Relationship between isometric strength parameters and specific volleyball performance tests: Multidimensional modelling approach

Abstract

BACKGROUND:

Volleyball player’s performance depends on a combination of technical-tactical skills and an optimum level of general and specific physical fitness.

OBJECTIVE:

The purpose of the study was to compare the results of three isometric strength tests with the results of four specific volleyball performance tests using a novel Multidimensional Modelling Approach.

METHODS:

In a cross-sectional study 80 male (age $=$ 16.2 $\pm$ 1.7 yrs.) and 116 female (age $=$ 16.1 $\pm$ 1.5 yrs.) volleyball players performed two testing sessions consisting of ankle extensor, handgrip, and lumbar isometric strength tests, followed by countermovement tests, modified X test and medicine ball throw.

RESULTS:

Principal Component Analysis, with 51.38% to 64.87% of variances explained, was used to group results from multiple tests into a single score: isometric force (F ${}_{\text{max}}$ Score), rate of force development (RFD ${}_{\text{max}}$ Score), and specific performance tests (Specific Score). Calculated F ${}_{\text{max}}$ Score, and RFD ${}_{\text{max}}$ Score values showed low ( $r=$ 0.310–0.416), but statistically significant ( $p<$ 0.01) correlations with Specific Score. Regression analysis showed 17.3% and 9.6% influence of F ${}_{\text{max}}$ and 16.9% and 10.1% influence of RFD ${}_{\text{max}}$ on specific abilities for male and female sample respectively.

CONCLUSIONS:

The findings derived from the isometric strength tests are not related to those obtained from specific volleyball performance tests. However, the advantages of isometric tests and their findings may be of a comparative clinical value in management of sports injury in volleyball players.

1. Introduction

Volleyball is an intermittent sport that requires players to participate in frequent short bouts of high-intensity exercise, followed by periods of low-intensity activity [1]. The game is characterized by a large number of various jumps, sprints, and high-intensity directional changes occurring repeatedly during each rally [2, 3]. Numerous researchers highlight hierarchical importance of certain abilities as volleyball specific abilities, jumping being mentioned most frequently as a dominantly manifested activity and a crucial factor in-game efficiency [4]. Besides jumping, agility is mentioned as crucially needed to successfully defend the court and transition into attack [5], as well as upper body strength, an integral part of every attacking action [6]. Volleyball player’s performance, similarly to any other athlete’s performance depends on a combination of technical and tactical skills as well as an optimum level of general and specific physical fitness [7]. These dimensions are all connected forming an overall athletic profile related to the sport in which athlete competes. Moreover, the need to observe such groups of inter-connected abilities is driven by their confirmed use in talent identification [1].

In contrast with the aforementioned specific abilities, general or basic physical abilities usually include conditions and testing procedures that are somewhat different from the activities in a given sport [8]. Isometric strength is considered to be one of general physical abilities, describing the neuromuscular function through maximal voluntary contractions. Advantages of these procedures include high reliability [9, 10] and controlled conditions, emphasized by the fact that there is not any actual movement. Moreover, this type of testing usually provides at least two variables for analysis: maximal isometric force produced (F ${}_{\max }$ ), and the rate of force development (RFD ${}_{\max }$ ), a term used to describe the ability to rapidly develop muscular force [11].

Previous research has demonstrated the importance of F ${}_{\max }$ and RFD ${}_{\max }$ in a variety of athletic populations [7, 12, 13, 14, 15, 16]. Several investigations have reported strong correlations ( $r=$ 0.76–0.97) between maximum dynamic strength and isometric force production during similar movement patterns [17]. Moreover, there are numerous studies aimed to investigate the influence that general physical abilities could have on the specific, sports-related abilities with contrasting results ranging from the evidence in favor of a relationship between both maximal isometric force (F ${}_{\max }$ ) and isometric RFD ${}_{\max }$ [18], to investigations indicating moderate to low correlations with other dynamic, sport-specific abilities [19]. Other authors, besides confirming correlations between F ${}_{\max }$ and RFD ${}_{\max }$ of the isometric squat with jumping and running abilities, point out the importance of knee angles of the test performance, further confirming the assumption that the isometric strength conditions must resemble, as close as it is possible, the conditions of specific tests if a relationship is expected [20].

