Table1_Longitudinal performance trajectories of young female sprint runners: a new tool to predict performance progression.docx

BackgroundLongitudinal performance tracking in sports science is crucial for accurate talent identification and prognostic prediction of future performance. However, traditional methods often struggle with the complexities of unbalanced datasets and inconsistent repeated measures.
PurposeThis study aimed to analyze the longitudinal performance development of female 60 m sprint runners using linear mixed effects models (LMM). We sought to generate a practical tool for coaches and researchers to establish benchmarks and predict performance development.
MethodsWe analyzed 41,123 race results from 8,732 female 60 m track sprinters aged 6–15 years, collected from the Swiss Athletics online database between 2006 and 2021. Only season-best times per athlete and only athletes with at least 3 season-best times in their career were included. LMM was used to generate performance trajectories, benchmarks, and individual predictions. A practical software tool was developed and made available to allow individual performance prediction based on race times from previous seasons. In addition, classic empirical percentile curves were constructed using the Lambda-Mu-Sigma (LMS) method.
ResultsLMM handled the dataset's complexities, producing robust longitudinal performance trajectories. Compared to empirical percentiles generated using the LMS method, which provided a retrospective view of performance development, the mixed model approach identified individualized longitudinal performance developments and estimated predictions of future performance. The best-fitting model included log-transformed chronological age (CA) as a fixed effect and random intercepts and slopes for each athlete. This model explained 59% of the variance through fixed effects (marginal R2) and 93% through combined fixed and random effects (conditional R2).
ConclusionLMM provided longitudinal sport performance data, enabling the establishment of performance benchmarking and prediction of future performance. The software tool can assist coaches in setting realistic training goals and identifying promising athletes.

研究背景
运动科学领域的纵向表现追踪，对于精准的人才选拔以及未来运动表现的预后预测至关重要。然而，传统方法往往难以应对非平衡数据集的复杂性以及重复测量不一致的问题。

研究目的
本研究旨在采用线性混合效应模型（Linear Mixed Effects Models, LMM）分析女子60米短跑运动员的纵向表现发展轨迹，并为教练员与科研人员构建性能基准、预测表现发展趋势提供实用工具。

研究方法
本研究分析了2006年至2021年间从瑞士田径（Swiss Athletics）在线数据库中获取的8732名6至15岁女子60米短跑运动员的41123条比赛成绩数据。筛选标准为：仅纳入每名运动员的赛季最佳成绩，且仅保留职业生涯中至少拥有3次赛季最佳成绩的运动员。本研究采用线性混合效应模型生成表现轨迹、性能基准及个体预测结果，并开发了一款实用软件工具，可基于运动员过往赛季的比赛成绩实现个体表现预测。此外，本研究还采用Lambda-Mu-Sigma（LMS）方法构建了经典的经验百分位曲线。

研究结果
线性混合效应模型可有效应对数据集的复杂性，生成稳健的纵向表现轨迹。相较于仅能回顾性展现表现发展趋势的LMS法经验百分位曲线，混合模型方法可识别个体化的纵向表现发展轨迹，并实现未来运动表现的预估。最优拟合模型以对数转换后的实足年龄（Chronological Age, CA）作为固定效应，并为每名运动员设置随机截距与随机斜率。该模型的固定效应可解释59%的变异（边际R²），固定与随机效应联合可解释93%的变异（条件R²）。

研究结论
线性混合效应模型可提供纵向运动表现数据，助力构建运动表现基准体系并预测未来运动表现。本研究开发的软件工具可辅助教练员设定合理的训练目标，并识别具有潜力的运动员。