Cross-Validation of Equations for Estimating 1 Repetition Maximum From Repetitions to Failure for the Bench Press and Leg Extension

Roberts, TD, Smith, RW, Arnett, JE, Ortega, DG, Schmidt, RJ, and Housh, TJ. Cross-validation of equations for estimating 1 repetition maximum from repetitions to failure for the bench press and leg extension. J Strength Cond Res XX(X): 000-000, 2024-Eighteen previously published equations (EQs) that estimate 1 repetition maximum (1RM) from repetitions to failure (RTF) were cross-validated for the bench press (BP) and leg extension (LE) movements. Forty-three recreationally active men (age: 20.58 ± 1.47 years; body mass [BM]: 81.66 ± 13.65 kg) completed a 1RM test and RTF at 80% of the 1RM test for the LE, and 39 of the 43 men (age: 20.61 ± 1.48 years; BM: 83.58 ± 12.73 kg) completed the same tests for the BP. The EQs were categorized as generic (the source did not indicate its applicability for a specific movement) or movement-specific (BP-specific and LE-specific EQs). The generic EQs were cross-validated for both movements, whereas the BP-specific and LE-specific EQs were cross-validated for their respective movements only. The cross-validation criteria included calculations of the constant error (CE) (mean differences between estimated and measured 1RM), Pearson Correlation Coefficient, standard error of the estimate, and total error. The level of significance was set at p ≤ 0.05. After the initial cross-validation analyses of the previously published EQs, the most accurate EQs were modified by subtracting their cross-validation CE from the original EQ to improve their accuracy for estimating BP and LE 1RM by eliminating systematic error. The modified EQs were then cross-validated using the same statistical procedures. Based on the cross-validation analyses, we recommend the following EQs: BP 1RM = (RTF0.1 × weight) + 1.49 and LE 1RM = (RTF0.1 × weight) + 1.06 using weights that result in 4-10 RTF.