averaged along the eccentric phase), resulting in higher values of ECC-RFD in our study. In addition, researchers have suggested that a threshold for ECC-RFD is necessary to attain to optimally activate the SSC (15).
The second goal of this study was to compare the way males and females jump. First, male jumps were 15.3 cm (+26.4%) higher than female jumps. This difference is slightly higher than those found in literature, where values ranged between 10.6 and 11 cm (3,33,44,45). This finding likely occurred because our sample is highly trained, and the values of JH are higher, and therefore their differences as well. This difference could be explained by higher values of ECC-RFD (+36.3%) in males than in females. When normalized to body mass, R-ECC-RFD is 11.6% higher in males than in females, showing that the difference in body mass is not purely enough to explain the difference in values even if it minimizes the effect (1.5 times higher in absolute value vs. 1.2 times higher in relative value). Thus, this shows a higher capacity to accelerate their body when performing a CMJ. To our knowledge, there are only 2 studies that have investigated lower-limb gender difference in RFD (1,15). In the first one, the RFD was assessed by using maximum voluntary isometric contractions for the knee extensors, and the authors found that men demonstrated approximately 1.5–2.0 times higher RFD than women. In the second study, RFD was assessed during the concentric phase of a CMJ with arm swing but no difference was found in RFD between skilled athletes. The present study reveals that men demonstrated approximately 1.5 times higher RFD than women (1.2 when normalized to body mass). This differs to the results of the aforementioned study (15), which is probably because of a difference in the calculation method of RFD.
Previous reports suggested that the lower RFD observed in women, compared with men, may be the result of structural differences in the muscles elastic properties (30). Indeed, the gender differences in RFD of a CMJ are probably related to the differences between men and women in body dimensions and muscle architecture, which influence the way force is produced between the 2 genders (e.g., disparities in tendon length, angle of pennation, and fascicle properties) (2). Despite these structural gender differences, the significance of muscle mass does still explain part of this difference in jumping performance because JH discrepancies between the 2 genders does decrease when RFD is normalized to body mass (1.5 times higher to 1.2 times higher). Furthermore, the previously mentioned study (2) revealed higher pennation angles in males than in females of the vastus lateralis (15.8° vs. 14.1°) and the gastronemius medialis (26° vs. 24.5°) and longer fascicles in the vastus lateralis in men and gastrocnemii in women, which where concluded to impact on jump performance (3).
The Figure 4 shows the difference in correlations for each variable between males and females. Few differences have been noticed. The eccentric-time seems to have a better link with JH for women (r = −0.28 vs. −0.21) and consequently, the ratio as well (r = −0.29 vs. −0.16). Regarding the force variables, better correlations have been found in males than in females in R-ECC-RFD (r = 0.42 vs. 0.35) and in CON-F (r = 0.59 vs. r = 0.50). These slight differences show that better jump performances within the genders are obtained by minimizing the key time variables in women while maximizing the key force variables in men, and implies that different muscular architecture could be the fundamental influence in differing JHs between the genders (3,30).
Despite these differences, another major result of this study was that the temporal structure of the jump is the same. Indeed, the ECC-TIME (223 ± 5 for men vs. 214 ± 6 ms for women, the TIME (502 ± 10 for men vs. 500 ± 10 ms for women) and the RATIO-TIME (43.5% for men vs. 42% for women) were similar, showing that the kinematics are highly comparable, as previously shown during CMJ (43) and DJ (33). This similar temporal structure (Figure 5) highlights that the motor patterns are comparable between males and females. So, the temporal structures are quite similar, but the difference of muscular architecture and structural dimensions like muscle thickness and size (3) allows men to provide a higher level of force by increasing the ECC-RFD during the same time. This means that men are perhaps able to more efficiently stretch their muscles by using larger angular displacements of the knee, hip, and ankle joints during a time compatible with the short stretch shortening cycle (less than 250 ms in eccentric phase), as previously described (40). The shorter duration allows for elastic energy to be stored in muscles and tendons during a preload (stretch) and then applied to a resulting contraction (shortening).
The third goal of this study was to explain the links between variables, using a PCA analysis. The accuracy of the PCA model found (76.8% of the JH variance) is in accordance with previous ones using the same statistical approach during vertical jumping in men (28,32) with percentages ranging from 74.1 to 78.8. Our model revealed 2 components: a time component and a force component.
The x-axis on Figure 3 corresponds to the first component, namely the time component. This component includes TIME and ECC-T, assuming that an increase in the time to peak force is linked to an increase of total time. When comparing our PCA model to previous models, during the 1-legged vertical jump (32) and squat jump (28), many similarities and few differences have been observed. First, the 2 components share similar mechanical characteristics, such as a time and a force component. The time component linked TIME and ECC-T for these 3 kinds of jump, but RFD was associated with this component for squat jump but not with the force component. This reveals the similarities between 1-legged vertical jump and CMJ, which both allow the jumper to stretch the muscles and tendons during the eccentric phase of jump, whereas squat jump does not allow such a beneficial pre-load.
The y-axis on Figure 3 corresponds to the second component, namely the force component. It links the force variables with positive loadings and the time ratio with negative loading. In other terms, the higher the RFD, the higher the ground reaction force and the smaller the time ratio. Therefore, this model very efficiently captures the fact that a high value of ECC-RFD allows an increase in the level of force (11) by rapidly recruiting motor units (12) through a higher preload and enhanced interaction between contractile and elastic elements by storage and utilization of elastic energy and activating the stretch reflex (7,9,12,16). Our PCA model is comparable to previous ones, especially to the 1-legged vertical jump (32) that linked RFD to CON-F. But the novelty of the present study is that the ratio of time has a main role on this force component, which has never been demonstrated before (to the best of our knowledge). The negative score of ECC-T:T on this force component shows that the ratio of time, i.e., the time available to develop force during the ECC phase on the total impulse time, is a crucial factor in allowing the activation of stretch reflex (6,8,11,16). In other terms, minimizing this time ratio increased the rate of force development and the ground reaction force in an explosive manner.
