[论文解读] A Weight-Dependent 1RM Prediction Equation Optimized on 303,494 Near-Failure Sets Across 388 Exercises

Thiago Marzagao|arXiv (Cornell University)|Mar 18, 2026

Sports Performance and Training被引用 0

一句话总结

论文推导出一个随重量相关的1RM预测方程，基于跨388种练习的大规模近失败数据拟合，显示相比经典固定系数模型具有更好的一致性。

ABSTRACT

Classical equations for predicting one-repetition maximum (1RM) from submaximal performance were derived from small samples performing a single exercise, yet are routinely applied to hundreds of exercises. All use a fixed conversion factor relating repetitions to estimated 1RM, regardless of exercise or load. We used large-scale observational data from a consumer fitness app (303,494 near-failure sets from 14,966 users across 388 exercises spanning 16 muscle groups) to derive and evaluate a generalization in which the conversion factor varies logarithmically with the weight lifted: 1RM = w * (1 + (r - 1)^0.85 / (-2.55 + 4.58 * ln(w))). Because the dataset contains no directly measured maxima, we optimized and evaluated the formula using an internal consistency criterion -- the degree to which different weight-repetition combinations from the same person, exercise, and time window yield the same estimated 1RM. The proposed formula reduced inconsistency by 17-22% relative to four classical benchmarks, with the improvement positive for every one of the 183 exercises with sufficient data. Five-fold user-level cross-validation confirmed near-zero overfitting. An ablation analysis attributed 91% of the improvement to the weight-dependent conversion factor and 9% to the sub-linear repetition exponent. The conversion factor increases with load: at light weights each additional repetition implies a larger fraction of maximal capacity than at heavy weights, consistent with prior evidence that the repetitions-%1RM relationship varies by exercise. Classical equations, by applying a single conversion factor across all loads, systematically underestimate this variation -- and the discrepancy is largest for the lighter, more diverse exercises that dominate real-world training programs.

研究动机与目标

• 需要 generalized 1RM预测模型以捕捉不同练习和负载之间的变异性。
• 利用消费健身应用的大规模近失败数据来优化一个随重量变化的转换因子。
• 使用内部一致性和交叉验证评估所提方程相较于经典基准。
• 识别重量相关性对预测改进的贡献以及亚线性重复效应的贡献。

提出的方法

• 推导一个随重量相关的转换因子，其中 1RM = w * (1 + (r - 1)^0.85 / (-2.55 + 4.58 * ln(w))).
• 使用来自14,966名用户和388种练习、涵盖16个肌群的303,494组近失败数据进行优化。
• 通过同一用户/练习/时间窗口的不同重量-重复组合对所估计1RM的一致性来评估。
• 进行五折用户层面的交叉验证以评估过拟合。
• 进行消融分析，将改进归因于重量相关因子与亚线性重复指数二者的贡献。

实验结果

研究问题

• RQ1 与固定转换基准相比，重量相关的1RM换算是否能在广泛练习中改善内部一致性？
• RQ2 在重复-1RM关系中的重量相关因子与亚线性指数对改进的贡献各占多少？
• RQ3 在跨越大量练习的用户层面验证时，该模型对过拟合是否稳健？

主要发现

• 所提公式相较于四个经典基准，在183个足够统计功效的练习中将不一致性降低了17%-22%。
• 五折用户层面交叉验证显示几乎零过拟合。
• 消融分析将改进的91%归因于重量相关转换因子，9%归因于亚线性重复指数。
• 转换因子随负载增加而增大，意味着相较于 heavier 重量，较轻重量的每次增加重复所占的最大容量比例更大。
• 应用单一转换因子的经典方程系统性低估了负载和练习的变异性，在较轻、更多样化的练习中差异最大。