Volleyball has been a popular sport for a long time, and its popularity continues to grow (Seminati and Minetti, 2013). Despite the non-contact nature of the gameplay, volleyball players nevertheless sustain a fair amount of injuries (Baugh et al., 2018; Keller et al., 2018; Kilic et al., 2017; Seminati and Minetti, 2013). Inter-limb asymmetries have been identified as a potential factor that may contribute to impaired sports performance (Bishop et al., 2018) and possibly increase injury risk (Croisier et al., 2008; Mokha et al., 2016). Therefore, regular assessment of inter-limb asymmetries should be a part of the strength and conditioning programs. Previous research has focused predominantly on investigating upper limb asymmetries in volleyball players, notably the inter-limb asymmetries in shoulder strength and flexibility (Hadzic et al., 2014; Keller et al., 2018; Seminati and Minetti, 2013). However, lower-limb injuries represent a considerable number of volleyball injuries (Kilic et al., 2017) and research in this field is currently lacking. The high incidence of lower-limb injuries in high school and collegiate volleyball players (Pollard et al., 2011) argues strongly for the inclusion of comprehensive routine assessment and integration of preventive intervention in early age, which is in line with the models for counteracting the negative effects of early sport specialization (Myer et al., 2015).

Previous investigations have shown that 27-34 % of basketball and volleyball players exhibit an asymmetry greater than 15 % in vertical jump height (Fort-Vanmeerhaeghe et al., 2016). Another study investigating male volleyball players reported a high (11.24%) mean inter-limb asymmetry index in knee extensor isokinetic strength at 60°/s, however, the mean index significantly dropped to (5.28 %) at 180°/s, showing inter-limb asymmetries may be contraction velocity-dependent (Schons et al., 2019). Similar findings were reported by Cheung et al. (2012), who showed higher (9.1 %) inter-limb asymmetries during isokinetic knee extension testing at 60°/s, compared to 300°/s (5.4 %), while the results were similar for both velocities for hamstring muscles (4.8-5.9 %) in volleyball players. Meanwhile, the inter-limb asymmetries were reported to be very low for various variables associated with the leg press task in a study investigating male volleyball players (Mattes et al., 2018). The discrepancy of these results is suggesting that a single testing procedure is perhaps not sufficient to detect all aspects of imbalances in strength between the limbs.

A recent systematic review has suggested that inter-limb asymmetries may be related to impaired performance, but the results are not consistent across studies (Bishop et al., 2018). Namely, inter-limb asymmetries in lower body strength were associated with poorer jumping performance and output power during cycling, while weak associations or absence of associations have been shown between inter-limb asymmetries during jumping and sprinting performance and change-of-direction (CoD) ability (Bishop et al., 2018). Specifically, for volleyball players, Schons et al. (2019) reported that asymmetries in knee extensor isokinetic strength at 60 °/s could be related to poorer jumping performance (r=-0.53), however, their findings were not statistically significant. CoD ability was shown to be related to lower-limb strength (Tramel et al., 2019), however, no previous studies have investigated the relationships between inter-limb asymmetries and CoD performance.

Previous studies investigating the presence of interlimb asymmetries or associations between inter-limb asymmetries and performance have mostly used only a few outcome measures within the same study, such as maximal torque or maximal force (Bishop et al., 2018). Other parameters of muscle capacity, such as rate of torque development (RTD) and particularly rate-of torque development scaling factor (RTD-SF), have been scarcely used so far. Moreover, studies focused on different muscle groups or tasks (jumps, single-leg strength tasks) to quantify inter-limb asymmetries and the associations with performance are inconsistent across athletes in general (Bishop et al., 2018) and specifically in volleyball (Cheung et al., 2012; Fort-Vanmeerhaeghe et al., 2016; Mattes et al., 2018; Schons et al., 2019). A comprehensive study is needed to assess the magnitude, agreement and relationships among inter-limb asymmetries in different tasks through different outcome measures. In line with the outlined paucity of evidence and differences between studies, the purpose of the present study was to explore a) the prevalence of strength and power lower body inter-limb asymmetries in volleyball players, b) the agreement between several different strength/power outcome measures (maximal isometric strength, RTD, RTD-SF, vertical jumping, jumping for distance and CoD tests) in terms of inter-limb asymmetry direction and magnitude, and c) the associations between inter-limb asymmetries and jumping and CoD performance.