With the development of isometric strength testing procedures [9], it has become more common for sport practitioners and scientists to monitor volleyball players abilities using this technique. Moreover, the connection of isometric strength testing and abilities which are considered an integral part of the volleyball game has been the topic of a large number of studies [8, 18]. However, almost all of these examinations have observed the influence or a relationship between a single isometric strength test with one specific volleyball performance test. Taking into account that there are more abilities manifested in a game of volleyball, a need emerges for an extensive approach in comparing isometric strength and specific volleyball performance tests. Therefore, in a novel approach, the purpose of the present study was to compare the conjoint results of three isometric strength tests with the results of four specific volleyball performance tests.

2. Methods

2.1 Participants

The subject sample consisted of 80 male (age $=$ 16.2 $\pm$ 1.7 yrs.; body height $=$ 181.3 $\pm$ 9.5 cm; body weight $=$ 70.2 $\pm$ 12.7 kg; training experience $=$ 4.7 $\pm$ 1.4 yrs.), and 116 female subjects (age $=$ 16.1 $\pm$ 1.5 yrs.; body height $=$ 174.5 $\pm$ 6.9 cm; body weight $=$ 63.6 $\pm$ 8.4; training experience $=$ 5.0 $\pm$ 1.3 yrs.) who took part in “Vanja Grbić” volleyball camp. In order to be part of the study, subjects had to be national-level competitors and had to have at least five 90 minutes long workouts per week during the last three years. Subjects had no previous injuries that could influence the results of the study. Upon obtaining consent and written approval from their parents and their clubs’ management, all subjects agreed and signed up to participate in this research voluntarily. The study was conducted in accordance with the requirements of the Helsinki declaration and recommendations guiding physicians in biomedical research involving human subjects [21]. The research was approved by the Ethics Commission of the Faculty of Sport and Physical Education, University of Belgrade (Number 484-2).

Figure 1.

Isometric ankle extensors strength measurement procedure.

2.2 Testing procedure

This was a cross-sectional study examining the physical performance data from 6 tests performed with volleyball athletes. Each subject performed two testing sessions separated by a day of rest. During the first day, subjects performed anthropometric and isometric strength tests, and during the second day of testing specific volleyball performance tests.

Body stature and body mass were assessed with a standard anthropometer (GPM, Swiss Made) and a digital scale (FitScan UM-028F, Tanita), respectively. Variables obtained from all isometric strength tests were maximal force (F ${}_{\max }$ ) expressed by Newtons (N) of force, and rate of force development (RFD ${}_{\max }$ ) results expressed by Newtons per second (N/s).

Testing sessions consisted of a 5-minute general warm-up, followed by 3 minutes specific warm-up for each test.

2.2.1 Bilateral isometric ankle plantarflexors strength (APF)

Following an explanation of the testing procedure subjects performed two familiarization attempts separated by 1-minute rest and three trials of measuring the maximal ankle extensor muscle force with 2 minutes of rest between trials [7]. In order to evaluate the isometric strength of the APF, participants were seated on the chair with knees and ankles bent, so that the thighs were parallel to the ground, and knees were in line with toes, thereby ensuring the leg position which is similar to the squatting and pre-jumping positions (Fig. 1). Subject’s thighs were firmly strapped to the chair, preventing him from performing any movement in his knees or hip joints. Subjects were instructed to sit on the front 2/3 of the chair, with back straight and legs hip-width apart. The strain-gauge force transducer (Hottinger, Type S9, Darmstadt, Germany; range 10 kN; tensile/compressive sensitivity 2 mV/N) position was exactly between the feet or two points of pressure during the isometric force production of ankle joint extensors. The strain-gauge was firmly fixed to the plate which was under the subject’s feet and connected by a thin metal rod to the plate on subject’s upper leg so that the force of upward plantar flexion push would be directly transferred and recorded by the strain gauge force transducer. The position of the plate on the subject’s upper leg ensured that there wouldn’t be any unpleasant or painful sensations during the testing, which could affect the results. A specially designed software-hardware system (Isometrics Lite, ver. 3.1.1) was used for data collection and processing. The force-time signal was sampled at 500 Hz and low-pass filtered (10 Hz) using a fourth-order (zero-phase lag) Butterworth filter [22]. Gravity correction was provided with baseline force in rest subtracted from all force recordings during an active phase. The onset of the contraction was defined as the point in time where the first derivative of the force-time curve exceeded the baseline by 3% of its maximum value. For the purpose of measurement, the participants were instructed to push as hard and fast as possible against the footplate by plantar flexing their ankle as if pushing on a gas pedal. Subjects performed three repetitions, and the best attempt (highest result of multiplied F ${}_{\max }$ and RFD ${}_{\max }$ ) was taken for further analysis.

