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The impact of test loads on the accuracy of 1RM prediction using the load-velocity relationship
BMC Sports Science, Medicine and Rehabilitationvolume 10, Article number: 9 (2018)
Numerous methods have been proposed that use submaximal loads to predict one repetition maximum (1RM). One common method applies standard linear regression equations to load and average vertical lifting velocity (Vmean) data developed during squat jumps or three bench press throw (BP-T). The main aim of this project was to determine which combination of three submaximal loads during BP-T result in the most accurate prediction of 1RM Smith Machine bench press strength in healthy individuals.
In this study combinations of three BP-T loads were used to predict 1RM Smith Machine bench press strength. Additionally, we examined whether regression models developed using peak vertical bar velocity (Vpeak), rather than Vmean, provide the most accurate prediction of Smith Machine bench press 1RM. 1RM Smith Machine bench press strength was measured directly in 12 healthy regular weight trainers (body mass = 80.8 ± 5.7 kg). Two to three days later a linear position transducer attached to the collars on a Smith Machine was used to record Vmean and Vpeak during BP-T between 30 and 70% of 1RM (10% increments).
Repeated measures analysis of variance testing showed that the mean values for slope and ordinate intercept for the regression models at each of the load ranges differed significantly depending on whether Vmean or Vpeak were used in the prediction models (P < 0.001). Conversely, the abscissa intercept did not differ significantly between either measure of vertical bar velocity at each load range. The key finding in this study was that 1RM Smith Machine bench press strength can be determined with high relative accuracy by examining Vmean and Vpeak during BP-T over three loads, with the most precise models using Vpeak during loads representing 30, 40 and 50% of 1RM (R2 = 0.96, SSE = 4.2 kg).
These preliminary findings indicate that exercise programmers working with normal healthy populations can accurately predict Smith Machine 1RM bench press strength using relatively light load Smith Machine BP-T testing, avoiding the need to expose their clients to potentially injurious loads.
The quantification of the maximum load that can be lifted through a full range of motion, or one repetition maximum (1RM), is fundamental to the design of resistance training programs . Typically, 1RM is either measured directly or calculated indirectly using predictive models. The direct determination of 1RM suffers from a number of pragmatic issues as it is not only time consuming, but the outcome is effected by factors such as athlete experience, technique, fatigue and motivation . Traditional 1RM testing is considered to be safe when it is conducted in appropriate settings under the supervision of qualified practitioners [3, 4]. Regardless, this 1RM exposes athletes to large musculoskeletal forces, and there is some evidence that 1RM testing can be potentially injurious [5, 6] and may also be impractical with novices and/or in clinical settings .
Indirect methods for 1RM quantification tend to follow two different protocols, both of which rely on the use of linear regression modelling. The most common indirect protocols involve lifting submaximal loads to failure [7,8,9], a procedure that is relatively common in trained athletes  and in agreement with the ACSM guidelines of 8–12 repetition that is often used in a clinical setting, but rare in everyday activities. Although relatively easy to administer, the accuracy of these ‘lift to failure’ models is also influenced by elements such as age, training experience, motivation and lifting tempo [7,8,9, 11]. The prediction of 1RM using these methods appears to be more accurate when heavier loads are used [12,13,14], with the optimal number of repetitions for these prediction models being less than 10 . Accordingly, these protocols potentially suffer from the same limitations associated with 1RM testing, with the need to lift high relative loads whilst fatigued. Additionally, these lift to failure protocols are also likely to generate post exercise muscle soreness in novices , potentially dissuading them from future exercise participation.
Alternative indirect methods rely on the load-velocity [6, 16] or force-velocity [10, 11, 17,18,19] relationships and linear or quasi linear models to predict 1RM from a series of maximal effort lifts with submaximal loads. These protocols use either isoinertial sensors or linear position transducers that are attached to the collars or bar of training devices like Smith Machines to record force, average and/or peak vertical lifting velocity data from the concentric phase of movements like jump squats or bench press throws (BP-T). Although these movements are more common in high performance training programs, the use of a Smith Machine and appropriately trained “Spotters” means that these exercises can be completed safely with novice participants (NB: some Smith Machines contain a pneumatic brake which prevents the bar from descending rapidly – hence improving exercise safety). Although 1RM data recorded on Smith Machines are typically 10% higher than those recorded using free weights, there are no significant differences between predicted 1RM values when using these devices . These protocols also have the advantage of being relatively quick to perform as they involve loads between 30 and 80% of 1RM [11, 16, 21] being lifted as rapidly as possible for only 2–4 repetitions. Accordingly, the overall loading in these protocols is less than ‘lift to failure’ protocols and so the risk of injury may be decreased, particularly when applied to relatively untrained populations .
