In the realm of competitive sports, understanding the performance dynamics of
athletes, represented by the age curve (showing progression, peak, and
decline), is vital. Our research introduces a novel framework for quantifying
age-specific treatment effects, enhancing the granularity of performance
trajectory analysis. Firstly, we propose a methodology for estimating the age
curve using game-level data, diverging from traditional season-level data
approaches, and tackling its inherent complexities with a meta-learner
framework that leverages advanced machine learning models. This approach
uncovers intricate non-linear patterns missed by existing methods. Secondly,
our framework enables the identification of causal effects, allowing for a
detailed examination of age curves under various conditions. By defining the
Age-Conditioned Treatment Effect (ACTE), we facilitate the exploration of
causal relationships regarding treatment impacts at specific ages. Finally,
applying this methodology to study the effects of rest days on performance
metrics, particularly across different ages, offers valuable insights into load
management strategies' effectiveness. Our findings underscore the importance of
tailored rest periods, highlighting their positive impact on athlete
performance and suggesting a reevaluation of current management practices for
optimizing athlete performance.

通过引入新的分析框架，本研究对运动员的表现动态进行了量化，提高了对性能轨迹的细致分析，揭示了隐含的非线性模式，并通过定义年龄条件化治疗效应（ACTE）的方式，探索了年龄对治疗效果的因果关系，最终发现个性化休息周期对运动员性能的积极影响，为优化运动员表现的管理实践提供了有价值的见解。