Classical one-rep max prediction equations — Epley, Brzycki, Lombardi, O'Conner — all assume a fixed conversion factor between repetitions performed and maximal strength. Lift any weight to failure, count the reps, apply a single multiplier. The formula doesn't care whether you're lifting 20 pounds or 200. It applies the same conversion regardless.
A dataset of 303,494 near-failure sets across 388 exercises from a fitness app reveals why this assumption fails. The conversion factor isn't fixed — it varies logarithmically with the weight lifted. At light weights, each additional repetition implies a larger fraction of maximal capacity than at heavy weights. The relationship between reps and %1RM changes depending on where you are on the load spectrum.
The proposed formula — 1RM = w(1 + (r-1)^0.85 / (-2.55 + 4.58·ln(w))) — reduces prediction inconsistency by 17-22% compared to all four classical benchmarks, and the improvement is positive for every one of 183 exercises with sufficient data. Ablation analysis attributes 91% of the improvement to the weight-dependent conversion factor and only 9% to the sub-linear repetition exponent.
The methodological innovation is the evaluation criterion. There are no directly measured maxima in the dataset — nobody tested their true 1RM. Instead, the formula is optimized for internal consistency: when the same person performs different weight-rep combinations on the same exercise in the same time window, how well do the estimates agree? The ground truth is self-concordance rather than external measurement. Classical equations, by applying a single conversion factor across all loads, systematically underestimate variation — and the discrepancy is largest for the lighter exercises that dominate real-world training.