Arguably, the simplest of the load-velocity models  applies standard linear regression equations to load and mean vertical propulsive lifting velocity (Vmean) data from three different loads to develop slope, abscissa (Load0) and ordinate (Vmean0) intercept data. Importantly, variables such as Vmean or peak vertical velocity (Vpeak) can be measured using relatively inexpensive technology that, due to large reductions in pricing, is becoming increasing accessible to strength coaches. Researchers report high correlations using this methods between Load0 and 1RM bench press (r = 0.98, n = 112, SEE = 4 kg [7%]), although the strength of this relationship is no doubt influenced by the large range in relative loads assessed (30 to 95% of 1RM) [16, 22]. Additionally, participants in the study by Jidovtseff and co-workers  were required to always hold the bar (i.e. prevented from performing a BP-T), which will have a marked effect on Vmean due to the deceleration of the bar near the end of the lift . Nevertheless, some questions remain as to whether Vmean or Vpeak provides superior predictive measures. Recently, Gracia-Ramos and co-workers  report that Vmean during Smith Machine bench press is a superior predictor of 1RM when compared to Vpeak. However, these findings appear to be specific to the testing protocols as these researchers highlight in another study that Vpeak during bench press throws is the superior predictor of 1RM . Regardless, Vmean and Vpeak appear to be greater predictors of optimal load for power training than traditional methods that advocate percentages of 1RM .
Nevertheless, the question remains as to the efficacy of the procedures proposed by Jidovtseff and co-workers , particularly when testing novice or inexperienced weight trainers for which higher lifting loads may be contraindicated. Therefore, it is important to determine whether such high relative loads are required during these submaximal test protocols (i.e. up to 95% of 1RM) and which combination of relative loads result in the most accurate predictive model of 1RM bench press strength. Accordingly, the purpose of this study was to use the prediction model developed by Jidovtseff and coworkers  to determine which combination of three submaximal loads during BP-T result in the most accurate prediction of 1RM Smith Machine bench press strength in healthy individuals. We also examined whether the ability to release the bar during the BP-T changes the nature of the prediction model. Additionally, we examined whether Vmean or Vpeak provides a better prediction of Smith Machine bench press 1RM strength in these participants.
Experimental approach to the problem
To determine which combination of three loads during BP-T results in the most accurate prediction of 1RM bench press strength we tested 12 healthy, regular weight trainers on two separate occasions. On the first occasion 1RM bench press strength was recorded using standard procedures and recorded to the nearest 1 kg . During the second data collection (2–3 days after the first testing session) participants performed three repetitions of BP-T at loads representing 30, 40, 50, 60 and 70% of their 1RM. We then processed these load-velocity BP-T data using the techniques proposed by Jidovtseff and coworkers  to determine which three load range (30–50% of 1RM, 40–60% of 1RM, 50–70% of 1RM) resulted in the most accurate prediction of 1RM bench press strength. We also examined whether BP-T Vmean or Vpeak provides a more accurate prediction of bench press 1RM by comparing each of the models developed using these variables.
Participants for this study (n = 12) were all recreational weight trainers who had been weight training at least twice a week for a minimum of 1 year (body mass (BM) = 80.8 ± 5.7 kg, 1RM 84 ± 18 kg, relative 1RM =1.04 BM [i.e. relative load is represented as a function of BM]). None of the participants were involved in heavy load strength training. Participants were informed of the experimental procedures and risks and provided their written informed consent prior to attending several familiarisation sessions. This research was approved by the institutional Human Research Ethics Committee (No. 2012-N-10).
All bench press and BP-T data were collected on a standard Smith Machine. This machine was modified with a custom made magnetic braking system as a safety mechanism. Once the bar was released this safety mechanism prevented it from falling back on the participant . The bar handle was attached permanently to this braking system, resulting in a total weight of 23 kg. To record the vertical position of the bar a linear position transducer (LPT) (WS17KT, ASM, Moosinning, Germany) was installed on the Smith Machine’s pneumatic brake, with data subsequently sampled at 1000 Hz, A/D converted and stored on a computer, Subsequent data analysis of the LPT measurement were performed in MATLAB, with velocity data developed from the raw LPT outputs using the first central difference method.
The BP-T testing was conducted in accordance with well-established protocols [23, 28, 29] at loads representing 30, 40, 50, 60 and 70% relative to 1RM. The execution order was determined randomly using Microsoft Excel in order to avoid possible order effects during the testing session. In order to minimise the effects of fatigue there were 2–4 min between repetitions with three repetitions completed at each load. The eccentric phase was at a self-chosen speed, with the participants required to wait for the start signal before commencing the concentric motion . There was approximately at 2 s pause between the eccentric and concentric phases.