2.2.2 Unilateral isometric handgrip strength (HG)

The test was conducted in accordance with the procedures described in previous studies [13, 23]. Each subject was tested while sitting upright, gripping the measuring device (Fig. 2) with the hand tested, while the arm was extended in the natural posture alongside the body. The hand gripping the device was approximately 5 to 10 cm away from the body. The examinees were not allowed to move from the initial position during the test trial, nor could they lean the hand or the device against the thigh or any other part of the body. The power grip, for which all the fingers are flexed around the device, was chosen as it could produce a higher level of force than the other grips (the precision grip, the manipulative grip, or various tool and pinch grips). The subjects’ handgrip strength was measured unilaterally, to obtain the results for left (HGL) and right (HGR) hand. Subjects performed two repetitions on both hands, and the best attempt (highest result of multiplied F ${}_{\max }$ and RFD ${}_{\max }$ ) was taken for further analysis.

Figure 2.

Unilateral isometric handgrip strength measurement device.

2.2.3 Isometric lumbar strength (LB)

Test for isometric lumbar extensor muscles strength was carried out using a standardized procedure and a dynamometric probe with a structure specially designed for this purpose [7]. Subjects were standing on a platform with feet a hip-width apart, facing a barbell rack. The barbell was firmly attached to a strain gauge force transducer. At its bottom, the probe was connected to the platform. The subjects were grasping the barbell, in position with arms and legs extended at the elbow and knee joints, while the body was in a half-forward bent position, with the chest protruded (Fig. 3). After having assumed a proper body position, subjects were instructed to perform a maximum contraction of the lumbar muscles in an attempt to make the extension movement. The examiner instructed them to lift as fast and as hard as possible. Subjects performed three repetitions, and the best attempt (highest result of multiplied F ${}_{\max }$ and RFD ${}_{\max }$ ) was taken for further analysis.

Figure 3.

Isometric lumbar strength measurement procedure.

2.2.4 Countermovement jump (CMJ)

The test was conducted in accordance with procedures described in the literature [4]. The subject started the CMJ in the standing position, with hands on hips. On the signal, he dropped into the squat position, and then immediately jumped as high as possible, without releasing his hands from the hips. The depth of knee flexion used during each CMJ was individually determined by each subject. The Optojump photoelectric cells (Microgate, Bolzano, Italy), which consist of two parallel bars (one receiver and one transmitter unit, each measuring 100 $\times$ 4 $\times$ 3 cm), were placed approximately 1 m apart and parallel to each other. The Optojump system measured the flight time of vertical jumps with an accuracy of 1/1000 seconds (1 kHz). Jump height was then estimated as 9.81 $\times$ flight time ${}^2$ /8 [24]. The assessed variable was the maximum jump height in cm.

2.2.5 Countermovement jump with arm swing (CMJa)

The test was conducted in accordance with the procedures described by previous studies [4]. The subject started the CMJa in the standing position, with relaxed arms in natural position. On the signal, he dropped into the squat position, and then immediately jumped as high as possible, with the arm swing. The depth of knee flexion, as well as the arm swing, used during each CMJa was individually determined by each subject. The Optojump photoelectric cells (Microgate, Bolzano, Italy), which consist of two parallel bars (one receiver and one transmitter unit, each measuring 100 $\times$ 4 $\times$ 3 cm), were placed approximately 1 m apart and parallel to each other. The Optojump system measured the flight time of vertical jumps with an accuracy of 1/1000 seconds (1 kHz). Jump height was then estimated as 9.81 $\times$ flight time ${}^2$ /8 [24]. The assessed variable was the maximum jump height in centimetres.

