## 2 Materials and Methods
### Statistical Analysis  
All statistical analyses were conducted using a multi-software ecosystem to ensure methodological robustness and reproducibility. This included RStudio (v4.3.1) with packages lme4, psych, e1071, glmnet, and ggstatsplot; Jamovi (v2.4.8) for classical inferential procedures; and Orange (v3.34) and KNIME (v4.7) for exploratory and machine learning-based modeling. Normality and homogeneity were confirmed using the Shapiro-Wilk and [PERSON]'s tests, respectively. When these assumptions were violated, non-parametric alternatives (e.g., Wilcoxon signed-rank test) were used. For novel indices (FER and AII), both raw and log-transformed data were examined to improve distributional properties; no \(Z\)-score standardization was applied since post-transformation distributions met statistical criteria. Where assumptions were met, parametric tests were used; otherwise, non-parametric equivalents were applied.  
To assess the within-group effects of the intervention, paired \(t\)-tests or Wilcoxon signed-rank tests were used for pre-post comparisons within both the experimental (EG) and control (CG) groups. Mixed-design ANOVA (2 \(\times\) 2) with factors Group (EG vs. CG) and Time (Pre vs. Post) was employed to detect between-group effects and interaction terms. For all key outcome variables Jump Height, Reactive Strength Index (RSI), Peak Power, and Active Stiffness effect sizes (Cohen's d) and 95% confidence intervals were reported in accordance with APA 7 th Edition standards (APA, 2020).  
To explore the functional consequences of asymmetry, bivariate correlations (Pearson or Spearman, depending on distribution) were calculated between asymmetry indices (Impulse, Average Force, Landing RFD, and Time to Peak Force) and performance outcomes. Particular attention was given to testing the predefined hypotheses, including relationships such as Impulse Asymmetry vs. Jump Height and RFD Asymmetry vs. Stiffness. Additionally, participants were stratified into \"High\" and \"Low\" asymmetry subgroups based on a 10% threshold, and between-subgroup differences in functional outcomes were examined.  
To reduce dimensionality and multicollinearity, Principal Component Analysis (PCA) was applied to asymmetry metrics. The extracted components were then entered into LASSO regression models to identify the most parsimonious predictors of performance decrements, such as reduced RSI or power output.  
For individual-level modeling of intervention response, a Linear Mixed-Effects Model (LMM) was constructed with random intercepts per subject and limb nesting structure. This enabled the detection of nuanced Group \(\times\) Time \(\times\) Asymmetry Class interactions.  
In a secondary analysis, machine learning classifiers (Random Forest and Support Vector Machine) were trained using pre-intervention FER and AII indices to predict binary post-intervention adaptation status. Due to the small sample size, a Leave-One-Out Cross-Validation (LOOCV) approach was used. To enable binary classification in the absence of naturally occurring non-responders under standard thresholds (e.g., \(\Delta\)RSI > 0.2), a median-split method was implemented: participants with RSI gains above the group median were classified as \"Responders\", while those below or equal were labeled \"Non-Responders\". ROC curves and AUC values were calculated from probabilistic outputs, and confusion matrices from discrete predictions. Cases where only one class was present during training were handled with default probability assignment to ensure computational stability.  
All results were interpreted at a significance level of \(p\) < 0.05. Multiple comparisons were corrected using false discovery rate (FDR) procedures. Missing data were minimal (<5%) and handled via pairwise deletion. Data integrity was ensured via reproducible pipelines (R Markdown and KNIME workflows), and all code and datasets were archived in an open-access repository (Zenodo).