## 1 Introduction  
Neuromuscular asymmetries are prevalent among elite athletes and have been increasingly recognized as potential contributors to performance variability and injury risk [1, 2]. In sports requiring rapid changes of direction, unilateral force production, and reactive movements such as badminton lower-limb asymmetries may impact kinetic efficiency and functional output [3]. While asymmetries have traditionally been viewed as deleterious beyond a threshold of 10-15% [4], recent evidence suggests that their interpretation must be context-dependent, accounting for sport-specific demands and individual compensation strategies [5]. Functional asymmetries and force efficiency are critical factors in the performance and injury risk of elite junior badminton players. Recent controlled trials and related studies have used hop test metrics and neuromuscular adaptation indices to assess these aspects, aiming to understand how training interventions can address asymmetries and enhance force efficiency. Significant functional asymmetries are commonly observed in both upper and lower limbs of elite youth athletes, including those in racquet sports like tennis and badminton. These asymmetries are measurable through tests such as single-leg hop and countermovement jumps, with notable differences between dominant and non-dominant limbs. The direction of asymmetry (which limb is favored) often varies between different tasks, indicating that asymmetries are task-specific and not consistently linked to one limb across all activities [6; 7]. Asymmetry magnitudes can be substantial, with some tests showing differences exceeding 14% between limbs [7; 8]. Improvements in hop test performance (distance, speed, and landing mechanics) are associated with enhanced biomechanical efficiency and reduced injury risk, particularly for lower limb injuries like ACL tears [9; 10]. Key neuromuscular metrics include time to peak muscle contraction, muscle elasticity, and explosive strength. Regular assessment and targeted training can lead to significant improvements in these indices, reflecting better force production and efficiency [10; 11; 12]. Adding cognitive challenges to neuromuscular training can further improve postural stability and hop performance, suggesting a holistic benefit for both physical and perceptual-motor skills [13; 14]. Among the various asymmetry metrics, impulse, peak force, and rate of force development (RFD) have been frequently used in both cross-sectional and longitudinal studies [15]. However, these conventional measures often suffer from statistical instability particularly when mean values are low and may lack sufficient predictive power when applied in isolation [1]. Consequently, the need for composite and functionally interpretable indices has been emphasized in recent sports science literature [16]. The reactive strength index (RSI), a ratio of flight time to ground contact time, has emerged as a key performance indicator in explosive movements such as single-leg hopping and drop jumping [17; 18]. Yet, few studies have systematically examined how RSI adapts in response to asymmetry-targeted interventions, particularly among elite adolescent athletes. Moreover, recent advances in machine learning and multivariate modeling provide a novel opportunity to characterize inter-limb neuromechanical profiles and predict training responses with higher precision [19; 20]. Algorithms such as Random Forest and LASSO regression have demonstrated superior classification and variable selection performance compared to traditional linear models, especially in datasets with multicollinearity and small samples [21; 22]. However, their utility in predicting training responsiveness based on asymmetry-based indices remains underexplored. This study examined whether a 4-week asymmetry-focused neuromuscular program could improve hop performance and predict training response in elite youth badminton players.