2.2.6 Modified X test (X)

In order to assess subjects’ agility, we used photocells (PAT 01, Uno lux, NS, Serbia) as a part of the standardized procedure. Subjects had the task to run as fast as they could through five points (A, B, C, D and E) placed so that they shape the letter X (Fig. 4). The initial position of the subject was behind the starting line (dashed line at the A point) on its middle part, and facing the B point. Time measurement started with the subject intercepting the infrared beam, aligned with the starting line (dashed line) positioned in the centre of the square with 4.5 m edges. Subjects were always facing the running direction and performed 4 forward and back distances to each of the corners of the square in the following order: (1) from point A to point B; (2) after 180 ${}^{\circ }$ turn from point B to point A; (3) from point A to point C; (4) after 180 ${}^{\circ }$ turn from point C to point A; (5) from point A to point D; (6) after 180 ${}^{\circ }$ turn from point D to point A; (7) from point A to point E and (8) after 180 ${}^{\circ }$ turn from point E to point A. The test was completed with the last infrared beam interception at the finish line. During the test, subjects had to cross the marked lines (red lines) with one foot while changing running directions at points A, B, C, D and E [5]. Subjects performed two trials, and the best result was taken for further analysis. Results were expressed by seconds (with two decimals) needed to complete the test.

Figure 4.

Modified X test procedure scheme.

2.2.7 Medicine ball throw (MB Throw)

The goal of this test was to measure upper body strength and explosive power. Subjects were instructed to stand behind the line with feet parallel and hip-width apart, facing the direction to which the ball was going to get thrown [25]. The medicine ball (2 kg) was held with both hands. Subjects were instructed to bring the medicine ball back behind the head, then throw it forward as far as possible. The distance in cm from the starting position to where the ball landed was taken as the final result. Three trials were recorded, and the best one was taken for further analysis.

2.3 Statistical analysis

All the raw data were initially analyzed by applying the basic descriptive statistical methods in order to calculate the mean value (Mean), the standard deviation (SD), the coefficient of variation (cV%) as well as the minimum (Min) and the maximum value (Max).

Data were evaluated using Keiser-Meyer-Olkin (KMO) and Bartlett’s test, to confirm sphericity of the data for both male and female subjects’ samples and its adequacy. The principal component analysis (PCA) with the explorative model was used to determine the main factors underlining the general and specific physical abilities data matrixes, as well as each components’ contribution to the factor variability. PCA (Bartlett method) was also used for defining general physical abilities by multidimensional transformation into one score number (F ${}_{\max }$ Score and RFD ${}_{\max }$ Score of all isometric strength tests), and the same methodological transformation was used for specific physical abilities (Specific Score).

Table 1

Descriptive statistics of both subject samples

Variable	Mean		SD		cV%		Min		Max		Mean		SD		cV%		Min		Max
F ${}_{\max }$ HGR (N)	392	.5	80	.46	20	.50	205		669		281	.5	46	.35	16	.44	165		424
RFD ${}_{\max }$ HGR (N/s)	2784	.4	557	.37	20	.02	1284		4065		1928	.4	356	.95	18	.51	1070		3211
F ${}_{\max }$ HGL (N)	362	.6	75	.95	20	.94	203		619	.2	267	.1	44	.37	16	.6	172		409
RFD ${}_{\max }$ HGL (N/s)	2598	.8	571	.5	21	.99	1482		4151		1808	.1	364	.97	20	.18	1060		3099
F ${}_{\max }$ LB (N)	1194	.4	232	.65	19	.48	680		2049		857	.3	142	.20	16	.59	572		1366
RFD ${}_{\max }$ LB (N/s)	9231	.7	2311	.6	25	.04	4445		14144		5966	.8	1845	.8	30	.94	2277		12332
F ${}_{\max }$ AE (N)	3275	.8	615	.62	18	.79	1866		4977		2902	.8	608	.51	20	.96	1417		4945
RFD ${}_{\max }$ AE (N/s)	16247	.3	3023	.4	18	.61	9487		24113		14322	.4	3004	.72	20	.98	6891		23632
CMJ (cm)	36	.7	6	.06	16	.53	26	.8	54	.4	29	.4	4	.51	15	.19	21	.1	40	.7
CMJa (cm)	45	.1	7	.04	15	.61	33	.5	64	.4	34	.7	5	.22	14	.94	26		51.2
X (s)	7	.9	0	.62	7	.77	6	.7	9	.8	8	.6	0	.65	7	.39	7	.2	10	.5
MB Throw (m)	10	.1	1	.71	17	.01	5	.8	14	.9	8	.2	1	.2	12	.25	6	.1	10	.4
Sample	Male										Female

Abbreviations: HGR $=$ right handgrip; HGL $=$ left handgrip; LB $=$ lumbar muscles; AE $=$ ankle extensors; CMJ $=$ countermovement jump; CMJa $=$ countermovement jump with arm swing; X $=$ modified X test; MB Throw $=$ medicine ball throw. F ${}_{\max }$ $=$ maximal force; RFD ${}_{\max }$ $=$ maximal rate of force development.

