Developmental changes of vertical jump performance in young female basketball and volleyball players: A Bayesian multilevel modeling approach

This study examined developmental trajectories of vertical jump performance in young female basketball and volleyball players using Bayesian multilevel modeling. Eighty-one Brazilian female athletes (basketball: n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 46; volleyball: n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 35) aged 11-18 years were assessed between 2016-2024 in a mixed longitudinal design. Models examined longitudinal age-related changes in countermovement jump performance, sport-specific differences, and body size effects. Results showed non-linear developmental patterns with accelerated improvement during early-to-mid adolescence followed by deceleration. Sport differences emerged in baseline performance levels rather than timing. Age effects strengthened after adjusting for body size ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>β</mml:mi> <mml:mtext>age</mml:mtext> </mml:msup> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 0.25, 68% credible interval [CI]: 0.17, 0.34; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>β</mml:mi> <mml:mrow> <mml:msup> <mml:mtext>age</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msup> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> -0.18, 68% CI: -0.28, -0.08), indicating neuromuscular adaptations distinct from increases in body size. Body mass negatively associated with jump performance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>β</mml:mi> <mml:mtext>body mass</mml:mtext> </mml:msup> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> -0.35, 68% CI: -0.44, -0.25), while stature positively associated ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> <mml:mi>a</mml:mi> <mml:mi>t</mml:mi> <mml:mi>u</mml:mi> <mml:mi>r</mml:mi> <mml:mi>e</mml:mi> </mml:mrow> </mml:msup> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 0.20, 68% CI: 0.10, 0.29). Volleyball players demonstrated lower baseline performance than basketball players ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>β</mml:mi> <mml:mrow> <mml:mi>v</mml:mi> <mml:mi>o</mml:mi> <mml:mi>l</mml:mi> <mml:mi>l</mml:mi> <mml:mi>e</mml:mi> <mml:mi>y</mml:mi> <mml:mi>b</mml:mi> <mml:mi>a</mml:mi> <mml:mi>l</mml:mi> <mml:mi>l</mml:mi> </mml:mrow> </mml:msup> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> -0.35, 68% CI: -0.43, -0.27). Substantial between-athlete variability in baseline performance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>σ</mml:mi> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi>n</mml:mi> <mml:mi>t</mml:mi> <mml:mi>e</mml:mi> <mml:mi>r</mml:mi> <mml:mi>c</mml:mi> <mml:mi>e</mml:mi> <mml:mi>p</mml:mi> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 0.31) suggests limited predictive validity of early assessments. Our findings provide substantial female-specific evidence for developmental patterns in youth team sport athletes and demonstrate the utility of Bayesian methods for handling incomplete longitudinal data.