## 3 Results
### Correlational Analysis--Asymmetry vs. Functional Output  
Correlation analyses across all participants did not confirm the originally hypothesized negative associations between asymmetry and performance. Contrary to Hypotheses H1-H3, no substantial correlations were observed between Impulse Asymmetry and Jump Height (r = 0.00), Landing RFD Asymmetry and Active Stiffness (r = \(-\)0.05), or Average Force Asymmetry and RSI (r = 0.02). These findings are visualized in the updated Pearson correlation matrix (Figure 1), and suggest that asymmetry-based predictors may exhibit high inter-individual variability or nonlinear effects in elite athletic populations.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Group** & **Cg-Post** & **CG-Pre** & **EG-Post** & **EG-Pre** \\ \hline Jump Height (Flight Time) [cm] & 21.01 \(\pm\) 8.05 & 20.64 \(\pm\) 7.01 & 31.21 \(\pm\) 7.86 & 28.97 \(\pm\) 8.79 \\ RSI (Flight/Contact Time) & 1.68 \(\pm\) 0.39 & 1.77 \(\pm\) 0.42 & 2.75 \(\pm\) 0.67 & 2.17 \(\pm\) 0.64 \\ Peak Power [W] & 5168.18 \(\pm\) 2858.47 & 4990.65 \(\pm\) 2034.14 & 7973.06 \(\pm\) 3360.97 & 7493.24 \(\pm\) 2245.16 \\ Active Stiffness [N/m] & 21,955.27 \(\pm\) 7983.13 & 50,635.18 \(\pm\) 10,308.38 & 36,234.0 \(\pm\) 17,153.25 & 26,241.18 \(\pm\) 15,426.95 \\ Average Force (Asymmetry) [\% L, R] & 0.86 \(\pm\) 15.51 & \(-\)1.05 \(\pm\) 13.52 & \(-\)14.42 \(\pm\) 18.68 & 0.77 \(\pm\) 25.23 \\ Impulse (Asymmetry) [\% L, R] & 0.86 \(\pm\) 15.51 & \(-\)1.04 \(\pm\) 13.51 & \(-\)14.42 \(\pm\) 18.68 & 0.78 \(\pm\) 25.24 \\ Landing RFD (Asymmetry) [\% L, R] & 3.84 \(\pm\) 17.89 & \(-\)4.47 \(\pm\) 16.74 & \(-\)17.5 \(\pm\) 24.66 & \(-\)3.7 \(\pm\) 31.14 \\ FER & 0.23 \(\pm\) 0.08 & 0.23 \(\pm\) 0.05 & 0.15 \(\pm\) 0.08 & 0.17 \(\pm\) 0.07 \\ AII & 3.57 \(\pm\) 3.21 & 9.97 \(\pm\) 25.91 & 3.61 \(\pm\) 2.98 & 5.1 \(\pm\) 11.62 \\ \hline \end{tabular} Mean \(\pm\) SD values for Jump Height, RSI, Peak Power, Stiffness, asymmetry indices, FER, and AII for EG-Pre, EG-Post, CG-Pre, CG-Post.  
\end{table}
Table 1: Descriptive statistics for main variables by group and timepoint.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Group** & **Variable** & **Test** & \(p\)**-Value** & **Effect Size (Cohen’s d)** \\ \hline EG vs. CG (Post) & Jump Height (Flight Time) [cm] & independent \(t\)-test & 0.001 & 0.74 \\ EG vs. CG (Post) & RSI (Flight/Contact Time) & independent \(t\)-test & 0.001 & 0.90 \\ EG vs. CG (Post) & Peak Power [W] & independent \(t\)-test & 0.186 & 0.28 \\ EG vs. CG (Post) & Active Stiffness [N/m] & independent \(t\)-test & 0.776 & \(-\)0.05 \\ EG vs. CG (Post) & Average Force (Asymmetry) [\% L, R] & independent \(t\)-test & 0.833 & \(-\)0.04 \\ EG vs. CG (Post) & Impulse (Asymmetry) [\% L, R] & independent \(t\)-test & 0.928 & \(-\)0.02 \\ EG vs. CG (Post) & Landing RFD (Asymmetry) [\% L, R] & independent \(t\)-test & 0.919 & \(-\)0.02 \\ EG vs. CG (Post) & FER & independent \(t\)-test & 0.031 & \(-\)0.46 \\ EG vs. CG (Post) & AII & independent \(t\)-test & 0.868 & 0.03 \\ \hline \end{tabular} Results of paired \(t\)-tests or Wilcoxon tests within groups and mixed ANOVA Group \(\times\) Time comparisons with effect sizes.  
\end{table}
Table 2: Pre–Post comparisons within and between groups (EG vs. CG).  
Additional Analyses Color-coded heatmap illustrating the bivariate relationships between inter-limb asymmetry measures (Impulse, RFD, and Force Asymmetry) and jump performance metrics (Jump Height, RSI, Peak Power, and Active Stiffness). No statistically meaningful correlations were observed, with all r values below the conventional effect threshold (r < 0.3), contradicting Hypotheses H1-H3 and suggesting high inter-individual variability or nonlinear mechanisms.