Comparison of the bench press one-repetition maximum obtained by different procedures: Direct assessment vs. lifts-to-failure equations vs. two-point method

Abstract

This study examined the differences in the bench press one-repetition maximum obtained by three different methods (direct method, lifts-to-failure method, and two-point method). Twenty young men were tested in four different sessions. A single grip width (close, medium, wide, or self-selected) was randomly used on each session. Each session consisted of an incremental loading test until reaching the one-repetition maximum, followed by a single set of lifts-to-failure against the 75% one-repetition maximum load. The last load lifted during the incremental loading test was considered the actual one-repetition maximum (direct method). The one-repetition maximum was also predicted using the Mayhew’s equation (lifts-to-failure method) and the individual load–velocity relationship modeled from two data points (two-point method). The actual one-repetition maximum was underestimated by the lifts-to-failure method (range: 1–2 kg) and overestimated by the two-point method (range: –3 to –1 kg), being these differences accentuated using closer grip widths. All predicted one-repetition maximums were practically perfectly correlated with the actual one-repetition maximum (r ≥ 0.95; standard error of the estimate ≤ 4 kg). The one-repetition maximum was higher using the medium grip width (83 ± 3 kg) compared to the close (80 ± 3 kg) and wide (79 ± 3 kg) grip widths (P ≤ 0.025), while no significant differences were observed between the medium and self-selected (81 ± 3 kg) grip widths (P = 1.000). In conclusion, although both the Mayhew’s equation and the two-point method are able to predict the actual one-repetition maximum with an acceptable precision, the differences between the actual and predicted one-repetition maximums seem to increase when using close grip widths.

Keywords

Load–velocity relationship maximal dynamic strength resistance training strength testing

Introduction

Resistance training intensity is commonly quantified and prescribed as a percentage of an individual’s one-repetition maximum (1RM).¹ The direct assessment of the 1RM consists of determining the maximum load that can be lifted just once for a given exercise (i.e. direct method).² However, the limitations associated with the direct method (e.g. time consuming or physically and psychologically demanding) have promoted the proliferation of different strategies for predicting the 1RM.^3–6 First studies proposed 1RM prediction equations based on the maximum number of repetitions completed to failure with a submaximal load (i.e. lifts-to-failure method).^5,7,8 More recently, the assessment of the individual load–velocity relationship has been recommended for predicting the 1RM,^3,4 being possible to estimate the 1RM from the velocity collected under only two loading conditions (i.e. two-point method).⁹

The bench press is probably the most used exercise for the development of upper-body strength and power during resistance training programs.^10,11 Previous studies have confirmed the validity of different lifts-to-failure equations to estimate the bench press 1RM in various populations.^8,12,13 Similarly, the individual load–velocity relationship modeled by the two-point method also seems to provide an accurate prediction of the bench press 1RM.^14,15 The main advantage of the lifts-to-failure method over the two-point method is that no sophisticated equipment is needed to estimate the 1RM (e.g. linear position transducer), while the main advantage of the two-point method is that subject do not need to reach muscular failure to estimate the 1RM.¹⁶ However, to the best of our knowledge, only two studies have compared the accuracy between the lifts-to-failure and velocity-based methods for predicting the 1RM.^16,17 García-Ramos et al.¹⁶ observed that the lifts-to-failure methods (Lombardi’s and O’Connor’s equations) overestimated the actual 1RM (range: 3–4 kg) during the free-weight prone bench pull exercise, while no significant differences were found when the 1RM was estimated through the individualized load–velocity relationship modeled either by the multiple- (∼50–60–70–80% of 1RM) or 2- (∼50–80% of 1RM) point methods (range: –1 to 0 kg). Pérez-Castilla et al.¹⁷ observed that the lifts-to-failure methods (Mayhew’s and Wathan’s equations) significantly underestimated the actual 1RM (range: –7 to –2 kg) during the lat pull-down and seated cable row exercises, while no systematic differences were reported for when the 1RM was estimated through the individualized load–velocity relationship modeled either by the multiple- (∼40–55–70–85% of 1RM) or 2- (40–85% of 1RM) point methods (range: –2 to 2 kg). Therefore, there is a need for more research to elucidate which prediction method (lifts-to-failure or two-point method) is able to estimate the bench press 1RM with a higher precision.

