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Original Research

Development of 1RM Prediction Equations for Bench Press in Moderately Trained Men

Macht, Jordan W.1; Abel, Mark G.1; Mullineaux, David R.2; Yates, James W.1

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Journal of Strength and Conditioning Research: October 2016 - Volume 30 - Issue 10 - p 2901-2906
doi: 10.1519/JSC.0000000000001385
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Muscular strength is now universally recognized as an important attribute for most sports. Assessing muscular strength is considered important for setting performance goals and evaluating athletes' progress. Also, upper-body muscular strength is important for the elderly, young adults, athletes at all levels, and all physically active populations. One of the most common techniques used for evaluating dynamic muscular strength is the 1 repetition maximum (1RM) procedure. Although this procedure is a popular assessment of maximal dynamic strength, it does have some limitations. First, many novice resistance trainers or those who do not often use a particular lift may be reluctant to continue adding weight to reach a true maximal effort (8). Second, because the 1RM protocol requires the lifter to perform multiple sets before attempting the 1RM, fatigue may occur and may reduce the accuracy of the 1RM assessment. Third, performing a 1RM may be time consuming because adequate recovery is required between sets. It is recommended that 2–4 minutes of rest be provided to the subject between each set of the 1RM protocol (2). Fourth, research has indicated that injuries may be associated with performing a 1RM procedure in some populations (25,29). Thus, the utilization of an accurate, time efficient, and safe procedure for estimating a 1RM may be warranted and could have practical benefit for coaches and strength and conditioning professionals.

An alternative approach to maximal dynamic strength performance which has gained some support is the estimation of 1RM with a prediction equation based on performing repetitions to fatigue (RTF). For individuals who are unfamiliar with strength training, attempting a 1RM with heavy loads may be difficult, intimidating, unsafe, and time consuming. Using a lighter load and performing RTF may not make the lifter apprehensive, will be less time consuming, and offer some margin of safety. The basis of these prediction equations is the strong association between 1RM and the number of repetitions needed to reach fatigue (4,15,16,19,26,28). However, some of these equations lack sufficient information regarding their sample characteristics from which they were developed, which makes it difficult to know which equation should be used to predict a given individual's 1RM. The use of 1RM determinations to set resistance levels of intensity (i.e., %1RM) for training purposes makes it essential to have an accurate measurement of an individual's strength level for a particular lift. Therefore, careful scrutiny of the methods used to estimate 1RM is required to avoid overestimating the 1RM which could increase the risk of injury or underestimating the 1RM which would provide a reduced training stimulus.

Some authors have suggested that the addition of anthropometric dimensions might help reduce the prediction error of some equations, making the estimation of 1RM when using RTF more accurate (9,30,33). Other studies have suggested that anthropometric variables alone may provide sufficient accuracy for 1RM prediction (7,21,24). For the bench press, the most common variables selected appear to be arm and chest circumferences, limb lengths, and relative body fat (7,21,24). To date, there seems to be no universally accepted proposal of which variables provide the best estimate of 1RM performance. Yet unexplored are ancillary measurements such as hand grip strength that might further enhance the accuracy of 1RM prediction equations. It would benefit the strength and conditioning specialist to know the degree to which ancillary variables might contribute to the prediction of 1RM strength. Therefore, the purpose of this study was to determine the degree to which selected anthropometric dimensions and grip strength might assist RTF in making accurate predictions of 1RM bench press performance in moderately trained men.


Experimental Approach to the Problem

The current study sought to determine the contribution of ancillary factors which might reduce the error in 1RM bench press prediction in moderately trained men. Anthropometric variables were selected based on previous studies that noted the improvement in prediction when these factors were incorporated with submaximal load and RTF to estimate 1RM bench press (1,9,21,24,30). Because previous studies have suggested that less than 10 RTF offered better estimation of 1RM bench press, the current subjects were randomly assigned loads equivalent to 75–95% of 1RM which were theorized to produce from 1 to 10 repetitions. Equations were then generated using anthropometric variables alone, submaximal loads and RTF alone, and a combination of the 2 approaches to estimate 1RM bench press.


