The one repetition maximum (1RM) assessment is a well-established, valid, and reliable method of determining maximal strength (13,20). However, the overall time commitment associated with performing 1RM assessments for large squads of team sport athletes can be problematic. In addition, maximal strength has been reported to change rapidly (23), and frequent testing can take valuable time away from training. Consequently, regression equations to estimate 1RM, using the maximum number of repetitions performed to concentric muscular failure with a submaximal load, have been established (4,5,21,24,26). However, the accuracy of these equations may vary according to the type of exercise, amount of repetitions completed, gender, and training status (13,19,33). Furthermore, if a strength coach wanted to frequently monitor changes in maximal strength using 1RM prediction equations, the requisite sets performed to exhaustion may result in excessive fatigue and diminish the force generating capacity in subsequent sets performed within the same training session leading to lower strength gains and power adaptations (15,16,28,29). Therefore, an alternate less fatiguing method for determining an individual's maximal strength is required.
Because of the advancement in kinetic and kinematic transducer technologies, it is now possible to accurately measure bar velocity (11,27). Specifically, 3 methods to quantify concentric movement velocity include peak concentric velocity, mean concentric velocity, and mean propulsive velocity (2,8,11,28). Importantly, even though peak concentric velocity is a pertinent measure for explosive-type resistance training exercises such as bench throws and countermovement jumps, mean concentric velocity is believed to better represent the different velocities observed through the entire phase of nonaerial movements like the squat (8,16,17,27,31). That being said, Sánchez-Medina, Pérez, and González-Badillo (28) suggested that during nonaerial movements, mean concentric velocity underestimates the barbell movement velocity at lighter loads because of the need for an individual to decelerate the barbell velocity at the top of the lift to maintain balance. Instead, they suggest using mean propulsive velocity, which measures the average velocity during the concentric phase of a lift when acceleration of the barbell is greater than the acceleration because of gravity (propulsive phase) (28). However, even though mean propulsive velocity has been shown to be a key variable in many studies (8,11,27,28), it is also noted that it may add an unnecessary level of complexity to velocity measurements for strength and conditioning practitioners (27).
During resistance training exercises, if repetitions are performed with maximal concentric effort and consistent displacement, heavier loads will be lifted at slower velocities than lighter loads. Furthermore, research has shown that an inverse linear relationship exists between load and mean concentric velocity (3,17). As a result, it has been suggested that individualized linear regression equations (using the load–velocity relationship) can be used to accurately predict the 1RM (18). Although helpful, the predicted 1RM findings from Jidovtseff et al. (17) were completed using a pause between the eccentric and the concentric portions of the bench press exercise performed on a Smith machine. Exercises using the stretch shortening cycle (SSC) are known to produce greater amounts of concentric force, velocity, and power than exercises performed with a pause technique or concentric-only exercises (1). Therefore, the mean concentric velocity used in the load–velocity relationship to predict 1RM is likely to differ in free-weight exercises compared with the back squat performed with a pause technique on a Smith machine. Furthermore, a traditional free-weight back squat with a barbell incorporates vertical and some horizontal movement (9). However, a Smith machine back squat is performed with a vertical movement only. Thus, the combination of the Smith machine and pause squat technique would likely provide different results in the measurement of mean concentric velocity compared with the free-weight back squat. As a consequence, the results of Jidovtseff et al. (17) may not be applicable to strength training exercises performed with free-weights or without a pause between the eccentric and concentric portions of the lift. Moreover, because exercises using the SSC are more frequently performed and known to provide great transfer to performance tasks such as running and jumping (1,30,31), it is important to understand whether the load–velocity relationship can predict the 1RM in these types of exercises.
Recently, a theoretical paper has suggested that the load–velocity relationship may be a useful tool for predicting the 1RM for the back squat exercise (18). If the prediction was found to be precise, the mean concentric bar velocity measured in sets performed during the warm-up of a strength training session could then be used to monitor any potential day-to-day variation in maximal strength that may occur when athletes are fatigued. Importantly, if the load–velocity relationship is sensitive enough to predict subtle changes in fatigued athletes, the stability of its predictions must first be established in nonfatigued conditions when maximal strength is theoretically stable. Thus, for accurate sessional predictions of 1RM to occur, the day-to-day variability of the 1RM and the mean concentric bar velocity at 1RM (V1RM) in a free-weight back squat must first be established. Such a finding could then help to determine whether V1RM could be used to predict changes in maximal strength throughout a season resulting in more accurately modified training loads. Therefore, the purpose of this study was to determine the reliability and validity of the load–velocity relationship to predict 1RM. It is hypothesized that the load–velocity relationship will be valid and reliable for the prediction of 1RM, with the 90% prediction being the most valid and reliable of the prediction methods.