One of the most important factors when assessing bench press performance is the grip width.^18–20 In this regard, it is important to note that previous studies that have assessed the feasibility of lifts-to-failure and velocity-based methods to estimate the bench press 1RM have used a standardized grip width slightly higher than shoulder-width apart or a self-selected grip width.^8,14,21 Therefore, it is unknown whether the precision in the estimation of the bench press 1RM could be affected by the grip width. Although slight variations in the grip width do not meaningfully affect the magnitude of the 1RM load,²² the decrease in the grip width has been associated with a lower number of repetitions completed to failure²² and higher bar velocities^18,23 when lifting the same absolute load. Therefore, it is plausible that the prediction of the bench press 1RM using the lifts-to-failure and two-point methods could be affected by the grip width. Specifically, based on the results presented above, the decrease in the grip width could be associated with an underestimation of the 1RM using the lifts-to-failure method and an overestimation of the 1RM using the two-point method.

To address the existing gaps in the literature, the present study was designed to examine the accuracy of lifts-to-failure (i.e. Mayhew equation) and velocity-based (i.e. two-point method) methods for predicting the 1RM during the bench press exercise performed in a Smith machine using four different grip widths (close, medium, wide, and self-selected). Specifically, the aims of this study were (I) to compare the magnitude of the bench press 1RM between the direct, lifts-to-failure, and two-point methods, and (II) to explore the concurrent validity of the lifts-to-failure and two-point methods for predicting the bench press 1RM using different grip widths. We hypothesized that (I) a comparable 1RM load would be obtained for the three methods using wider grip widths (self-selected and wide grip widths), while the highest 1RM would be obtained for the two-point method (i.e. overestimate the actual 1RM) and the lowest 1RM for the lifts-to-failure method (i.e. underestimate the actual 1RM) using closer grip widths (close and medium grip widths), and (II) both prediction methods would report an acceptable and comparable level of precision for estimating the bench press 1RM.

Methods

Experimental approach to the problem

A randomized crossover design was used to examine the accuracy of the Mayhew’s lifts-to-failure equation and the two-point method for predicting the 1RM during the bench press exercise performed in a Smith machine using four grip widths. Following a familiarization session, the close, medium, wide, or self-selected grip widths were tested in a randomized order during four sessions separated by 48–72 h (Figure 1). All sessions consisted of an incremental loading test until reaching the 1RM, followed by a set of lifts-to-failure against the 75% 1RM load. All sessions were performed at the same time of the day for each subject (±1 h) and under similar environmental conditions (∼22°C and ∼60% humidity).

Figure 1.

Overview of the experimental design.

Subjects

Twenty male collegiate sports science students volunteered to participate in this study (mean ±standard deviation (SD): age = 22.5 ± 3.7 years (range: 19–33 years), body mass = 77.9 ± 13.1 kg, height =1.78 ± 0.06 m). The sample size was calculated to detect a 7.5 kg difference between the actual and predicted 1RM with an effect size (ES) of 0.7.³ All subjects were physically active and none of them had injuries or musculoskeletal pain that could compromise bench press performance. Subjects were instructed to avoid any strenuous exercise over the course of the study. All subjects were informed of the procedures to be utilized and signed a written informed consent form before initiating the study. The study protocol adhered to the tenets of the Declaration of Helsinki and was approved by the University of Granada Institutional Review Board (IRB approval: 491/CEIH/2018).

Testing procedures

The bench press was performed according to the five-point body contact position technique (head, upper back, and buttocks firmly on the bench with both feet flat on the floor). Subjects started the bench press exercise lying supine on a flat bench, with their feet resting on the floor, their elbows fully extended, and their hands placed on the bar using either a close, medium, wide, or self-selected grip width. From this position, they lowered the bar in a controlled manner until it made contact with the chest, hold this position for approximately 2 s, and then lifted the bar as fast as possible until their elbows reached full extension.²⁴ The position of the bench was adjusted so that the vertical projection of the bar corresponded to each subject’s intermammary line. The close grip width represented a 100% of the biacromial width (38.6 ± 2.5 cm (35–45 cm)), the medium grip width a 150% of the biacromial width (57.8 ± 3.8 cm (53–68 cm)), the wide grip width a 200% of the biacromial width (77.1 ±5.0 cm (70–90 cm)), and the self-selected grip width a 174 ± 22% of the biacromial width (67.0 ± 8.6 cm (44–78 cm)).