Sixty moderately trained men qualified for and agreed to participate in this study (age range of 18 to 30 years). Subjects qualified for this study if they had been resistance training for at least 2 months (training frequency ≥2 days per week) before the study, and did not have upper extremity orthopedic issues that would limit their full participation. Subject characteristics are presented in Table 1. The study was approved by the University's Institutional Review Board, and written informed consent was obtained from each subject before participation in the study.

Table 1.
Table 1.:
Physical characteristics of the subjects (n = 60).*


Data collection took place on 2 days for each subject, separated by at least 48 hours to minimize the effects of fatigue. Subjects performed the 1RM bench press protocol during the first testing session and were assessed for selected anthropometric dimensions. During the second session, subjects completed the RTF protocol. Before any procedures were administered, the subjects were required to complete the Physical Activity Readiness Questionnaire form to ensure that they met minimum standards for healthy participation.

During the first testing session, anthropometric characteristics were recorded before strength assessment. Standing height was measured without shoes (to the nearest 1 cm) using a wall-mounted stadiometer. Body mass was measured without shoes (to the nearest 0.1 kg) using a digital scale (Model DI-10; Teraoka Weigh-System, Ltd., Summerset, NJ, USA). Body density was estimated from the sum of 7 skinfolds measured with Lange calipers (Beta Technology, Inc., Cambridge, MD, USA) according to the procedures of Jackson and Pollock (12,13). Body density was converted to percent body fat using the Siri equation (32). Chest circumference was assessed with a spring loaded retractable tape (Medco Supplement Company, Fort Worth, TX, USA) and measured around the subject's chest at nipple level at midexpiration. The maximum circumference of the flexed arm was taken with the subject's arm abducted to 90° (parallel to the floor), and the shoulder and arm flexed at 90°. Upper extremity skeletal lengths were also taken with an anthropometer (Rosscraft Campbell Caliper 20; QuickMedical Instruments, Issaquah, WA, USA) from the acromion process to the olecranon process (arm length) and the olecranon process to the styloid process (forearm length). Biacromial width was measured in the horizontal plane between the acromium processes using an anthropometer (Rosscraft Campbell Caliper 20; QuickMedical Instruments). Cross-sectional area (CSA) of the flexed arm was determined from circumference corrected for triceps skinfold (18). Bench press drop distance was measured as the vertical distance the bar traveled from full arm extension to the sternum.

Handgrip Strength Testing Protocol

A handgrip dynamometer (Model 78010; Lafayette Instrument Co., Lafayette, IN, USA) was used to determine right and left isometric grip strengths. The dynamometer was set at position 2 of the handgrip dynamometer and was ensured that it was a comfortable grip width for each subject and held with the elbow bent at 90°. They were instructed to provide a maximal effort in 3 trials for each hand, separated by 1 minute rest. The best trials for each hand were added to determine total grip strength.

One Repetition Maximum Testing Protocol

A standard 1RM testing protocol was used for the assessment of the 1RM as outlined by the National Strength and Conditioning Association (2). Specifically, the subject warmed up with a light resistance that easily allowed 5–10 repetitions. After a 1-minute rest, 4–9 kg was added, and the subject attempted to complete 3–5 repetitions. After a 2-minute rest, another 4–9 kg was added, and the subject attempted to complete 2–3 repetitions. After a 4-minute rest, another 4–9 kg was added, and the subject attempted 1 repetition. If the attempt was successful, a 2–4-minute rest was given, and more weight was added, based on the subject's judgment, until the subject could not complete 1 repetition. The reliability for technique has been shown to exceed r = 0.94 (11,31).

Repetitions to Fatigue Testing Protocol

To begin the RTF protocol, the subjects performed a warm-up consisting of static stretching of the chest, arms, shoulders, and upper back and 1 set of push-ups from the floor with the subject on his toes or knees, whichever they preferred. Subjects were then randomly assigned a percentage of their 1RM between 75 and 95% to use for their RTF weight. Each subject performed as many repetitions as possible with the assigned load, with no pause between repetitions. The bar was slowly lowered until it touched the lower border of the pectoralis and then pressed slowly over the AC joints until the elbows were locked out. If the subject performed more than 10 repetitions with the assigned load, 4–9 kg was added and another set was performed after a 5-minute rest.

