Vertical jumping, quick accelerations, and change of direction (CoD) maneuvers are crucial components of volleyball game (Künstlinger et al., 1987; Giatsis, 2001). The higher a player is able to jump, the greater his/her potential for successful performance in offensive and defensive actions (Forthomme et al., 2005). Due to its court, volleyball requires very short-distance sprints and quick and agile movements for successful performance in defensive actions (Cengizel, 2020). The performance of a volleyball player is directly affected by the capacity of producing power in jumping and sprinting actions (Sattler et al., 2015; Schons et al., 2019). Different forms of jumps are used to evaluate the jumping power (unilateral and bilateral, vertical and horizontal) with the use of different measurement devices. CoD ability, which is underlying agility (Sheppard and Young, 2006), is usually evaluated with various tests of changes of direction in the horizontal plane (Nimphius et al., 2018), while acceleration ability is evaluated with sprint times on different distances (Kumagai et al., 2000). With more analytical approach and biomechanical testing, we can evaluate these abilities throughout more complex forms of performance tests. Those tests provide a more detailed insight into the athlete’s neuromuscular capacity and thus offer the opportunity for training optimization.

The force-velocity (FV) profiling has recently been proposed as a tool to identify the neuromuscular capabilities of athletes and to optimize the training (Jiménez-Reyes et al., 2017a). The FV relationship allows to characterize the mechanical capabilities of musculoskeletal system to produce force, power and velocity (Jaric, 2015; Samozino et al., 2016). Since the first study on the topic (Hill, 1937) it has been known that the FV relationship of individual muscles is approximately hyperbolic, while the novel studies show that FV relationship of multi-joint performance tasks is quasi-linear (Bobbert, 2012; Sánchez-Medina et al., 2014; Jaric, 2015; Sreckovic et al., 2015; Zivkovic et al., 2017). This allows using simple linear model to calculate the maximal theoretical force (i.e., the F-intercept; F₀), maximal theoretical velocity (V-intercept; V₀) and maximal power (P_max = F₀ ⋅ V₀/4) (Jaric, 2015). The X and Y-axis intercepts (F₀ and V₀) determine the slope of the FV relationship, which presents the FV mechanical profile (i.e., the individual ratio between force and velocity qualities). Steep FV relationship is reflecting that the individual is better at generating high forces at low velocities (i.e., force dominance), and vice versa if the FV relationship is less steep, the individual is better at producing high velocity at lower force (i.e., velocity dominance) (Jaric, 2015; Jiménez-Reyes et al., 2017a).

Due to its simplicity and cost-effectiveness, the FV profiling is often applied to different multi-joint movement tasks such as vertical jump (Jiménez-Reyes et al., 2017a) and sprint (Samozino et al., 2016). In addition to F₀, V₀, P_max and the slope of the FV relationship, the FV profiling in sprint allows the evaluation of the ability to produce force in horizontal direction in the acceleration phase (Samozino et al., 2016). In addition to the variables mentioned above, we can also evaluate the sprinting mechanical efficiency (maximal ratio of horizontal-to-resultant force, RF) (Morin et al., 2011). The literature suggests that FV profile can provide meaningful data to implement individualized training programs (Morin and Samozino, 2016; Jiménez-Reyes et al., 2017a). Maximal strength training increases the ability of muscles to produce force (and thus increases F₀), while training in high velocity conditions (i.e., plyometric training) increases the V₀ (Jiménez-Reyes et al., 2019). Vertical jump height largely depends on the maximal power output (Markovic and Jaric, 2007). Nevertheless, by changing the slope of the FV relationship, we can improve the jumping performance independently of the changes in maximal power (Samozino et al., 2012; Jiménez-Reyes et al., 2017a), which indicates the practical applications of the FV relationship.

Despite the fact that FV is well documented in the scientific literature, the question arises about its association with sport-specific movement tasks. Most of the studies have focused mainly on the explanation of the biomechanical characteristics of the FV relationship, while its direct relationship with athletic performance has not been investigated much. The optimal FV profile, well-established in jumping tasks (Samozino et al., 2012), may not transfer to optimal performance in other tasks. For instance, it has been reported that the CoD ability is related to F₀ and P_max of the FV profile, while the parameters of the FV relationship in the vertical jump showed only few small correlations with CoD (Baena-Raya et al., 2020). In terms of correlations of FV profiles across tasks, only high correlations between P_max in sprint and P_max in jumping, and moderate correlations between V₀ in sprint and V₀ in jumping were reported (Marcote-Pequeño et al., 2019). The results of this study suggest that P_max could present a general measure of lower limb capacity, while F₀ and V₀ are more specific to the movement task. To the best of our knowledge, only one study to date have examined the association between FV relationship and athletic performance of volleyball players (Baena-Raya et al., 2021). The authors reported strong correlations between F₀ in jumping FV relationship (r = 0.81–0.82) and V₀ in sprinting FV relationship (r = 0.70–0.72) with ball speed in the volleyball spike and serve. The mechanical variables F₀ in jump and V₀ in sprint individually explained 20–36% variance of ball speed.