Table 2

Principal component analysis structure matrix

Specific physical abilities					General physical abilities
Variable	Male		Female		Variable	Male		Female		Variable	Male		Female
CMJa	0.	914	0.	925	F ${}_{\max }$ HGR	0.	903	0.	829	RFD ${}_{\max }$ HGR	0.	887	0.	852
CMJ	0.	870	0.	899	F ${}_{\max }$ HGL	0.	907	0.	909	RFD ${}_{\max }$ HGL	0.	843	0.	836
X	$-$ 0.	695	$-$ 0.	399	F ${}_{\max }$ AE	0.	669	0.	720	RFD ${}_{\max }$ AE	0.	666	0.	744
MB Throw	0.	461	0.	482	F ${}_{\max }$ LB	0.	773	0.	750	RFD ${}_{\max }$ LB	0.	655	0.	670
Cum. %	57.	19	51.	38	Cum. %	67.	07	64.	87	Cum. %	59.	21	60.	68

Abbreviations: HGR $=$ right handgrip; HGL $=$ left handgrip; LB $=$ lumbar muscles; AE $=$ ankle extensors; CMJ $=$ countermovement jump; CMJa $=$ countermovement jump with arm swing; X $=$ modified X test; MB Throw $=$ medicine ball throw. F ${}_{\max }$ $=$ maximal force; RFD ${}_{\max }$ $=$ maximal rate of force development.

Table 3

Pearson correlations results between single variables of both samples

Variable	F ${}_{\max }$		RFD ${}_{\max }$		F ${}_{\max }$		RFD ${}_{\max }$		F ${}_{\max }$		RFD ${}_{\max }$		F ${}_{\max }$		RFD ${}_{\max }$		Sample
	HGR		HGR		HGL		HGL		LB		LB		AE		AE
CMJ	0.	226 ${}^{\ast }$	0.	246 ${}^{\ast }$	0.	165	0.	146	0.	077	$-$ 0.	035	0.	119	0.	291 ${}^{\ast \ast }$	Male
CMJa	0.	306 ${}^{\ast \ast }$	0.	381 ${}^{\ast \ast }$	0.	325 ${}^{\ast \ast }$	0.	311 ${}^{\ast \ast }$	0.	205	0.	156	0.	119	0.	251 ${}^{\ast }$
X	$-$ 0.	209	$-$ 0.	252 ${}^{\ast }$	$-$ 0.	179	$-$ 0.	208	$-$ 0.	294 ${}^{\ast \ast }$	$-$ 0.	088	$-$ 0.	247 ${}^{\ast }$	$-$ 0.	136
MB Throw	0.	652 ${}^{\ast \ast }$	0.	573 ${}^{\ast \ast }$	0.	570 ${}^{\ast \ast }$	0.	500 ${}^{\ast \ast }$	0.	704 ${}^{\ast \ast }$	0.	420 ${}^{\ast \ast }$	0.	353 ${}^{\ast \ast }$	0.	168
CMJ	0.	233 ${}^{\ast }$	0.	277 ${}^{\ast \ast }$	0.	292 ${}^{\ast \ast }$	0.	370 ${}^{\ast \ast }$	0.	081	0.	056	0.	122	0.	051	Female
CMJa	0.	189 ${}^{\ast }$	0.	248 ${}^{\ast \ast }$	0.	266 ${}^{\ast \ast }$	0.	314 ${}^{\ast \ast }$	0.	03	0.	016	0.	085	$-$ 0.	7003
X	$-$ 0.	165	$-$ 0.	163	$-$ 0.	147	$-$ 0.	16	$-$ 0.	191 ${}^{\ast }$	$-$ 0.	12	$-$ 0.	161	$-$ 0.	072
MB Throw	0.	178	0.	207 ${}^{\ast }$	0.	318 ${}^{\ast \ast }$	0.	261 ${}^{\ast \ast }$	0.	325 ${}^{\ast \ast }$	0.	317 ${}^{\ast \ast }$	0.	357 ${}^{\ast \ast }$	0.	359 ${}^{\ast \ast }$