Experimental Approach to the Problem
In this study, we investigated the reliability and validity of the load–velocity relationship to predict 1RM for the back squat. The load–velocity relationship was used to develop individualized linear regression equations using mean concentric velocity of 3 (20, 40, 60% of 1RM), 4 (20, 40, 60, and 80% of 1RM), or 5 (20, 40, 60, 80, and 90% of 1RM) incremental loads. As a consequence, the individualized 1RM prediction models based on 3, 4, or 5 sets were termed 60, 80, and 90%, respectively. Once the individualized regression equation was determined, the mean concentric velocity at 1RM (V1RM) for that session was used in the regression equation to predict the 1RM (Figure 1).
Seventeen healthy male resistance-trained volunteers were recruited for this study (25.4 ± 3.3 years, 181.6 ± 6.4 m, 81.8 ± 9.9 kg). All subjects were free from any musculoskeletal injuries, able to perform the full depth back squat with at least 1.5 times their body mass, and had 5.9 ± 2.9 years of resistance training experience, which ranged from 1 to 10 years. The subject's average one repetition maximum (1RM) back squat, 1RM to body mass ratio, and peak knee flexion angle at the bottom of the squat were: 140.3 ± 27.2 kg, 1.71 ± 0.16 kg·kg−1, and 121.2 ± 10.9°, respectively. All volunteers read and signed informed consent forms before participation in the present study in accordance with the ethical requirements of Edith Cowan University Human Research Ethics Committee.
All subjects performed four 1RM assessments with each trial separated by 48 hours (Figure 2). The initial 1RM assessment performed in the familiarization session was not included in the analyses of this study but was conducted, so that accurate relative 1RM loads could be lifted for the remaining three 1RM sessions (trials 1, 2, and 3). In session 1, subjects were informed of the testing procedures and had their height, body mass, safety rack height, and barbell rack height recorded. They then completed all required documentation, which was then followed by the initial 1RM assessment.
One Repetition Maximum (1RM) Assessment
The 1RM assessments were performed in a custom-built power cage (Fitness Technology, Adelaide, Australia) using a 20-kg barbell (Eleiko, Halmstad, Sweden). As shown in Figure 2, at the commencement of session 1 and each trial, the subjects performed a warm-up procedure consisting of 5 minutes pedaling on a cycle ergometer (Monark 828E cycle ergometer; Vansbro, Dalarna, Sweden) at 100W at 60 revolutions per minute, 3 minutes of dynamic stretching, followed by a squat protocol comprising 3 repetitions at 20% 1RM, 3 repetitions at 40% 1RM, 3 repetitions at 60% 1RM, 1 repetition at 80%, and 1 repetition at 90% 1RM (the load at each relative intensity was estimated for the initial 1RM assessment). The selection of multiple repetitions at 20, 40, and 60% of 1RM was to establish a reliable mean velocity without inducing fatigue as suggested by previous research (17). For the repetitions performed at 20, 40, and 60% of 1RM, the highest mean concentric velocity was selected for analysis providing full depth was achieved, which is in accordance with previous research (17). For each 1RM assessment, a maximum of five 1RM attempts were permitted, which did not include the submaximal warm-up repetitions performed up to and including 90% of 1RM. In consultation with each subject, following a successful 1RM attempt, the barbell weight was increased between 0.5 and 2.5 kg until no further weight could be lifted. Rest periods comprised passive recovery of 2 minutes between warm-up sets and 3 minutes between 1RM attempts.
In the familiarization session, a goniometer was used to measure knee angle at the bottom of the squat, which corresponded to a specific barbell depth that was recorded on a LabView analysis program. The barbell depth at full knee flexion was then monitored for each repetition by visual displacement curves on the LabView analysis program to ensure that the same barbell depth was maintained throughout the assessments (32). For each squat repetition, subjects were instructed to perform the eccentric phase in a controlled manner until full knee flexion was achieved. Once the eccentric phase was completed, the subject was told to immediately perform the concentric phase as fast and explosively as possible (with the assistance of verbal encouragement) to use the SSC. Importantly, the barbell was placed in a high bar position on the superior aspect of the trapezius muscle and had to remain in constant contact with the shoulders, whereas the feet were required to maintain contact with the floor. The heel and toe locations of each participant were recorded on the force plate using a 1-cm intersecting vertical-horizontal grid and the same position was maintained for every trial.