From the perspective of physical capabilities, the main components for successful volleyball performance are vertical jumps, quick accelerations and CoDs (Künstlinger et al., 1987; Giatsis, 2001). Those capabilities are often addressed in the training process to improve physical performance of the players. Those capabilities are usually tested through conventional performance tests (i.e., approach jump, different variants of CoD test, and linear acceleration on different distances), which offer only limited amount of information for further training adjustments. Based on that the aim of this study is to check for correlations between individual physical capabilities and FV relationship in similar movement task, to get a deeper insight into selected physical capabilities of volleyball players. This could provide a more detailed insight into selected volleyball specific physical capabilities, which is overlooked in conventional testing, and thus could potentially help with guiding training related decision-making.

The purpose of this study was to examine the relationship between FV profile obtained from linear sprint and vertical jump tasks with CoD performance (T-test, 505 test, CoD deficit), linear sprinting ability, and volleyball specific approach jump performance, on a sample of young male volleyball players. With these performance tests, we want to cover the key components of the volleyball movement (Forthomme et al., 2005; Hedrick, 2007). If FV relationship is associated with sports performance, it could be used to guide training-related decision making for improving performance of specific movement tasks.

Figure 1 depicts a representative FV profile for one participant. The descriptive statistics for all variables are presented in Table 1. The correlations among FV relationship variables and performance outcomes are available in Table 2.

The approach jump height was in moderate correlation with F₀ in countermovement jump (r = 0.45, p < 0.01) and in moderate to high correlations with F₀ in sprint (r = 0.35, p = 0.022), P_max in sprint (r = 0.53; p < 0,001), and RF_max (r = 0.51; p = 0.001). In linear regression model, 62.2% of the variance in approach jump was explained by sprint P_max, Jump F₀, and Jump V₀ (21.3% and 36.0% with sprint P_max, and sprint P_max + Jump F₀, respectively).

Modified T-test was in moderate to high negative correlation (p < 0.01) with F₀, P_max and RF_max in sprint (r = −0.42 to −0.58). The negative correlation means that the subjects with faster T-test times exhibited higher values of FV outcome variables. In linear regression model, 34.7% of the variance in modified T-test times was explained with sprint P_max, with no additional contribution of other variables.

The performance of 505 test on the left leg was in moderate negative correlation (p = 0.011–0.032) with RF_max (r = −0.32) and sprint P_max (r = −0.38). The direction of these correlations implied that 505 test performance on the left leg improved with higher values of reported FV outcome variables. In linear regression model, 13.7% of the variance in 505 time on the left leg was explained with sprint P_max, with no additional contribution of other variables. 505 test performance on the right leg was not correlated with any of the FV variables (p = 0.059–0.724). CoD deficit on the left leg (p = 0.045–0.021) was in moderate correlation with sprint F₀ (r = 0.35), slope of the FV relationship in sprint (r = −0.30) and RF_max (r = −0.32). CoD deficit on the right leg was in moderate to high correlation with F₀ (r = 0.54), P_max (r = 0.38), slope of the FV relationship (r = −0.45), RF_max (r = 0.48), and DRF (r = −0.44). Sprint F₀ explained 11.6% and 34.1% of the variance CoD deficit on left and right legs, respectively. There were no significant correlations between the outcome variables of FV variables in vertical jump and CoD performance or CoD deficit.

The 5 and 10 m sprint time was in moderate to very strong correlation (r = 0.43–0.93; p < 0.05) with F₀ (negative correlation), P_max (negative correlation), slope of the FV relationship, RF_max (negative correlation), and DRF. In linear regression model, RF_max alone explained 85.6 and 78.2% of the variance in 5 and 10 m sprint times, respectively, with additional contribution of F0 for 5 m time (88.2% of the variance explained). The 15 and 25 m sprint times were in moderate to very strong negative correlation (r = −0.33 to −0.93; p < 0.05) with RF_max, V_opt and maximal speed. P_max alone explained 71.9% of the variance in 15 m sprint and 87.7% of the variance in the 25 m sprint, with no contribution from other variables.

Overall, the sprint Pmax showed the highest associations with performance measures. Four selected relationships with sprint Pmax are depicted on Figure 2.