Statistical Analyses

Pearson product moment correlations were used to determine the relationship of independent variables with 1RM bench press, repetition weight, and RTF. Modified Bland-Altman (17) plots were used to assess the level of agreement (LoA) between the predicted and actual 1RM. Stepwise multiple regression analysis was used to generate prediction equations from the anthropometric and performance data. The presence of multicollinearity among multiple predictor variables was determined if there were large changes in the regression coefficients of a predictor variable when another predictor variable was added or deleted from the model (27). Secondly, multicollinearity was evaluated through the use of variance inflation factor (VIF) (27). In this formal detection tolerance test, a VIF >5 indicates that multicollinearity exists in the model (27). In addition to determining the absolute mean difference in predicted 1RM load between weaker and stronger individuals, the percentage of the measured 1RM was calculated as a relative index of prediction equation accuracy (RIPA) using the following equation: RIPA = 100 − ([measured 1RM − predicted 1RM]/measured 1RM × 100).


The relationships between the subjects' anthropometric characteristics and measured 1RM bench press strength are presented in Table 1. Seven of the 11 anthropometric dimensions were significantly correlated with 1RM. The same variables were significantly correlated with repetition weight (RepWt) but to a lesser degree. None of the anthropometric dimensions were significantly correlated with RTF.

Several equations were developed to predict 1RM bench press (Table 2). In the best anthropometric equation, arm CSA contributed the largest part to the explained variance in bench press (61%), with chest circumference (18%), %fat (17%), and arm length (4%) offering considerably less. Because of their small contribution to the overall variance, removing %fat and arm length from the equation reduced the multiple correlation and increased the standard error of estimate only slightly.

Table 2.
Table 2.:
Regression equations to predict 1RM bench press (n = 60).*

Although the best anthropometric equation yielded a small mean difference between predicted and actual 1RM, it tended to produce wide limits of agreement and an unfavorable correlation (r = −0.24, p ≤ 0.05) between prediction equation bias and measured 1RM. If the stronger lifters were considered the top 40% of the sample and the weaker lifters were consider the bottom 40%, this equation tended to underestimate the measured 1RM for stronger subjects (0.9 ± 2.6 kg) and overestimate the measured 1RM for weaker subjects (0.9 ± 4.4 kg) (Figure 1).

Figure 1.
Figure 1.:
Modified Bland-Altman plot of the anthropometric prediction equation for 1 repetition maximum bench press in high- and low-strength male subjects.

Stepwise regression using only performance characteristics (RepWt, RTF, and grip strength) selected RepWt and RTF as the significant variables to estimate 1RM (Table 2). This equation had the highest correlation with 1RM with no significant correlation between prediction equation bias and measured 1RM (r = −0.13, p = 0.33) and an acceptable LoA (Figure 2). It estimated 1RM equally well in stronger and weaker subjects (Figure 2).

Figure 2.
Figure 2.:
Modified Bland-Altman plot of the performance prediction equation for 1 repetition maximum bench press in high- and low-strength male subjects.

In an attempt to evaluate the effect of the addition of various anthropometric variables to the performance equation, each variable was added in a hierarchical regression model. Using this approach, none of the anthropometric variables added more than 0.1% contribution to the known variance of the performance model of RepWt and RTF.


A major finding of this study was that various combinations of anthropomorphic variables had almost as high a correlation with 1RM bench press as did a performance-based equation. This agreed with previous work on moderately trained men (7,21), adolescent powerlifters (23), and college football players (24). The current work supports a pattern suggesting that arm size is the most important factor in estimating bench press potential. Keogh et al. (14) concluded that individuals wishing to enhance their lifting performance should concentrate on muscular hypertrophy. Indeed, the only variable significantly different between their stronger and weaker powerlifters was flexed arm size. Thus, it might benefit individuals wishing to improve their bench press performance to gain arm size. Because of lack of magnetic resonance imaging of the arm to determine CSA of the triceps, we can only speculate on the degree to which the hypertrophy should be focused on that muscle. Although greater prediction precision might be achieved by determining the triceps area alone, it is worth noting that the biceps is a major stabilizing muscle during the movement (21). Although arm CSA was positively related to body mass (r = 0.78, p < 0.001), when the influence of body mass was held constant, the relationship of CSA with bench press was reduced only slightly (r = 0.76).

