[Paper Review] 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 Training0 citations

TL;DR

The paper derives a weight-dependent 1RM prediction equation fitted to a large-scale near-failure dataset across 388 exercises, showing improved consistency over classical fixed-factor models.

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.

Motivation & Objective

• Motivate the need for a generalized 1RM prediction model that accounts for variation across exercises and loads.
• Leverage large-scale near-failure data from a consumer fitness app to optimize a weight-dependent conversion factor.
• Evaluate the proposed equation against classical benchmarks using internal consistency and cross-validation.
• Identify the contribution of weight-dependence versus sub-linear repetition effects to prediction improvement.

Proposed method

• Derive a weight-dependent conversion factor where 1RM = w * (1 + (r - 1)^0.85 / (-2.55 + 4.58 * ln(w))).
• Use 303,494 near-failure sets from 14,966 users and 388 exercises spanning 16 muscle groups for optimization.
• Evaluate consistency by how different weight-repetition combinations from the same user/exercise/time window yield the same estimated 1RM.
• Perform five-fold user-level cross-validation to assess overfitting.
• Conduct ablation analysis to attribute improvement to the weight-dependent factor versus the sub-linear repetition exponent.

Experimental results

Research questions

• RQ1 Does a weight-dependent 1RM conversion improve internal consistency across a wide range of exercises compared to fixed-conversion benchmarks?
• RQ2 How much of the improvement arises from the weight-dependent factor versus the sub-linear exponent in the repetitions-1RM relationship?
• RQ3 Is the proposed model robust to overfitting when validated at the user level across many exercises?,

Key findings

• The proposed formula reduced inconsistency by 17-22% relative to four classical benchmarks across 183 sufficiently powered exercises.
• Five-fold user-level cross-validation showed near-zero overfitting.
• 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, implying lighter weights have a larger fraction of maximal capacity per added repetition than heavier weights.
• Classical equations applying a single conversion factor systematically underestimate load- and exercise-specific variation, with the largest discrepancies for lighter, more diverse exercises.