For this study, 54 young volleyball players (25 males, 29 females; mean age: 17.8±3.3 years; mean body height: 1.77±0.11 m; mean body mass: 69.5±12.9 kg) were recruited through two regional clubs. Inclusion criteria were: > 3 years of regular (> 3 times per week) volleyball training and age ≥ 15 years. Exclusion criteria were the presence of serious musculoskeletal injuries or pain syndromes at the time of testing or in the previous 6 months. The study protocol was approved by Slovenian National Medical Ethics Committee (approval number: 0120-99/2018/5) and conducted in accordance with the Helsinki declaration. Informed consents were obtained prior to the onset of the experiment. For underage participants, informed parental consents were obtained.

The present study was conducted as a single-visit cross-sectional investigation. The participants were required to complete the following unilateral tasks: a) single-leg vertical counter-movement (CMJ) jump on force plates, b) single-leg forward (SJ_For) and single-leg lateral jumps (SJ_Lat) for distance c) single-leg triple forward jumps (TJ_For) for distance, d) unilateral knee extension maximal isometric voluntary contraction (MVC) and rapid isometric pulses for RTD-SF calculation and e) two CoD tests, one requiring 90° turn (CoD₉₀) and the other requiring 180° turn(CoD₁₈₀). All tests were performed separately for each limb (or movement direction in case of CoD). The order of the tasks was random and counter-balanced across participants. The order of the limbs was randomized for each participant separately for each task.

Single leg CMJs (Figure 1C) were performed on force platforms (Quattro Jump, type 9290DD, Kistler, Winterthur, Switzerland). Participants were instructed to place their hands on the hip and to lift off the opposite leg by bending the knee to ~90° and wait for the examiner’s que. They were instructed to lower themselves as quickly as possible and jump as high as possible. The depth of the counter-movement was instructed to be to the knee position of 90° which was visually controlled for. Familiarization trials (2-3 repetitions) were carried out for each participant. The technique of the jump as well as output force signals were monitored by the investigator. Special attention was given to the opposite leg, which was strictly forbidden to touch the force plate or to use its swing during the jump.

The remaining jump tasks (SJ_For, SJ_Lat and TJ_For) were performed on a flat surface (sport parquet). Detailed description of the procedures may be found elsewhere (Haitz et al., 2014; Meylan et al., 2009). In brief, measuring tapes were affixed to the ground and participants kept their hands on the hips. For SL_For (Figure 1 A) and SL_Tri (Figure 1D), the participants started with their toes aligned to the starting line. When ready, they were instructed to perform a single jump (SJ_For) or three consecutive jumps (TJ_For) for distance. The distance was recorded from the starting line to the point where the heel landed upon the completion of the jump (last jump in case of TJ_For). For the SJ_Lat (Figure 1B), the participants placed the medial border of the stance foot behind the starting line, with the other leg facing in the direction of the jump. Counter-movement was allowed and the participants landed on both limbs. The distance from the starting line to the medial border of the leg that executed the jump was recorded by the investigator. For all jumps, the average of the three repetitions was taken for further analysis for each leg for all of the jumps.

CoD₉₀ and CoD₁₈₀ were performed on a flat, non-slippery surface, as described before (Rouissi et al., 2016). To ensure accurate time measurements, we used a laser photo gate system (TCi Timing System, Brower Timing Systems, Draper, USA). For the CoD₉₀, the participants performed 5+5 m straight-line sprints, with a 90° turn in the middle. For CoD₁₈₀, the participants performed 5+5 m sprints with a 180° turn. For both tests, three repetitions were completed for each direction, and the best repetition was taken for further analyses. The turning point was marked with a cone for both tests. At all times, the participants started the test at their own will.