Abbreviations: HGR $=$ right handgrip; HGL $=$ left handgrip; LB $=$ lumbar muscles; AE $=$ ankle extensors; CMJ $=$ countermovement jump; CMJa $=$ countermovement jump with arm swing; X $=$ modified X test; MB Throw $=$ medicine ball throw. F ${}_{\max }$ $=$ maximal force; RFD ${}_{\max }$ $=$ maximal rate of force development. ${}^{**}$ – significant correlation ( $p<$ 0.00). ${}^{*}$ – significant correlation ( $p<$ 0.05).

Figure 5.

Regression analysis results of F ${}_{\max }$ Score and Specific Score.

Figure 6.

Regression analysis results of RFD ${}_{\max }$ Score and Specific Score.

Pearson Correlation was used to determine the levels of the relationships between the individual test results, as well as the correlations between Score values of variables from isometric strength testing and specific physical abilities area. After that, Simple linear regression was used to investigate the influence of F ${}_{\max }$ Score and RFD ${}_{\max }$ Score as a general factor of maximal muscle isometric strength and explosivity, on Specific Score as a general factor of specific volleyball physical abilities level. Fisher’s Z transformation was used to compare the between-gender differences in correlations of F ${}_{\max }$ Score and RFD ${}_{\max }$ Score with Specific Score.

All the statistical analyses were calculated using the SPSS 22.0 software, while statistical significance was defined at the level of a 95% probability, for the value of $p<$ 0.05.

3. Results

The results for the PCA are presented in Table 2. The initial KMO analysis has shown a high enough sampling adequacy, at the level of 0.666, indicating that the PCA was justified. Bartlett method indicator was statistically significant (Sig. $<$ 0.001) for both genders, confirming the sphericity of data for further analysis. Table 2 shows the component matrix results of both samples and regarding both specific and general physical abilities. All components, with the exception of MB Throw (Male $=$ 0.461; Female $=$ 0.482) and X test (Female $=$ $-$ 0.399), have had high participation in the main factors extracted with the PCA. Cumulative variance explained by the extracted factors was moderate to high (Table 2).

Table 4

Pearson correlations between Score values of both samples

Variable	F ${}_{\max }$ Score	RFD ${}_{\max }$ Score	Specific Score
F ${}_{\max }$ Score	x	Female 0.824 ${}^{\ast \ast }$	Female 0.310 ${}^{\ast \ast }$
RFD ${}_{\max }$ Score	Male 0.794 ${}^{\ast \ast }$	x	Female 0.318 ${}^{\ast \ast }$
Specific Score	Male 0.416 ${}^{\ast \ast }$	Male 0.411 ${}^{\ast \ast }$	x

${}^{**}$ – significant correlation ( $p<$ 0.00).

The correlations between the individual variables shown in Table 3 were statistically significant in 48/66 cases for both samples, with X test correlating significantly with other tests the least for female sample (2/11), and CMJ for male sample (5/11). Correlation coefficients were ranging from low ( $r=$ 0.191–0.248) to high ( $r=$ 0.697–0.831) for some The correlations between Score values (Table 4) obtained from PCA for different groups of variables were correlated, showing a low to moderate but significant relationships ( $r=$ 0.310–0.416) between the Score values of general (F ${}_{\max }$ Score, and RFD ${}_{\max }$ Score) and specific physical abilities (Specific Score).

The regression analysis showed 17.3% and 9.6% influence of F ${}_{\max }$ (Fig. 5) and 16.9% and 10.1% influence of RFD ${}_{\max }$ (Fig. 6) on specific abilities for men and women, respectively.

4. Discussion

The main findings from our study suggest that the results from isometric strength tests, as well as specific volleyball performance tests, can be grouped into a single factor each (Table 2) with principal components explaining variances ranging 51.4–64.9%. Calculated score values from the isometric strength tests had low, but statistically significant correlations with specific abilities score (Table 4). The main observed relationships between the individual variables of men were the high coefficients of correlations between F ${}_{\max }$ LB and MB Throw ( $r=$ 0.704), and the low-moderate coefficients between RFD ${}_{\max }$ HGL and CMJ ( $r=$ 0.370) for the women (Table 3).