Each testing session began with a standardized warm-up consisting of jogging, dynamic stretching, arm and shoulder mobilization exercises, and one set of five repetitions with an external load of 15 kg (mass of the unloaded Smith machine bar). The warm-up was followed by a standard incremental loading test²¹ using one of the four grip widths (close, medium, wide, or self-selected). The initial external load was set at 15 kg and was progressively increased in 10 kg until the attained mean velocity was lower than 0.50 m⋅s⁻¹ and afterward the load was increased from 5 to 1 kg until the 1RM load was reached. Two repetitions were performed with light–moderate loads (mean velocity ≥ 0.50 m⋅s⁻¹) and one repetition with heavy loads (mean velocity < 0.50 m⋅s⁻¹). Intra-set rest between repetitions was 10 s and inter-set rest 3 min. Once the 1RM was determined, subjects rested for 10 min, and then they performed a single set of lifts-to-failure against the 75% 1RM load. The lifts-to-failure assessment ended when the subjects were not able to perform a repetition with the full range of motion. Subjects were instructed to perform all repetitions at maximal intended velocity, and they received velocity performance feedback immediately after each repetition to encourage them to give maximal effort.

Equipment

Height, body mass, and biacromial width were measured using a wall-mounted stadiometer (Seca 202, Seca Ltd., Hamburg, Germany), a contact electrode foot-to-foot body fat analyzer system (TBF-300A, Tanita Corporation of America Inc., Arlington Heights, IL, USA), and a large sliding caliper (Campbell 20, Rosscraft Innovation Inc., Vancouver, Canada), respectively. All tests were performed in a Smith machine (GervaSport, Madrid, Spain). A linear velocity transducer (T-Force System, Ergotech, Murcia, Spain), which sampled the instantaneous vertical velocity of the bar at 1000 Hz, was used to collect the mean velocity of all repetitions. Validity and reliability of the T-Force system for the recording of mean velocity during the bench press exercise has been reported elsewhere.²⁵

1RM prediction methods

Lifts-to-failure method

The Mayhew et al.⁸ equation (1RM = (load/52.5 + 41.9⋅e^−0.055⋅repetitions)/100) was used to predict the bench press 1RM from the load (kg) and number of repetitions completed. The Mayhew et al.⁸ equation was used for statistical analyses since it provided lower absolute errors (3 ± 2 kg) than other lifts-to-failure equations such as the Brzycki⁷ equation (6 ± 7 kg), Epley²⁶ equation (4 ±4 kg), Lander²⁷ equation (6 ± 7 kg), Lombardi²⁸ equation (5 ± 2 kg), O’Connor et al.²⁹ equation (6 ± 3 kg), and Wathan³⁰ equation (4 ± 4 kg).

Velocity-based method

The individual load–velocity relationship was determined from the mean velocity recorded against only two loads (i.e. two-point method). The closest load of the incremental loading test to a mean velocity of ≈ 0.90 m⋅s⁻¹ (46.4 ± 3.8% of 1RM) and ≈ 0.40 m⋅s⁻¹ (84.5 ± 3.6% of 1RM) were considered for the application of the two-point method. The bench press 1RM was estimated from the individual load–velocity relationships as the load (kg) associated with a mean velocity of 0.17 m⋅s⁻¹.¹⁴