Knee extension maximal strength was evaluated on a custom-made dynamometer (S2P, Science to Practice, Ltd., Ljubljana, Slovenia) by performing the MVC task (Figure 1). The participants were instructed to contract as fast and as strong as possible (Maffiuletti et al., 2016), which enabled both maximal torque and rate of torque development (RTD) analysis. The participants were verbally encouraged to exert maximal effort for 3-5s. For each limb, the task was repeated three times, with 30-s rest periods in between. The best repetition for each limb was taken for further analysis. Additionally, we performed the assessment of the rate of torque development scaling factor (RTD-SF), which is the slope of the relationships between the contraction intensity (torque) and RTD during rapid isometric pulses of varying intensities (Bellumori et al., 2011). For this purpose, the participants were instructed to produce quick bursts of contractions at four different intensities (20, 40, 60 and 80% of maximal torque recorded during MVC). The order of the intensities was randomized between participants, but was kept the same within the participant for each leg. For each intensity, 25 trials were completed. Participants were provided with a computer screen that displayed continuous real-time feedback regarding the torque level, with a horizontal line placed at the desired intensity. Familiarization trials (5-10) were provided at each intensity to allow the participants to adjust the contraction intensity to the desired torque level. Participants were instructed to make sure that each individual contraction burst is as explosive as possible and to relax quickly.

Data for SL_For, SL_Lat, SL_Tri CoD₉₀, and CoD₁₈₀ was collected into pre-prepared printed spreadsheets and transcribed to MS Excel Software (Version 2016, Microsoft, Redmond, Washington, USA). Ground reaction force data from the force plates were sampled at 1000 Hz and low-pass filtered with Butterworth filter (10 Hz cut-off frequency, 2nd order). CMJ jump height (CMJ_H), average force (CMJ_F) and average power (CMJ_P) were automatically calculated from the force data in the acquisition software (MARS, Kistler, Winterthur, Switzerland). Knee extension torque data were sampled at 1000 Hz (ARS Software, S2P Ltd., Ljubljana, Slovenia) and low-pass filtered with Butterworth filter (20 Hz cut-off frequency, 2nd order). The maximal torque was determined as the maximal value during the 1-s interval of each repetition. RTD was calculated as the first derivative of the torque with respect to time and was assessed at 50 and 100 ms (RTD₅₀ and RTD₁₀₀) after the contraction onset. Maximal RTD on the ascending part of the force-time curve was taken for computation of the RTD-SF, which was calculated as the slope of the linear regression line (peak RTD =RTD-SF *PeakTorque+ Intercept) (Bellumori et al., 2011), using all data points from isometric pulses for each leg. The slope of this relationship (RTD-SF_k) was the primary outcome measure of interest. The other outcome measures were the R² coefficient, which is used to verify the linear relationship between peak torque and peak RTD. Before calculating the linear regression, each isometric pulse was visually inspected offline. Raw isometric pulses signals, as well as a scatter plot of the linear regression for a representative participant is presented in Figure 2. For all of the outcome measures, inter-limb asymmetry indexes were calculated, using the following equation:

The dominant leg was defined as the ‘’leg you would use for single-leg jumps to achieve maximal jump height’’.

