Cross-Validation of Original and Modified Equations for Estimating Bench Press One-Repetition Maximum from Repetitions to Failure in Recreationally Active Men

Justin S. Pioske^1, , Jocelyn E. Arnett¹, Dolores G. Ortega¹, Trevor D. Roberts¹, Richard J. Schmidt¹ and Terry J. Housh¹

¹Department of Nutrition and Health Sciences, University of Nebraska Lincoln, Lincoln, NE 68583, USA

Cite this paper:
Justin S. Pioske, Jocelyn E. Arnett, Dolores G. Ortega, Trevor D. Roberts, Richard J. Schmidt and Terry J. Housh. Cross-Validation of Original and Modified Equations for Estimating Bench Press One-Repetition Maximum from Repetitions to Failure in Recreationally Active Men. American Journal of Sports Science and Medicine. 2025; 13(1):1-7. doi: 10.12691/ajssm-13-1-1

Abstract

The purpose of this study was to cross-validate four (two original and two modified) equations (EQs) that estimate 1-repetition maximum (1RM) from repetitions to failure (RTF) for the bench press (BP). Thirty-five recreationally active men (mean ± SD: age = 20.5 ± 1.4 yrs; height = 181.3 ± 6.4 cm; body mass = 84.8 ± 12.5 kg) with previous resistance training experience (5.0 ± 2.9 yrs) participated in this study. Each participant completed BP 1RM testing followed by a single set of RTF at ~80% 1RM. The values from the RTF at ~80% 1RM were inputted into the EQs for estimating BP 1RM. The cross-validation analyses consisted of examining the constant error (CE) values using paired t-tests, Pearson Correlation Coefficients (r), standard error of estimate (SEE), and total error (TE) values. The RTF at 80% 1RM ranged from 4-11 repetitions. The results revealed that EQs 2, 3, and 4 significantly (p < 0.05) overestimated BP 1RM with CE values of 2.13 kg, 0.92 kg, and 1.70 kg, respectfully, while EQ 1 did not differ (p = 0.091) from the measured 1RM values (CE = -0.57 kg). The cross-validation analyses indicated that modified EQ 3 (TE = 2.12 kg) did not improve the accuracy of BP 1RM estimations compared to original EQ 1 (TE = 1.99 kg). Modified EQ 4, however, exhibited slightly more accurate BP 1RM values (TE = 3.27 kg) than original EQ 2 (TE = 3.51). In addition, EQ 1 provided the lowest CE and TE values as well as the smallest difference between TE and SEE values (0.03 kg). Therefore, EQ1 (RTF^0.1 x weight) is recommended for estimating BP 1RM with a weight that results in 4-11 RTF in recreationally active men when directly testing 1RM is not feasible or to assist in training intensity prescription.

Keywords:
error prediction bench press one-repetition maximum equations repetitions to failure muscular strength

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