Statistical analyses

Data are presented as means and SDs. The normal distribution of the data (Shapiro–Wilk test) and the homogeneity of variances (Mauchly’s sphericity test) were confirmed (p > 0.05). A two-way repeated measures ANOVA (method × grip width) with Bonferroni post-hoc corrections was conducted to compare the magnitude of the 1RM as well as the absolute differences between the actual and predicted 1RM. The magnitude of the differences was reported by the partial eta squared ( $η_{p}^{2}$ ) and Hedge’s g ES, as appropriate. The criteria to interpret the magnitude of the ES was as follows: trivial (<0.20), small (0.20–0.59), moderate (0.60–1.19), large (1.20–2.00), and very large (>2.00).³¹ The validity of the 1RM prediction methods with respect to the actual 1RM was assessed from the magnitudes of the absolute errors, Pearson’s correlation coefficient (r), the standard error of the estimate (SEE), and Bland–Altman plots. The following criteria was used to examine the strength of the correlations: trivial (<0.1), small (0.1–0.3), moderate (0.3–0.5), high (0.5–0.7), very high (0.7–0.9), or practically perfect (>0.9).³¹ Heteroscedasticity of error in the Bland–Altman plots was defined as a coefficient of determination (r²) > 0.1.³² Statistical analyses were performed using the software package SPSS (version 22.0; SPSS, Inc., Chicago, IL, USA). Alpha was set at p < 0.05 level.

Results

The average number of loads tested during the incremental loading test was 8 ± 1 (close grip width), 9 ± 1 (medium grip width), 9 ± 2 (wide grip width), and 9 ± 1 (self-selected grip width). The average number of repetitions performed during the lifts-to-failure assessment was 10 ± 3 (close grip width), 10 ± 2 (medium grip width), 11 ± 3 (wide grip width), and 11 ± 3 (self-selected grip width).

The ANOVA did not reveal a significant method ×grip width interaction (F_(6,126) = 1.96, p = 0.077, $η_{p}^{2}$ = 0.09). By contrast, the ANOVA revealed significant main effects for method (F_(2,42) = 14.2, p < 0.001, $η_{p}^{2}$ = 0.43) and grip width (F_(3,63) = 4.09, p =0.011, $η_{p}^{2}$ = 0.18). The main effect of method was caused by the higher 1RM observed for the two-point method (83 ± 3 kg) compared to the direct (81 ± 3 kg, p = 0.001, 95% confidence interval (CI) = –3 to –1 kg, ES range = 0.10–0.22) and lifts-to-failure (79 ± 3 kg, p = 0.001, 95% CI = –6 to –1 kg, ES range = 0.15–0.40) methods. The main effect of grip width was caused by the higher 1RM observed for the medium grip width (83 ± 3 kg) compared to the close (80 ± 3 kg, p = 0.025; 95% CI = –6 to –0 kg, ES range = 0.19–0.29) and wide (79 ± 3 kg, p = 0.036, 95% CI = 0–7 kg, ES range = 0.18–0.33) grip widths, but no significant differences were observed between the medium and self-selected (81 ± 3 kg, p = 1.000, 95% CI = –2 to 5 kg, ES range = 0.08–0.13) grip widths. Finally, it should be noted that a progressive reduction in the differences between the lifts-to-failure method (underestimated the actual 1RM) and the two-point method (overestimated the actual 1RM) with respect to the direct method was observed with the increment of the grip width (Figure 2).

Figure 2.
Comparison of the bench press one-repetition maximum obtained by different methods using a close (upper-left panel), medium (upper-left panel), wide (lower-left panel), and self-selected (lower-right panel) grip width. Data depicted as means and standard deviation, whereas each point represents the data of an individual subject.

Both 1RM prediction methods reported low absolute errors (range: 3–4 kg) and practically perfect correlations (r ≥ 0.95 and SEE ≤ 4 kg) with respect to the actual 1RM (Figure 3). The absolute differences between the actual and predicted 1RM did not reveal a significant main effect either for method (F_(1,19) =0.04, p = 0.843, $η_{p}^{2}$ = 0.00), grip width (F_(3,57) = 0.62, p = 0.607, $η_{p}^{2}$ = 0.03), or their interaction (F_(3,57) =0.65, p = 0.585, $η_{p}^{2}$ = 0.03).

Figure 3.
Absolute differences between the actual and predicted one-repetition maximum (1RM) during the bench press exercise performed in a Smith machine using a close (upper-left panel), medium (upper-right panel), wide (lower-left panel), and self-selected (lower-right panel) grip width. The Pearson’s correlation coefficient (r) and the standard error of the estimate (SEE) between the actual and predicted 1RM are also indicated.