The Vmean, and Vpeak and maximum bar acceleration were calculated from the first and second differentials of the linear transducer data. These data were then used to develop a linear regression model for the prediction of 1RM  (Fig. 1). We subsequently developed slope, Load0 and Vmean0 data for each of these regressions models over each of the load ranges (i.e. 30–50% 1RM, 40–60% 1RM and 50–70% 1RM).
The influence of load on the various bar kinematic variables were determined via a series of repeated measures analysis of variance (ANOVA) tests. Post-hoc analyses were undertaken using paired t-Test with Bonferroni corrections. Shapiro-Wilk and Mauchly’s test of sphericity were applied during all ANOVA testing. Where data violated the sphericity assumption Greenhouse-Geisser corrections were applied. The relative magnitude of differences were quantified using standard Cohen’s Effect Size (ES) analyses, with the following descriptors used to define the relative magnitude of the ES: < 0.2 = trivial, 0.2–0.6 = small, 0.6–1.2 = medium/moderate, 1.2–2.0 = large, and > 2.0 = very large . The predictive accuracy of the model developed by Jidovtseff and coworkers  was assessed using the three lightest loads (30–50% 1RM), the three middle loads (40–60% 1RM) and the three heaviest loads (50–70% 1RM), with these data then compared with the measured 1RM values. Bland-Altman plots were used to assess whether there were any levels of bias in any of the models, with simple t-tests used to assess for differences between the actual and predicted values. The coefficient of variance (CV%) and the intra class correlations (ICC, 3,1) for the predicted versus the measured 1RM were also calculated. Statistical analysis were performed using the statistics package SPSS for Windows (version 20), with a confidence level of 95%. All data are presented at means ±1 standard deviation (SD) unless stated otherwise.
ANOVA testing indicated that Vmean and Vpeak both showed large, significant reductions (P < 0.001, ES > 1.2) for each respective increase in relative BP-T load, except for Vmean between 40 and 50% of 1RM (Fig. 2). Results also showed that the mean values for slope and Vmean0 at each of the load ranges differed significantly depending on whether Vmean or Vpeak were used in the prediction models (Table 1). Conversely, Load0 data did not differ significantly between either bar velocity measures at each load range. The CV% values range from 7.2 up to 27.5% (Table 2), with the ICC (Table 3) data show excellent reliability for Vpeak at the lightest range weight whereas only moderate reliability was observed for the weights between 40 and 60%. All other cases showed good reliability. Typically, greater levels of acceptable reliability  were recorded for Vpeak compared to Vmean.
There were no noticeable differences in any of the models that used Vmean to predict 1RM Smith Machine bench press strength (R2 between 0.85–0.89). Similarly, there were no significant differences between predicted and actual 1RM Smith Machine (P = 0.21 to 0.95) when using Vmean, although the corresponding Bland-Altman plots highlighting some issues with the accuracy of these data (Fig. 3). Conversely, there were significant differences between the predicted and actual 1RM Smith Machine bench press values when using Vpeak at the lightest of the load ranges to (P < 0.001). However, the predicted 1RM values for Vpeak for these light relative loads (30, 40 and 50% of 1RM) resulted in the most accurate prediction of 1RM bench press strength (Fig. 4), although there was a constant fixed bias towards under estimating 1RM by approximately 9 kg.
This study used the well-established linear-regression techniques proposed by Jidovtseff and coworkers  to examined which combination of three relative submaximal loads during BP-T testing results in the best prediction of 1RM Smith Machine bench press strength. We also examined whether regression models developed using Vpeak, rather than the variable suggested by these researchers (Vmean), provide the best prediction of bench press 1RM. Finally, we examined whether performing a BP-T (instead of an explosive bench press) influences the nature of the regression model when using either of these bar velocity measures.
This study builds upon the findings of Gracia-Ramos and co-workers [24, 25], highlighting that 1RM bench press strength on a Smith Machine can be determined with acceptable levels of precision by examining Vmean and Vpeak during Smith Machine BP-T over three submaximal loads. Perhaps even more importantly, our data suggests that the best and most reliable prediction model was based on relative loads representing just 30, 40 and 50% of 1RM. Importantly, as the prediction is robust for the light relative loads, a rough estimate of the 1RM appears to be sufficient for this method. Although a fixed bias exists to under predict 1RM by approximately 9 kg with using these loads, the accuracy of the model to predict Smith Machine bench press 1RM when using Vpeak during BP-T is quite high. Additionally, the high precision of this regression model is at least comparable to other established prediction procedures that use more time-consuming protocols and/or also possibly have a greater potential for injury or soreness [5, 7,8,9, 12,13,14,15]. From a practical perspective, our findings suggest that there is no need to test over heavy relative and absolute loads [5, 6] when using the force-load technique to estimate Smith Machine 1RM in recreational and novice level weight trainers [5, 7, 8, 12, 14].
