## 4 Discussion  
This study aimed to assess whether lower limb flexibility levels correlate with vertical jump height, balance and speed, in adult amateur football players. After data analysis, correlations were found between flexibility and vertical jump height, balance and speed, with weak to moderate strength associations. It was found that the lower the knee flexion angle and therefore the flexibility of knee extensors, the greater the vertical jump height, with statistical significance only for the left side (right: \(\rho=-0.311\); \(p=0.160\); left: \(\rho=-0.426\); \(p=0.048\)). Vertical jumps are frequent actions in football. Although the relationship between a bipedal test and single-limb flexibility may be questionable, this can be explained from a movement efficiency perspective. Players need to jump quick and explosively, with a short eccentric movement phase, and cannot be required for large knee stretching muscle units, generating larger muscle stiffness. A study developed by [PERSON] et al. [7] indicated that the group of professional football players with lower knee extensors flexibility had greater muscle stiffness (r = 0.516; \(p<0.001\)) compared with the most flexible group, which can facilitate the production and transmission of contractile force and energy release in relatively fast stretching-shortening activities such as jumping and sprinting. In this sense, the same authors observed that the less flexible players had better performance in all anaerobic performance tests, particularly the countermovement jump (difference between groups = 5.26%; \(p=0.042\)), which was also noticed in the present study. It should be noted that the knee flexors' flexibility did not show a statistically significant correlation, with vertical jump height (\(\rho=0.330\); \(p=0.133\)). Although with a sample of amateur players and considering the differences this group may have when compared with top level players, these findings follow [PERSON] et al. [7], who did not find evidence that flexibility limitations in the knee flexors of professional football players decrease the jump performance (difference between groups = 1.28%; \(p=0.617\)). However, [PERSON] et al. [12] observed that young semiprofessional players with greater knee flexors flexibility presented better results in all tasks studied, particularly the countermovement jump (between-group difference = 10.49%; \(p=0.024\)). In addition, [PERSON] et al. [39] reported that the countermovement jump performance was significantly better in the group of young elite football players who showed higher \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Vertical Jump** & \
\begin{tabular}{c} **Composite Reach** \\ **Distance, Right Side** \\ \end{tabular} &
\begin{tabular}{c} **Composite Reach** \\ **Distance, Left Side** \\ \end{tabular} & **Speed** \\ \hline Modified Thomas Test & & & & \\ Right hip flexion & \(0.097\) (\(p=0.667\)) & \(-0.004\) (\(p=0.986\)) & \(-0.026\) (\(p=0.908\)) & \(-0.151\) (\(p=0.501\)) \\ Left hip flexion & \(-0.152\) (\(p=0.498\)) & \(-0.016\) (\(p=0.942\)) & \(-0.035\) (\(p=0.878\)) & \(-0.025\) (\(p=0.912\)) \\ Right knee flexion & \(-0.311\) (\(p=0.160\)) & \(-0.100\) (\(p=0.659\)) & \(-0.202\) (\(p=0.366\)) & \(0.360\) (\(p=0.100\)) \\ Left knee flexion & \(-0.426\) (\(p=0.048\)) & \(-0.129\) (\(p=0.567\)) & \(-0.203\) (\(p=0.364\)) & \(0.386\) (\(p=0.076\)) \\ Sit-and-Reach Test & \(0.330\) (\(p=0.133\)) & \(0.411\) (\(p=0.040\)) & \(0.364\) (\(p=0.096\)) & \(-0.173\) (\(p=0.440\)) \\ \hline \hline \end{tabular}  
* Correlation coefficients \(\rho\) of Spearman; \(p<0.05\).  
\end{table} 
Table 5: Correlation coefficients between data on flexibility tests and data on vertical jump balance and speed tests a.  
levels of knee flexors flexibility (\(p=0.023\)). The reasons for this variance in the results still need to be determined. However, age (adults and young people) and the competitive level of the sample (amateurs, semiprofessional, professionals and elite) may explain it.