The purpose of this study was to examine the association between the FV relationship variables obtained in linear sprint and vertical jumps, and volleyball-specific approach jump performance, linear sprint and CoD ability (modified T-test, 505 test and CoD deficit) on a sample of young male volleyball players. Our results show that the only correlation between FV relationship in vertical jump and performance variables was between F₀ and approach jump height. While in sprinting FV relationship we found: (a) weak to moderate correlations with approach jump, (b) weak to moderate negative correlations with CoD performance, except of correlations with right leg in 505 test, and (c) negative weak to very strong correlations with sprinting ability on different distances. In regression models, sprinting P_max was included as a predictor of approach jump performance and T-test performance, while RF_max was a predictor of sprinting ability on all distances. Therefore, approach jump performance seems to be influenced both by sprint and jumping FV profiles, while FV sprint variables alone contributed to explaining linear sprinting and CoD ability.

To our knowledge, only one study to date have examined the association between FV relationship and specific sport performance of volleyball players (Baena-Raya et al., 2021). The main finding of their study was that the F₀ obtained from vertical jumping and the V₀ obtained from sprinting, were strongly associated with both spike and serve ball speeds. These mechanical variables were able to explain approximately 20–36% of the variability in spike and serve speeds. Along with results in our study, those observations could help coaches implement specific FV profile-based training programs to improve specific mechanical capabilities that determine specific athletic performance, such as approach jump height, linear acceleration, and CoD ability, as well as to improve specific volleyball performance such as spike and serve ball speed in male volleyball players. The specific finding of our study is that performance proxies (approach jump, CoD tests, and sprinting) were related mostly to sprint-based FVP variables. It seems that producing high horizontal power is one of the paramount abilities underpinning sports performance. It has already been shown that maximal horizontal power is key determinant of linear sprinting performance (Morin et al., 2012). This study highlights that sprint P_max is also related to superior CoD performance and jumping ability. On the other hand, approach jump performance appears to be related to vertical force and horizontal power production capacity.

A somewhat surprising finding in this study is that sprinting FV variables have similar and some even stronger correlation with approach jump performance than jumping FV variables, which at first glance does not agree with the principle of specificity and force vector theory. Briefly, the direction of the resistance force vector relative to the body play a role in transference to sport specific performance (axially resisted movements appear to better transfer to vertical-based movements such as vertical jump and anteroposterior resisted movements appear to better transfer to horizontal-based activities such as linear sprint) (Randell et al., 2010; Contreras et al., 2017). Thus, it is important to consider the direction of movement, both in terms of training optimization and as well as in terms of relevance of biomechanical testing for analyzing sport-specific movement performance. Approach jump consists of short running approach, following by two-legged jump. One leg is usually in front of the other, with foot directed slightly inward, to emphasize vertical direction of the jump and prevent too much horizontal flight (Prsala, 1982; Honish, 2005). This movement is quite complex, requiring good movement coordination (Ciapponi et al., 1996; Honish, 2005). The purpose of approach is to create high horizontal force, which is later transferred into vertical direction to jump as high as possible. The penultimate step (the last step of the approach) is the longest, and is performed in explosive manner. Studies reported the importance of penultimate step for approach jump performance (Liu et al., 2001). Longer and more explosive penultimate step has larger horizontal velocity and momentum, which is reflected in higher approach jump (Liu et al., 2001). In this study, we did not control the penultimate step length, so we cannot explain the obtained correlations to be actually dependent on penultimate step. These findings could present an important consideration for volleyball training optimization. Volleyball players on average perform 250–300 explosive actions in a single game, with more than half of these actions being vertical jumps (Mattes et al., 2018). Furthermore, a study looking into the association between volleyball training duration and number of jumps reported, that players on average performed 63 jumps per training hour (Bahr and Bahr, 2014). Thus, overuse injuries are common in volleyball players (Reeser and Bahr, 2008; Kilic et al., 2017). In regard to FV relationship, a recent study has reported that sprint F₀ might be associated with increased hamstring injury risk (Edouard et al., 2021). Further studies are needed to determine if FV profiling could be also used to determine the risk of injuries in volleyball.

Sprinting FV profile provides information on how effectively the athlete applies high levels of force onto the ground at different contraction velocities (Hicks et al., 2020). This is especially interesting for volleyball players, who need to accelerate their own body quickly over a very short distance, in order to perform a fast tempo attack, spike after a previous action, dig or transition from defensive action (Fuchs et al., 2019). Results in this study, show that correlation between F₀ and RF_max in sprinting FV with sprint performance is dropping with increasing distance. This indicates an importance of maximal force production and ability of horizontal force application for acceleration performance over short distance. Conversely, the correlations between sprint performance and P_max increases with sprint distance. The FV relationship explained little variance in CoD performance ability. A reason for that could be in quite homogeneous CoD performance results. In addition, CoD ability is a complex movement task that requires good movement coordination (Sheppard and Young, 2006) and is highly dependent on eccentric power (Spiteri et al., 2014; Jones et al., 2017), which is not largely reflected in FV relationship outcomes. Nevertheless, our results regarding the association between FV profiles and CoD performance are in agreement with a previous study (Baena-Raya et al., 2021), although they showed larger associations. Overall, the sprinting FV profile could be a useful assessment tool when trying maximize acceleration capabilities through training interventions, which, in turn, may translate into improved CoD performance. However, further longitudinal and experimental research is needed to confirm this hypothesis.

