(26) CROSS-VALIDATION OF ORIGINAL AND MODIFIED EQUATIONS FOR ESTIMATING BENCH PRESS ONE REPETITION MAXIMUM FROM REPETITIONS TO FAILURE

Purpose: The purpose of this study was to use cross-validation procedures to determine the validity of the original equations (EQs) developed by Lombardi in 1989 (EQ 1) and Mayhew et al. in 1992 (EQ 2), as well as the modified versions of EQ 1 and EQ 2 proposed by Roberts et al. in 2025 (EQ 3 and EQ 4, respectively) for estimating bench press (BP) one repetition maximum (1RM) from a single set of repetitions to failure (RTF) at ~80% 1RM. Methods: 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) volunteered to participate in this study. Each participant completed BP 1RM testing followed by a single set of RTF at ~80% 1RM. The 1RM testing procedure was consistent with the protocol established by the National Strength and Conditioning Association. Repetitions were considered successful if the participants maintained 5-points of contact (head, shoulders, buttocks, left foot, and right foot) throughout the repetition; the bar was lowered in a controlled manner to lightly touch the mid-chest region; and the elbows reached full extension at the end of the concentric phase. For the RTF at ~80% 1RM, participants were instructed to avoid resting between repetitions at the starting position, and the test was terminated when participants rested for more than 1-2 seconds or could not complete a repetition with proper technique. The following four EQs were used to estimate BP 1RM from RTF: EQ 1 (Lombardi original = RTF^0.1 x weight); EQ 2 (Mayhew et al. original = W/([52.2 + 41.9e^-0.055-RTF]/100)); EQ 3 (Roberts et al. modified EQ 1 = ([RTF^0.1 x weight] + 1.49)); and EQ 4 (Roberts et al. modified EQ 2 = ([W/([52.2 + 41.9e^-0.055-RTF]/100)] – 0.43)). EQ 3 and EQ 4 were derived using a previously determined constant error (CE) value (CE = estimated mean – measured mean) to adjust the y-intercepts of the original EQ 1 and EQ 2. The cross-validation analyses in the present study consisted of examining the CE values using paired t-tests, Pearson Correlation Coefficients (r), standard error of estimate (SEE), and total error (TE = √[∑estimated value – measured value]²/n) values. Results: The participants’ RTF at 80% 1RM ranged from 4-11 repetitions. EQ 2, EQ 3, and EQ 4 significantly (p < 0.05) overestimated BP 1RM with CE values of 2.13 kg (EQ 2), 0.92 kg (EQ 3), and 1.70 kg (EQ 4), while EQ 1 did not differ (p = 0.091) from the measured 1RM values (CE = -0.57). All four EQs exhibited r values of 0.99. The SEE values for the four EQ were 1.96 kg (EQ 1 and EQ 3) and 2.79 kg (EQ 2 and EQ 4). The TE values for the four EQ were 1.99 kg (EQ 1), 2.12 kg (EQ 3), 3.27 kg (EQ 4), and 3.51 kg (EQ 2). Conclusions: The modified version of EQ 1 (EQ 3) did not improve the accuracy of BP 1RM estimations compared to the original EQ 1. The estimations of EQ 4, however, exhibited slightly more accurate BP 1RM values than EQ 2. In addition, EQ 1 provided the lowest CE and TE values as well as the smallest difference between TE and SEE values. Practical Applications: Based on these cross-validation analyses, the original of Lombardi (EQ 1 = RTF^0.1 x weight) with a resistance that results in 4-11 RTF is recommended for estimating BP 1RM when directly testing 1RM is not feasible or to assist in training intensity prescription. Acknowledgements: None.