The present isometric handgrip results of volleyball players (Table 1) are comparable with those reported in previous studies which focused on similar groups of subjects [6, 26, 27, 28]; the F ${}_{\max }$ results ranged 368N–415N and 276N–335N for male and female volleyball players, respectively. Some of the smaller differences could be explained by different procedures, including the handgrip force measurements in standing position [27], or the 90 ${}^{\circ }$ flexed elbow [26]. There is not much evidence concerning the bilateral plantar flexor isometric strength in the literature, as most of the studies investigated the effects on unilateral force [29] and torque [30, 31]. Only comparable procedures to ours were performed by researchers observing bilateral plantar flexor muscle forces on recreational subjects, with extended [32] and flexed knees [33] thus reporting results (male subjects 3910N $\pm$ 1106N) similar to our study (Table 1). Isometric lumbar strength, although present in the literature, have not been reported in volleyball players but usually on adult recreational physically active subjects, or athletes from other sports [34]. Still the F ${}_{\max }$ results did not deviate significantly from the current results. In contrast to isometric strength investigations, there is an abundance of research regarding the jumping ability of volleyball players [18, 35] comparing them to samples from soccer, basketball, handball [19], track and field [29], with CMJ, and CMJa results similar to the findings in our study. Besides jumping which is the most researched ability, agility and upper body strength [36] are also considered to be volleyball specific, and throughout the literature agility data [5], and medicine ball throw data [26] are comparable to observations from our research (Table 1).

Isometric strength is believed to have a moderate relationship to volleyball specific abilities, which is well documented for HG tests associated with upper body strength ( $r=$ 0.65) [37] and jumping ability ( $r=$ 0.55–0.65) [27], as well as the quality of some actual volleyball elements such as spike and serve speed [6]. Jumping and upper body strength are important because of their influence on the athletes’ performance level in volleyball [1, 3], meaning that these connections could be followed back to isometric strength. The correlations of HG F ${}_{\max }$ and RFD ${}_{\max }$ ranged from non-existent with agility (modified X test), to some tendency of correlation with jumping (CMJ, CMJa: $r=$ 0.23–0.38), to moderate with male subjects’ medicine ball throw (MB Throw: $r=$ 0.50–0.65). Isometric HG strength test is the most widespread in both literature and practical use, its procedure is relatively simple, and easy to perform, usually causing the results from this test to be the best representation of subject’s isometric strength. This could explain the relationships with jumping tests that we observed in our study even though jumping results should mainly depend on the lower body. As opposed to jumping, agility is highly dependent on coordination and change of direction speed, so the fact that there are no correlations is not surprising, even though previous researchers reported meaningful correlations [38]. Moderate correlations with MB Throw we observed in this study come from the obvious effect of HG strength in this type of activity. Moreover, stronger arms and upper body are most often followed by the development of a stronger HG in order to support lifting and manipulating heavier weights. In contrast to research concerning upper body strength, lower body strength is dominantly investigated with the use of leg press dynamometry [4, 27, 39] which was found to correlate moderately to highly ( $r=$ 0.5–0.7) with jumping. Having that in mind we selected two isometric tests from a kinetic chain involved in the leg press, the lumbar and ankle extensor isometric strength tests, hoping to closely investigate the separate contributions involved in the force production of leg press. Another advantage of procedures suggested by our paper is that they are all field-based, and can be performed in the conditions that are outside of the laboratory, making them more efficient and utilizing for broader use. However, correlations to volleyball specific abilities in the present study were low to non-existent (Table 3), except for the strong relationship between male subjects’ lumbar F ${}_{\max }$ and MB Throw ( $r=$ 0.704). These inconsistent results could be explained by the younger age of the subjects selected for this research and the fact that most of them have not had an experience with maximal force contractions [40], or weight lifting, as opposed to adult subjects in similar studies across the literature. The inconsistent connections between contractile characteristics and volleyball specific movements, demonstrated through isometric strength and specific physical abilities respectively, indicate separate contributions of these two aspects of volleyball profile.