Statistical analyses were performed in SPSS Statistical Software (Version 20., IBM, Armonk, USA) and MatLab (Version R2018a, Mathworks, Natick, USA). All data are presented as means± standard deviations. For each of the outcome measures, the participants were assigned into two categories (symmetrical or asymmetrical, based on the >10 % threshold). The agreement between outcome variables regarding the categorization of the individuals was assessed by Cohen’s Kappa (κ) coefficient, using a custom-made MatLab script (Mobahi, 2020). A similar analysis was also performed for categorization according to the direction (i.e. towards the self-reported dominant or non-dominant side). The agreement between the two outcomes was interpreted as slight (κ = 0.0 – 0.20), fair (κ = 0.21 – 0.40), moderate (κ = 0.41-0.60), substantial (κ = 0.61-0.80) and almost perfect (κ ≥ 0.81)(Sim and Wright, 2005). Additionally, the χ² test was performed to assess whether the frequency of asymmetries was different between the dominant and non-dominant side. Finally, we assessed the associations between asymmetries and performance measures (CMJ_H and CoD tests), and between all asymmetries themselves, with the Pearson correlation coefficient (0.0-0.1: no association; 0.1-0.4: weak association; 0.4-0.6: moderate association; 0.6-0.8: strong association; ≥ 0.8: very strong association) (Akoglu, 2018). For these analyses, the inter-limb asymmetry indexes were converted to absolute values (preserving the magnitude). For all analyses, the threshold for statistical significance was set to p < 0.05.

Participants on average reported 4.4 ± 0.8 (range 4-8) training sessions per week, and to perform regular training for 7.3 ± 3.4 years (range 3-21). The mean values for all outcome measures for the dominant and non-dominant limb, as well as mean absolute asymmetry indexes, are presented in Table 1. The number of asymmetry indexes was evenly distributed between the non-dominant and dominant limb across participants for most outcome measures. The exceptions were SJ_For (66.7 % participants with superior dominant limb; χ² = 6.0; p = 0.014), CMJ_H (66.7 % participants with superior dominant limb; χ² = 6.0; p = 0.014) and CMJ_P (64.8 % participants with superior dominant limb; χ² = 4.7; p = 0.029).

Based on the >10% inter-limb asymmetry threshold, we categorized each participant as symmetrical or asymmetrical. There were substantial differences among the outcome measures in terms of the percentage of participants that were categorized into each category. The results are summarized in Table 2. For both CoD tests, none of the participants were categorized as asymmetrical, therefore, the χ² test could not be computed.

The first set of analyses was calculated to assess the agreement between outcome measures in terms of categorization of participants according to the direction of the asymmetry (i.e. towards the self-reported dominant or non-dominant side). The agreement between outcome measures was poor in general (most κ < 0.2). The exceptions are the almost perfect agreement between all RTD₅₀ and RTD₁₀₀ (κ = 0.86; p < 0.001), substantial agreement between CMJ_P and CMJ_F (κ = 0.73; p < 0.001), moderate agreement between CMJ_H and CMJ_P (κ = 0.48; p < 0.001) and fair agreement between CMJ_H and CMJ_F (κ = 0.40; p = 0.002).

The second set of analyses was performed to assess the agreement between outcome measures in terms of categorization of participants to ‘’symmetrical’’ or ‘’asymmetrical’’, based on the 10 % threshold. As with the first categorization, the agreement between outcome measures was poor in general (most κ < 0.2). There was a substantial agreement between RFD₅₀ and RFD₁₀₀ (κ = 0.63; p < 0.001). No other agreements above κ = 0.40 were found.

Correlations coefficients between inter-limb asymmetry indexes, obtained with different tests and outcome measures are summarized in Table 3. All associations were very similar between genders. Most coefficients were small and statistically non-significant, with few exceptions. There was a very high correlation between asymmetries in RTD₅₀ and RTD₁₀₀ (r = 0.96). Moreover, moderate associations were shown between maximal knee torque and CMJ_F in males (r = 0.41), but not in females (r = 0.29). There was also a strong relationship between asymmetries in CMJ_H and CMJ_F in both genders (r = 0.83-0.89), moderate between CMJ_P and CMJ_F (r = 0.50-0.68), but there was no association between CMJ_P and CMJ_H (r = 0.20-0.33). Asymmetries in CMJ_H were also moderately related to asymmetries in SJ_Lat and TJ_For (r = 0.39-0.47).