The final purpose of the present study was to investigate whether inherent demands of a particular sport have a relationship with certain force-time variables. If so, these trends could therefore be labeled “sport specific (force-time) signatures.”
First, JH performance is higher for outdoor team sports than for indoor sports, with values ranging from 59.1 ± 8.6 cm for baseball players to 46.8 ± 12.7 cm for basketball players (p < 0.0001). Second, the individual PCA plotting revealed different profiles of jumpers depending on their sporting background. The indoor team sports (basketball and volleyball) revealed negative scores on the force component and high scores for volleyball players on the time component. Outdoor team sports such as football and baseball, revealed an explosive profile, with high scores on the force component. This slow profile for volleyball players, and to a slightly lesser extent Basketball (Figure 3), is because of the specificity of the jumping actions involved during competition. Volleyball does not involve a direct and physical confrontation with the opponent but a complex optimal requirement to time the jump to be at the highest point of the parabola at the right time to attack the ball. This method of force application is only possible during the ground contact phase of the jump so this therefore requires development of force throughout a longer period of time when compared with sporting skills where ground contact times are typically shorter because of the smaller response times typically found in the outdoor sports of football and baseball. The time available to reach maximum JH is much greater in volleyball (525 ± 12 ms; p < 0.001) compared with other sports. This result is in accordance with Laffaye et al. (32) who discovered time-dominant profiles in volleyball players who performed 1-legged vertical jumps.
The game of basketball involves a lot of jumping in a constrained environment, often requiring time-dominant jumping actions in reaction to an open but small court of opponents. Examples of these movements are when feinting at an opponent through the use of multiple eccentric phases of a jump (loading then braking), and also, then often having to maximally accelerate through a prolonged concentric phase of a jump to out-jump an opponent, yet without the benefit of a quick preload. This behavior is very well captured by the PCA model, which shows high negative scores on the force component, which in turn are characterized by a high ratio of eccentric time to total time in basketball (49.6 ± 4) and Volleyball (46.8 ± 4.3), a variable we have found to be higher in those aforementioned indoor sports when compared with the outdoor team sports studied (baseball: 40.2 ± 5 and football: 41.3 ± 3.3).
Finally, football and baseball players tend to display explosive profiles, with high values of R-ECC-RFD and CON-FORCE. It is interesting to notice that these 2 sports have the higher values of JH (50.1 ± 15.9 cm and 59.1 ± 8.6 cm, respectively), confirming the strong link between force, rate of force, and jumping performance (13,37,38). When compared with the other sports tested, football and baseball are not primarily characterized by repetitive jumping actions during competition, but require more maximal rested explosive muscular actions, such as pitching, sprinting, or tackling within short time frames. This could mean that the force component is dependent on muscle-tendon system properties, regardless of the direction of the ground reaction force (39).
The present study highlights the role of average eccentric RFD on JH. The PCA has linked this force-time variable with the relevant time ratios, and subsequent JHs to clearly indicate that the depth of the load during a jump plays a major role in JH. Lowering the center of mass could be useful only under the condition that the ratio of the eccentric time on the total time is low (<42%) and by taking into account, first, the gender difference because of the difference in muscular architecture, and finally, the sport-specific differences because of the inherent demands of the athletic requirements.
The present study has 3 main applications for practice. The first one is that a valid method to increase vertical performance or JH is to increase one of the predictive factors. Indeed, increasing CON-F (13,38,41,42) or ECC-RFD could perhaps change musculotendinous properties and increase the vertical velocity at take-off. Specifically, minimizing the eccentric phase and utilization of the resultant speed of stretch, contribute to improved stretch-shorten cycle performance after training (11) by altering muscular architecture, such as pennation angle or fascicle length (3,4) and/or through neuromuscular adaptations specific to the training program.
The second practical application is highlighted by the link between the time ratios on the force variables. The PCA model implies that decreasing the time ratios, meaning shortening the eccentric time of jump without changing the total time, increases the values of the force variables and the performance as well. This implies that advice could be given during jumping tasks (drop jumping, CMJs) to decrease the eccentric time to increase performance Finally, the use of biofeedback devices for jumping could be a good and rational way to increase the stretch shortening cycle to become more explosive, by using a criterion of time ratios. Based on the present study, a threshold of 42% makes the difference between good jumpers (JH > 50 cm) and average jumpers (JH < 50 cm).
Finally, the sporting requirements have to be taken into account in the athletes training program because the exact athletic demands and, more specifically, the force-time profiles are not comparable between the sports analyzed in this study. These findings reveal a time-prevailing profile for basketball and volleyball players and a force-prevailing profile for football and baseball players. Consequently, trainers should focus on the need to adapt jumping/plyometric programs to the time requirements of the tasks presented in indoor jumping team sports, whereas as a greater focus is required to increase explosive force for dynamic outdoor sports such as football and baseball.
This might imply an individual training program based on the analysis of 1 of the force-time variables, as these qualities are fundamental elements that influence sprinting, bounding, or any activities that require ground reaction force.
There is no conflict of interest in the manuscript, including financial, consultant, institutional, and other relationships that might lead to bias or a conflict of interest. The results of the present study do not constitute endorsement of the product by the authors or the National Strength and Conditioning Association.
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Keywords:Copyright © 2014 by the National Strength & Conditioning Association.
strength; concentric; athletic