An interesting finding of this study is that all the participants were velocity dominant (imbalance from the optimal FV relationship in vertical jump was 2–82%; on average 43%), which means that velocity dominance in vertical jump could be: (a) a general adaptation to volleyball training, or (b) necessary predisposition to play volleyball at this level. This is in accordance with a study conducted on male and female elite volleyball players, who also showed exclusively velocity-dominant profiles (FV imbalance = 33–37%) (Broussal et al., 2016). A few other studies also reported high homogeneity toward velocity dominance of various athletes such as young ballet dancers (FV imbalance = 42–51%) (Escobar Álvarez et al., 2020), trained male track and field athletes (sprinters and jumpers; FV imbalance = 44 ± 16% for sprinters and 46 ± 14% for jumpers) (Jiménez-Reyes et al., 2014) female soccer players (FV imbalance = 65 ± 16%) (Marcote-Pequeño et al., 2019). Thus, the amount of ballistic actions such as CoDs, sprinting, jumping could explain predominance of velocity qualities. On the other hand, a study on rugby players reported mixed results considering FV dominance (Jiménez-Reyes et al., 2017a), with seven out of total forty-eight participants showing a FV profile toward force capabilities (FV imbalance = 130 ± 12%). Rugby players are usually included in heavy resistance training programs, which could explain their orientation toward force dominance in jumping FV profile. This shows that FV profile orientation is different across sports, while a very high variability between individuals is also present within each sports (Haugen et al., 2019). The correlations between FV relationship variables and performance outcome variables obtained in our study could be different if the sample would be more heterogeneous from the perspective of FV relationship dominance (i.e., including both force-dominant and velocity-dominant athletes). Consequently, it is recommended to perform correlation analysis between FV relationship in different movement tasks for each sport separately, using specific-sport performance indicators in order to better understand the potential for training optimization through monitoring and changing FV capabilities.

Some limitations of the study with implications for future research must be underlined. The study was conducted on a sample of well-trained male volleyball players, which means that the results should not be generalized to females and athletes from other sports, and even volleyball players of lower training status. The cross-sectional design precludes establishing any causal relationships, thus, further prospective and experimental research is needed to corroborate our results. Moreover, the variables in the study covered only a limited aspect of performance. Future studies should analyze the relationship (and changes in time) of different variables of the FV profile in other frequent actions in volleyball game. Moreover, it would be interesting to see an interventional study looking into the changes in FV relationship variables through the entire season. Fitness testing often occurs at multiple time points throughout a year for team sport athletes (pre, mid, and post-season is common) and it should not be assumed that FV relationship variables would be the same during the whole season. Finally, although a fair amount of breaks was provided between tasks and repetitions, the overall experimental protocols was relatively demanding, thus, some effects of fatigue cannot be excluded.

In this study, we found that approach jump performance seems to be influenced by both, sprinting and jumping FV profiles, while FV sprint variables alone contributed to explaining linear sprinting and CoD ability. An interesting finding is that sprinting FV variables have similar and some even stronger correlation with approach jump performance than jumping FV variables, which could present an important consideration for volleyball training optimization. Evaluating FV profile in volleyball players seems to have a potential for training optimization through implementing specific FV profile-based training programs to improve specific mechanical capabilities that determine volleyball athletic performance (approach jump height, linear acceleration, and CoD ability), as well, to improve performance in specific volleyball movement tasks (spike and serve ball speed). Future studies should assess the effects of interventions with implementing specific exercises to optimize certain parameters of the FV relationship, and check if the results of the performance tests changed. Moreover, it would be interesting to see the differences in FV profile characteristics between different volleyball player roles (middle blocker, outside hitter, opposite, setter, and libero). Finally, longitudinal studies would be also desirable to see if FV profiling could be used to determine risk of the injuries in volleyball.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by Republic of Slovenia National Medical Ethics Committee. The patients/participants provided their written informed consent to participate in this study.

ŽK and NŠ conceptualized the idea, overviewed the measurement procedures and administration, and finalized the manuscript. JP carried out the measurements and wrote the manuscript. JP and ŽK analyzed the collected data. All authors contributed to the article and approved the submitted version.

NŠ was employed by company S2P, Science to Practice, Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.