Pearson correlation coefficients were computed between the arithmetic mean of the left and right leg outcome measures that are considered as measures of performance (CMJ_H and both CoD tests) and all inter-limb asymmetry indexes. CoD₁₈₀ performance was weakly associated with asymmetry in CMJ_H (r = 0.29; p = 0.032) and asymmetry in RTD-SF_k (r = 0.30; p = 0.031). Since shorter times indicate better CoD₁₈₀ performance, these correlations imply that more pronounced asymmetries were associated with worse performance. CoD₉₀ performance was associated SJ_Lat (r = 0.31; p = 0.028). Since shorter times indicate better CoD₉₀ performance, these correlations imply that asymmetries were associated with better performance. No additional associations were found when analyzing male participants alone, whereas for female participants, we found an additional moderate negative association between CMJ_H performance and asymmetry in CMJ_H (r = -0.42; p = 0.024).

The aims of the present study were (a) to investigate the prevalence of lower body inter-limb strength and power asymmetries in volleyball players, (b) to assess the agreement between different strength/power outcome measures regarding the categorization of individuals in view of inter-limb asymmetry direction and magnitude and (c) to explore the associations between inter-limb asymmetries and performance. We found that the percentage of individuals that were classified as “asymmetrical” (based on the >10 % threshold) varies substantially among the outcome measures (e.g. 0 % for CoD tests and 68-75 % in RTD) and no clear tendency for one limb/side to be stronger/superior to the other for most outcome measures, with few exceptions (SJ_For, CMJ_H and CMJ_P), where the dominant limb was more often stronger.

The agreement among different outcome measures on whether the individual is “asymmetrical” and on the direction of the asymmetry was poor in general, with the exceptions of outcome measures within the same task (e.g. different RTD outcomes). Finally, both positive and negative associations between inter-limb asymmetries and performance outcome measures were found. In summary, this study challenges the common >10% asymmetry threshold by demonstrating that the magnitude and the direction of inter-limb asymmetries vary considerably between different outcome measures related to strength and power capacity. The second important novelty of the study is inclusion of the RTD-SF, a novel approach towards the assessment of muscular capacity that could represent an important addition to current assessment protocols.

Average inter-limb asymmetry indexes ranged from 2.1 to 26.3 %. Previous studies have reported high mean inter-limb asymmetry for CMJ_H (12.3 ± 9.5 %) (Fort-Vanmeerhaeghe et al., 2016), which is similar to our results (10.2 ± 9.4). The mean CMJ_H values were also very similar. Knee extensor strength asymmetries of volleyball players were previously tested in isokinetic conditions, and the mean values of the samples mostly fell within the range between 5 and 10 % (Cheung et al., 2012; Schons et al., 2019). In the present study, we found a mean asymmetry in isometric knee extension torque to be 10.9 ± 8.5 %, which is similar to what was recorded for slow, but not high isokinetic velocities (Cheung et al., 2012; Schons et al., 2019). Fort-Vanmeerhaeghe et al. (2016) also reported the number of participants with either stronger dominant (57 %) and non-dominant limb (43 %) in terms of CMJ_H results, which is similar to our results (67 % with stronger dominant limb). It seems that our results are generally in agreement with the data that has been collected before in volleyball players.

To the best of our knowledge, this is the first study that assessed the agreement between different strength/power tests regarding the classification of individual athletes as symmetrical or asymmetrical, or depending on the direction of the asymmetry. For the former, we used the >10% threshold, which is currently accepted as the value above which the difference between the limbs becomes meaningful (McGrath et al., 2016; Schiltz et al., 2009; Theoharopoulos and Tsitskaris, 2000). However, it appears that this threshold might not be appropriate for all outcome measures, and thus, the categorization of participants will not be uniform across outcome measures if the same threshold is used for all outcomes. Additionally, the agreement on the direction of the asymmetry was also poor among outcomes, suggesting that multiple assessment tasks should be performed during routine testing to obtain a comprehensive overview of individual’s strength/power capabilities and inter-limb asymmetries. In terms of rehabilitation outcomes, some authors have advocated that a lower threshold such as 5 % should be used (McGrath et al., 2016). On the other hand, it has been suggested 10 % threshold is too low to expect a serious detrimental impact on performance (Lockie et al., 2014; Yoshioka et al., 2010). Clearly, further research is needed to determine the appropriate clinically meaningful thresholds.

