# Isometric Strength in Volleyball Players of Different Age: A Multidimensional Model
## 4 Discussion
This procedure makes it possible to unite a greater number of muscle groups and to calculate their \(\mathrm{F_{max}}\) and \(\mathrm{RFD_{max}}\) results into a single Score using PCA multidimensional transformation. The Score result summarises the effects of all three isometric strength tests on a scale of 0-100, thus describing the upper body, back, and lower body characteristics together, and making it possible to model the whole-body contractile potentials of different age groups. PCA distinguished a single factor underlining both \(\mathrm{F_{max}}\) and \(\mathrm{RFD_{max}}\) from all of the isometric strength tests, with statistically significant components participations. Previous authors used the PCA for a reduction of the multidimensional structure in handball [53] to obtain three variables describing body massiveness, strength, and the length and height aspect of the body. Those variables proved to be significant predictors of playing position and level of handball players. Furthermore, PCA proved to be a useful method for eliminating the large number of highly interrelated variables to a fewer number of independent factors that would better reflect the characteristics of observed abilities [54]. A previous study suggested PCA in quantitative evaluation of an athlete's jumping performance while combining useful information from some of the most critical mechanical variables that have been proposed as potential predictors in the literature [55]. Dimension reduction has even been used for recognition and decomposition of actions in volleyball, as it can help understand the different, but connected components in abundant data [56]. The calculated Score values in our study, which represent the contractile potentials of every participant relative to the whole sample, are presented as descriptive statistics of age groups (Table 5). Demonstrated mean values for all age groups indicate the appropriate fit for an average volleyball player regarding his strength, both in terms of maximal and explosive muscle contractions. The results of ANOVA showed statistically significant differences between the youngest and the oldest age groups compared to all other groups. For male subjects, those differences were at the level of 24.8% between U15 group and U17 group, and 26.9% between the U19 group and U21 group, in favour of the older groups. In contrast, the U17 and U19 age groups had only 5.4% difference between them. A slightly more balanced trend, demonstrated by the slope in the best fit line equation (a = 6.277 and a = 3.915 for male and female subjects, respectively), was observed for female subjects, with 11.5% difference between U15 and U17, and 19.3% between U19 and U21, but still only 6.4% difference between U17 and U19. Moreover, based on a regression model of Score changes as an integral measure of muscle potential development in the function of age groups, the average yearly \(\mathrm{F_{max}}\) and \(\mathrm{RFD_{max}}\) rise of selected male subjects was 6.3%, while for female subjects the rise was somewhat more moderate at 3.9% (Figure 2). Changes in strength are not uniform throughout development. For boys, the window for increased trainability starts somewhere around the ages of 14-16, and for girls a little bit earlier [3], which could explain the differences observed for the U15 group. Previous studies also showed age-related differences in strength of volleyball players, but mostly while observing a single muscle group [17], or measuring the strength in dynamic conditions [44]. We speculate that characteristics of volleyball training in that younger age could not yet affect innate strength ability, which was different for every participant, thus also explaining the higher variability in the youngest group. Moreover, even though the participants had to have at least three years of training experience to meet the study inclusion condition, usually a big part of that initial period of volleyball development is dedicated to acquiring basic volleyball skills.