Dimension reduction has been previously suggested by the authors [41] to be used for a better understanding of the relationships between different groups of abilities. This procedure makes it possible to unite a greater number of physical abilities, describing a certain sport, into a single Score value comparable to other variables. Although previous PCA [42] studies on vertical jumping accounted for a higher percentage of variance (ranging from 74.1% to 78.8%) the reliability scores of the extracted rotated principal components revealed the validity of our findings (Table 2). PCA grouped variables describing the general physical abilities (F ${}_{\max }$ and RFD ${}_{\max }$ ) and specific physical abilities were low to moderate (F ${}_{\max }$ : $r=$ 0.310–0.416; RFD ${}_{\max }$ : $r=$ 0.318–0.411), although statistically significant correlations ( $p<$ 0.001) for both genders (Table 4). There was a gender similarity in correlations between the male and female groups of subjects, which was confirmed by the Fishers Z transformation results. The Score results evaluating the maximal force component and the RFD component summarized the effects of all three isometric strength tests, thus describing the upper body, back, and lower body characteristics and making it possible to compare the whole-body force and explosiveness to specific abilities crucial in the volleyball game. Lower levels of correlation between those Score values account for both low to moderate relationships of HG test and weaker relationships from other two tests for isometric strength (LB, AE).

Low to moderate relationships were also reported in the previous studies [8], with slightly stronger correlations for RFD ${}_{\max }$ compared to F ${}_{\max }$ [43], but these studies focused on a single muscle group, as opposed to three muscle groups which are important in volleyball. These dimensions are obviously just a segment of the entire abilities profile included into the actual athlete’s performance in a volleyball game, but being able to evaluate them and observe their connections is an important task for every research investigating volleyball and those who are a part of it. Those segments were described through Simple regression analysis results, which showed that F ${}_{\max }$ Score, as a representation of athlete’s maximal force in general, explained 17.3% and 9.6% of the Specific Score variability for male and female samples respectively (Fig. 5). Similarly, the variable used to describe athletes’ explosiveness RFD ${}_{\max }$ Score participated in 16.9% and 10.1% of Specific Score variability explanation (Fig. 6). The results indicate that male subjects tend to use both F ${}_{\max }$ and RFD ${}_{\max }$ slightly more than female subjects when performing a specific volleyball movement represented throw specific agility non-linear maximal running task, different jumping, and throwing strength tests. The significant, but very low influence of general maximal force and explosiveness on specific volleyball abilities performance speaks in favour of separate contributions, which should both be monitored in order to acquire a complete and integral understanding of volleyball players physical capabilities.

One limitation of the present study is the unequal gender sample size, a consequence of more female volleyball players being able to participate in the study. Another relate to the age of the participants, around 16, thus not allowing generalization into adult volleyball players.

5. Conclusions

The main finding of this study is that findings derived from general isometric strength tests are not related to those obtained from specific volleyball performance tests. On the other hand, isometric strength tests of the type described in this study are easy to perform using affordable yet accurate devices which may provide some relevant information regarding Fmax and RFDmax, especially with respect to lumbar and plantarflexion strength. Especially, in case of an injury to specific body parts (e.g. back or ankle), the availability of results recorded in a systematic way (e.g. once a year using the same protocol), enables comparison to pre-injury level, when functional tests cannot still be performed. This may be a substantial advantage in this sport which presents with a significant rate of injuries [44].

Author contributions

CONCEPTION: Nikola Majstorović, Goran Nešić and Milivoj Dopsaj.

PERFORMANCE OF WORK: Nikola Majstorović, Vladimir Grbić, Zoran Savić and Aleksandar Vićentijević.

INTERPRETATION OR ANALYSIS OF DATA: Nikola Majstorović.

PREPARATION OF THE MANUSCRIPT: Nikola Majstorović and Goran Nešić.

REVISION FOR IMPORTANT INTELLECTUAL CONTENT: Nikola Majstorović and Milivoj Dopsaj.

SUPERVISION: Goran Nešić and Milivoj Dopsaj.

Ethical considerations

The study was conducted in accordance with the requirements of the Helsinki declaration and recommendations guiding physicians in biomedical research involving human subjects [21]. The research was approved by the Ethics Commission of the Faculty of Sport and Physical Education, University of Belgrade (Number 484-2). Written informed consent was obtained from all participants.

Funding

The study was partly supported by the grant III47015 of the Research Council of the Republic of Serbia.