Similar consideration might be given to chest circumference as a predictor of bench press performance. In addition to the involvement of the pectorial muscles as prime movers in the bench press, the latissimus dorsi is also a stabilizer of the shoulder girdle during the maneuver (21). Although chest (r = 0.23, p = 0.08) and subscapular (r = 0.31, p = 0.02) skinfolds were related to 1RM bench press, it is virtually impossible to calculate the cross-sectional area of the torso muscle mass using chest circumference (r = 0.75, p < 0.001) and skinfolds. The positive relationship between chest circumference and bench press was reduced significantly when body weight was held constant (r = 0.28). This suggests that perhaps some of the ability to achieve larger loads in the bench press may be more related to arm size than to chest or overall body size.

In the current study, the addition of anthropometric variables did not reduce the prediction error associated with the performance-based equations. The performance-based equations produced an SEE of 3.7 kg and the anthropometric equation produced an SEE of 13.0 kg (Table 2). This agreed with a previous study on college football players (22) but disagreed with other studies (9,33). Part of the discrepancy with previous studies may lie in the repetition performance method used to assess the football players. In each of the studies, an absolute endurance task (i.e., the NFL-225 test) was used. When such a test is used, larger individuals tend to produce greater 1RM values. In addition, larger individuals tend to have greater anthropometric dimension which could spuriously inflate the relationship between these dimensions and muscle strength. Furthermore, the %1RM represented by the absolute load had a much greater range than used in the current study, allowing a higher number of RTF. Several sources have suggested that better prediction occurs when RTF are maintained at 10 or less (7,15,19,20).

Braith et al. (3) and Hoeger et al. (10) earlier suggested that training may alter the relationship between muscle strength and muscle endurance. More recent studies have found no significant change in the relationship between muscle strength and endurance (20). It may be that the association between endurance and strength is curvilinear and may reach an asymptote with long duration of training (19,20). It may also be that dissociation between muscle strength and endurance does not manifest until a specific duration or level of resistance training has occurred. However, the overriding factor in the relationship between muscle strength and muscle endurance is likely to be the resistance training program. Heavy-resistance, low-repetition training programs are more likely than endurance to develop strength whereas low-resistance, high-repetition training may improve muscle endurance to a greater degree (5,6).

The lack of relationship between grip strength and bench press strength was similar to previous findings and probably points to the specificity of training. Agbuga et al. (1) noted little support for grip strength as a general representation of upper-body strength in college football players. Despite the frequent activation of forearm muscles when gripping the bar during arm exercises, the stimulus to the muscles may be more related to muscle endurance than to strength. The isometric measurement of grip strength may not correlate with a multijoint dynamic movement such as the bench press. No studies appear to have been done to determine the concomitant change in grip strength with gains in bench press.

Practical Applications

This study suggests that anthropometric measures may be used to determine a rough estimate of maximal bench press potential. However, the prediction error from an anthropometric equation was 3 times larger than that of a performance prediction equation. Thus, the addition of anthropometric variables to performance variables does not appear to enhance the prediction of 1RM bench press in moderately trained men. Furthermore, the magnitude of the multiple R for the performance equation might suggest that a moderate level of training may refine the relationship between high-intensity endurance repetitions and strength in a multi-joint exercise such as the bench press. Previous research has shown that the number of familiarization trials required to reach a true 1RM decreases with experience (31).

The equation that used the CSA of the upper arm developed in this study is among the first nonperformance-based equations to predict the 1RM in the bench press. This equation can also be used to predict the starting load for a lifter performing a 1RM prediction protocol. Once this load is identified, a percentage of it can be taken to find the weight that can be used for RTF. Then, a 1RM prediction equation can be used to accurately predict a subject's 1RM. If an estimated 1RM is known, the measured 1RM can be completed in fewer sets. These techniques may improve the efficiency and decrease the fatigue associated with 1RM and RTF testing protocols. These techniques will benefit strength and conditioning professionals by saving time, and aid in reaching a more accurate 1RM or a predicted 1RM. To measure the CSA of the upper arm a strength and conditioning professional should have experience in performing a triceps skinfold and a flexed upper-arm circumference.


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strength prediction; resistance training; upper body

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