Bland–Altman plots revealed that the predicted 1RMs obtained from the lift-to-failure (Figure 4) and two-point (Figure 5) methods presented low systematic bias (range: 1 to 2 kg and –1 to –3 kg, respectively) and random error (range: 3–4 kg and 3–4 kg, respectively) when compared with the actual 1RM for the different grip widths. Of particular note is that the lifts-to-failure method systematically underestimated the actual 1RM, while the two-point method tended to overestimate the actual 1RM. No heteroscedasticity of the errors was observed between the actual and predicted 1RMs (r² ≤ 0.04) with the exception of the 1RM estimated from the lifts-to-failure method using the medium grip width (r² = 0.12).

Figure 4.
Bland–Altman plots showing the differences between the actual one-repetition maximum (1RM) and the 1RM predicted from the lift-to-failure method during the bench press exercise performed in a Smith machine using a close (upper-left panel), medium (upper-right panel), wide (lower-left panel), and self-selected (lower-right panel) grip width. Each plot depicts the systematic bias and 95% limits of agreement (±1.96 SD; dashed lines), along with the regression line (solid line). The systematic bias ± random error together with the strength of the relationship (r²) are depicted in each plot.

Figure 5.
Bland–Altman plots showing the differences between the actual one-repetition maximum (1RM) and the 1RM predicted from the two-point method during the bench press exercise performed in a Smith machine using a close (upper-left panel), medium (upper-right panel), wide (lower-left panel), and self-selected (lower-right panel) grip width. Each plot depicts the systematic bias and 95% limits of agreement (± 1.96 SD; dashed lines), along with the regression line (solid line). The systematic bias ± random error together with the strength of the relationship (r²) are depicted in each plot.

Discussion

This study was designed to compare the 1RM performance during the bench press exercise performed in a Smith machine using four different grip widths between the direct, lifts-to-failure, and two-point methods. The main finding of the present study revealed an underestimation of the actual 1RM by the lifts-to-failure method and an overestimation of the actual 1RM by the two-point method, being these differences accentuated using closer grip widths. However, a practically perfect correlation was always observed between the predicted and actual 1RM. Taken together, although an acceptable level of precision for the estimation of the bench press 1RM was observed regardless of the prediction method and the grip width, it should be noted that the differences between the actual and predicted 1RMs may increase when using closer grip widths.

The 1RM is commonly considered as the primary reference to evaluate an individual’s maximal dynamic strength capacity and to prescribe training intensity during resistance training programs.¹ To our knowledge, this is the first study that has compared the magnitude of the 1RM between three methods (i.e. direct, lifts-to-failure, and two-point methods) during the bench press exercise using four different grip widths (i.e. close, medium, wide, and self-selected). Supporting our first hypothesis, the 1RM load did not significantly differ between the three methods using the two wider grip widths (self-selected and wide grip widths), while the highest 1RM was obtained using the two-point method (i.e. overestimated the actual 1RM) and the lowest 1RM using the lifts-to-failure method (i.e. underestimated the actual 1RM) for the two closer grip widths (close and medium grip widths). The results regarding the comparisons between the grip widths may be explained by the higher number of repetitions that can be performed before reaching muscular failure²⁰ and the higher bar velocities^18,23 observed using closer grip widths. In addition, the differences in the 1RM between the methods could also be explained by the different degree of fatigue. Namely, the two-point method may have overestimated the actual 1RM because the subjects were less fatigued when performing the last repetition used for the application of the two-point method (∼85% of 1RM) in comparison to the 1RM trial, while the underestimation of the actual 1RM by the lifts-to-failure method may be explained because subjects were more fatigued at the beginning of the set of lifts-to-failure in comparison to the 1RM trial.