The finding that bar velocity data decreases with increasing relative load is not unique and simply confirms the standard exponential force velocity profile first developed by Hill  nearly 80 years ago. Our data for Vmean does however contain an anomaly at 50% of 1RM (Fig. 2), suggesting that the Vmean may be too gross a measure to be able to detect known changes in performance that occur across our load ranges. Similarly, our results also suggest that Vpeak is a more effective measure than Vmean when using this technique to predict 1RM in regular (but non-athletic) weight trainers with a mean 1RM Smith Machine bench press approximately equivalent to 1 body weight. While these findings are agreement with earlier research [20, 25] other studies favour Vmean [24, 26], highlighting that the specific loading regime influences this outcome.
Our Vpeak data are similar to data from physically active collegiate men performing a similar BP-T task , with values between studies differing by less than 0.07 m/s at similar loads. Conversely the slope and Vmean0 data from our models using Vmean to predict 1RM differ considerably from values from the original research using this method . No doubt this is a function of the protocols adopted by these researchers that prevented the participants from releasing the bar (hence performing a dynamic bench press and not a BP-T per se). The use of this approach by these researchers is somewhat surprising as their Vmean data would have been effected by a pronounced bar deceleration near the end of the movement  and so the accuracy of these data could be optimised. Importantly, Vpeak during BP-T testing is not only reliable (CV% values between 1.7 and 3.3), but also presents with smaller CV% values than for dynamic bench press movements [21, 25]. From a practical stand point Vpeak is relatively simple to quantify, as it can be measured using inexpensive devices (e.g. optical encoders or linear position transducers), or estimated using bar throw height. These approaches can be adopted easily in health clubs or commercial gymnasiums and provide acceptable predictions of 1RM that can be used in the development of more effective training programs.
We acknowledge that our testing was based on a relatively small sample of a diverse but specific population of beginning weight training adults, however these samples sizes are relatively common in this domain. Additionally, our sample characteristics are typical for many healthy individuals who attend health clubs and/or commercial strength training facilities. We also acknowledge that it the accuracy of regression models that attempt to predict values outside of the range of the collected data is severely compromised. However, this process is fundamental to all research in this domain and so largely unavoidable. Importantly, we have not suggested that the protocols presented in this project offer an exact estimate of a participant’s Smith Machine 1RM bench press.
Our results suggest that within this target population reliable estimates of Smith Machine 1RM bench press strength can be achieved using the load-velocity approach with BP-T loads between 30 and 50% of 1RM. We do however acknowledge that the reliability and accuracy of the velocity based method presented here can suffer from fatigue or lack of motivation of the athletes. However, issues such as these are systemic in nearly all strength assessment protocols and can be managed with appropriate testing regimens. We also acknowledge that these data are specific to Smith Machine bench press and BP-T, and may not be transferable to conventional free weight testing. Future research should attempt to confirm these results with a larger sample of participants and conduct appropriate between session reliability assessments. Additionally, it would also be appropriate prospectively compare the incidence of soreness and injury between the methods proposed in this study and traditional 1RM determination.
Conventional 1RM bench press strength testing exposes people to very high relative loads. Our findings indicate that in normal healthy populations bar velocity data recorded during relatively light load Smith Machine BP-T testing can be used to accurately predict 1RM Smith Machine bench press strength. The large range in the submaximal load range allows practitioners to estimate the 1RM as start point by using a team average, last season values or a weight dependent 1RM to define the submaximal test weights. Additionally, it is simple to determine Vmean and Vpeak during BP-T testing and the linear regression models are easy to apply. Importantly, our results show that the most accurate and reliable models are created from BP-T Vpeak data (not Vmean), a variable that developed with minimal post-testing processing, from loads representing just 30, 40 and 50% of 1RM. Using the approach described in our study exercise programmers can predict 1RM Smith Machine bench press strength and monitor performance enhancement with acceptable accuracy without the need to expose their clients to extremely heavy loads, or lift to fatigue protocols.
One repetition maximum
Bench press throw
Coefficient of variance
- ICC, 3,1:
Intra class correlations
The abscissa from the linear regression equation derived from load and mean vertical propulsive lifting velocity
Linear position transducer
The gradient of the linear regression equation derived from load and mean vertical propulsive lifting velocity
- Vmean :
Mean vertical propulsive velocity
The ordinate from the linear regression equation derived from load and mean vertical propulsive lifting velocity
- Vpeak :
Peak vertical lifting velocity
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This project received no external funding.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Ethics approval and consent to participate
This research was approved by the ETH Human Research Ethics Committee (No. 2012-N-10). Participants were informed of the experimental procedures and risks and provided their written informed consent prior to attending several familiarisation sessions.
The authors declare that they have no competing interests.
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