Another novelty of the study is the inclusion of RTD-SF (Bellumori et al., 2011), which has not been studied before in volleyball players. The mean values for RDT-SF_k we obtained (7.1 – 7.5) were similar to those recorded in previous studies that investigated knee extensors (Bellumori et al., 2011; Boccia et al., 2018; Djordjevic and Uygur, 2018). To the best of the authors’ knowledge, there are no studies published that examined the inter-limb asymmetries in RTD-SF_k. According to the >10 % threshold, 58.5 % of the participants had symmetrical values for RTD-SF_k. The inter-limb asymmetries in RTD-SF_k were moderately associated with CoD₁₈₀ performance time. Although further investigation is needed to confirm this, the inter-limb symmetry in RTD-SF_k could represent an important performance-determining factor. We encourage future investigators to include RFD-/RTD-SF measurements in their experimental protocols. Previous studies have already shown high sensitivity of RTD-SF_k to ageing (Bellumori et al., 2013) and motor impairments (Uygur et al., 2020). More studies are needed to elucidate whether RTD-SF_k could be useful in strength and conditioning, as well as rehabilitation research and routine testing.

CoD performance time was also negatively associated with the magnitude of the CMJ_H inter-limb asymmetry. Previous studies have demonstrated positive relationships between CMJ_H and CoD performance (Barnes et al., 2007), however, the present study was the first to show that inter-limb asymmetries in CMJ_H are linked with lower CoD performance. Inter-limb asymmetries in CMJ_H were also associated with the performance in the same task, but only in female participants. The remaining associations that we have found indicated that larger inter-asymmetries contributed to better performance. Such a phenomenon has been reported before for the cycling task (Bini and Hume, 2015), however, other studies to date have reported either negative associations or no association between inter-limb asymmetries and performance (Bishop et al., 2018). The positive associations that we have obtained corroborate our previous statement that multiple tests should be performed for obtaining a comprehensive picture of the athlete’s status. Subsequent research should further explore the association between inter-limb asymmetries of various outcome measures and athletic performance.

Correlations among different asymmetry indexes were generally low. Exceptions include high correlations between RTD₅₀ and RTD₁₀₀, and between CMJ_H and CMJ_F. The frist association implies that one RTD measure could be sufficient to detect the asymmetries in explosive strength. The second correlation highlights that asymmetries in jumping performance (jump height) and underlying mechanics (force) are related, which means that field-based measurements of jump height can be used to comprehensively assess inter-limb asymmetries, when instrumented measurement methods (e.g., force plates) are not available.

This study showed that the different lower-limb strength and power tests may produce substantially different results in view of inter-limb asymmetry indexes and associations with performance. Routine testing in young volleyball players should include the assessment of both simple single-joint, as well as multi-joint strength/power tests. We advise the practitioners caution when referring to inter-limb asymmetry cut-off values (expl. 10%) as the threshold above which the inter-limb asymmetries become detrimental. The results of this study can serve as guidance regarding the expected values and ranges of inter-limb asymmetries in different strength/power outcomes, in order to consider intervening when the detected values for a given athlete exceed this range. For example, this study found that inter-limb asymmetry in CMJ_H was associated with poorer performance in CoD tasks. Since CMJ_H inter-limb asymmetries ranged from 0.5-20 %, which is in accordance to previous investigations (Fort-Vanmeerhaeghe et al., 2016), it would be reasonable to reasonable to try to reduce these asymmetries below 10%. On the other hand, the mean inter- asymmetries in CoD tasks and hops for distance were much lower (2-4 %), and a value of 10 % could already represent a red flag in view of these variables.