Researchers are constantly trying to find practical methods to objectively prescribe the strength training stimulus in an attempt to maximize athletic performance gains and to minimize the likelihood of overtraining and injuries.⁴ Supporting our second hypothesis, both lifts-to-failure and two-point methods reported an acceptable level of precision to estimate the bench press 1RM regardless of the grip width. These results are in line with previous research that proposed generalized equations based on lifts-to-failure^8,12,13 or movement velocity^24,33 to estimate the bench press 1RM using either a self-selected or standardized grip width slightly higher than shoulder-width apart. More importantly, our findings are in consensus with the available evidence that supports the feasibility of the two-point method as a practical and objective procedure for predicting 1RM in a variety of upper-body resistance training exercises.^14,16,17 However, unlike previous studies that suggested that the individualized load–velocity profile could provide a more accurate estimation of the 1RM compared to the lifts-to-failure methods for the free-weight prone bench pull,¹⁶ lat pull-down, and seated cable row exercises,¹⁷ no systematic differences were observed between both methods in the present study for the estimation of the 1RM during the bench press exercise performed in a Smith machine. Therefore, sport professionals should weigh the particular advantages of lifts-to-failure method (e.g. no equipment needed) and the two-point method (e.g. less prone to fatigue) to select their preferred method for predicting the 1RM during the bench press exercise.

It is well documented that changes in the grip width affect the biomechanics and muscle activation patterns during the bench press exercise.^18,23,34 In this regard, previous studies have been conducted to identify which is the most advantageous grip width to maximize the bench press 1RM performance.^18,19,23 For example, Wagner et al.¹⁹ showed that medium grip widths (130–165% of biacromial width) allowed a greater force production compared to both closer (95–130% of biacromial width) and wider grip widths (235–270% of biacromial width) in resistance-trained individuals. Gomo and Van Den Tillaar¹⁸ also found that both a self-selected and medium grip widths (74.5 ± 9.8 cm and 56.8 ± 6.0 cm, respectively) resulted in a significantly higher 1RM load compared to a close grip width (39.2 ± 3.5 cm) in competitive powerlifters. In line with the results presented above,^18,23 our results evidenced a significantly higher 1RM using a medium grip width compared to the extreme grip widths (i.e. close and wide grip widths). However, it should be noted that the magnitude of the differences were trivial or small. It is plausible that the higher load lifted using medium grip widths is caused by a superior mechanical advantage¹⁸ and higher contribution of the pectoralis major.³⁴ Of particular note is that no significant differences were observed between the medium and self-selected grip widths. The average self-selected grip width in the present study (174% of biacromial width) was comparable to the self-selected grip width previously reported in the literature (175–189% biacromial width).^19,23 Therefore, the self-selected grip width could be recommended for a more practical and ecologically valid assessment of the bench press 1RM in a Smith machine.

Several limitations should be acknowledged. First, our study sample was composed exclusively of young physically active men and, therefore, it is questionable whether our findings can be extrapolated to other populations (e.g. elderly people or strength-trained athletes). Second, it is plausible that the relationship between the actual 1RM and the 1RM predicted by the lifts-to-failure and two-point methods could be affected by the anthropometric characteristics (e.g. arm length, chest depth, etc.)¹³ and this is an important point to explore in future studies. Finally, since the Smith machine restricts the movement of the barbell to the vertical direction, it is also plausible that the main finding of the present study could differ for the free-weight bench press exercise.

Conclusions

The Mayhew’s lifts-to-failure equation and the two-point method reported an acceptable and comparable level of accuracy for predicting the 1RM during the Smith machine bench press exercise performed using different grip widths. The 1RM load did not significantly differ between the three methods using the two wider grip widths (self-selected and wide grip widths), while the highest 1RM was obtained using the two-point method (i.e. overestimated the actual 1RM) and the lowest 1RM using the lifts-to-failure method (i.e. underestimated the actual 1RM) for the two closer grip widths (close and medium grip widths). Therefore, it seems that the accuracy of both 1RM prediction methods could be slightly affected by the grip width (higher differences with respect to the actual 1RM using closer grip widths).

Footnotes

Acknowledgements

We would like to thank all the subjects who selflessly participated in the study.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the Ministerio de Educación y Formación Profesional under a pre-doctoral grant (FPU15/03649) awarded to AP-C. This research was funded by the Universidad Católica de la Santísima Concepción (DINREG 09/2019).

ORCID iDs

Alejandro Pérez-Castilla

Amador García-Ramos

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