Barbell displacement and mean concentric velocity were monitored by 4 fixed position transducers (Celesco PT5A-250; Chatsworth, CA, USA), which were mounted to the top of the power cage and attached to the side of the barbell (32). The concentric phase of each repetition commenced at the point of maximal displacement (greatest descent) and terminated at zero displacement (standing). The position transducer data were collected via a BNC-2090 interface box with an analogue-to-digital card (NI-6014; National Instruments, Austin, TX, USA) and sampled at 1000 Hz. In addition, the position transducer data were collected and analyzed using a customized LabVIEW program (National Instruments, version 14.0). All signals were filtered with a fourth-order low-pass Butterworth filter with a cut-off frequency of 50 Hz. The 4 transducers had a total retraction tension of 23.0 N, which was accounted for in all calculations.
For trials 1, 2 and 3, individualized regression equations to predict 1RM were analyzed using Excel software (Microsoft; Redmond, WA, USA). A Shapiro–Wilk test of normality was performed and indicated that all data were normally distributed (p > 0.05). Reliability of the 1RM, predicted 1RMs, and V1RM was determined from the magnitude of the intraclass correlation coefficient (ICC), standard error of the measurement (SEM), coefficient of variation (CV), and the effect size (ES) (12). Similarly, validity of the predicted 1RMs compared with the actual 1RM was assessed from the magnitudes of the Pearson product moment correlation (r), standard error of the estimate (SEE), CV, and the ES (12). The magnitude of the ES (Cohen's d) was considered trivial (<0.2), small (0.2–0.59), moderate (0.60–1.19), large (1.2–1.99), or very large (>2.0) (14). In addition, the strength of the correlations was determined using the following criteria: 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) (6). Fisher's r to z transformation analysis was used to ascertain significant differences between 1RM and predicted 1RM. Magnitude of CV was based on the following parameters: poor (>10%), moderate (5–10%), or good (<5%) (10). Confidence limits were set at 95% for all reliability and validity analyses. Finally, 1RM comparisons for reliability and validity were also assessed using repeated measures analysis of variance with a type-I error rate set at α < 0.05, and Tukey’s post hoc comparisons used where appropriate (IBM SPSS version 22.0, Armonk, NY, USA).
No significant differences were seen between trials 1, 2, and 3 for the 1RM (140.7 ± 26.9 kg, 139.7 ± 27.8 kg, 140.4 ± 27.0 kg, p > 0.05) and 1RM predictions based on the submaximal measures up to 90% (159.7 ± 28.8 kg, 160.6 ± 24.7 kg, 158.8 ± 27.9 kg, p > 0.05), 80% (162.3 ± 28.3 kg, 163.3 ± 23.7 kg, 161.4 ± 29.6 kg, p > 0.05), and 60% (168.4 ± 27.3 kg, 170.6 ± 22.7 kg, 170.6 ± 34.5 kg, p > 0.05) (Figure 3). Individual variation ranges between trials for the 1RM (−5.6 to 4.8%) and 90% (−10.7 to 10.8%), 80% (−20.9 to 23.5%), and 60% (−22.0 to 35.8%) 1RM predictions are shown in Figure 3. Intraclass correlation coefficients for the 1RM (ICC = 0.99), and 90% (ICC = 0.92), 80% (ICC = 0.87), and 60% (ICC = 0.72) 1RM predictions were practically perfect, very high, and high, respectively (Figure 4C). Furthermore, a Fisher’s r to z transformation revealed no significant differences (p > 0.05) for the correlations between trials for the 1RM and predicted 1RMs. Interestingly, the 1RM was very stable between trials with a small SEM (2.9 kg) and good CV (2.1%), in addition to a trivial effect size (d = 0.03), as seen in Figure 4. However, for the 90, 80 and 60% 1RM predictions, there was a moderate-to-large SEM (8.6, 11.1, 16.8 kg), moderate-to-poor CVs (5.7, 7.2, 12.2%), but trivial effect sizes (−0.02, −0.05, −0.05), respectively. Lastly, the SEM (0.05 m·s−1) and CV (22.5%) for the V1RM (0.24 ± 0.06 m·s−1) were large and poor between trials although the ICC (0.42) was moderate along with a trivial effect size (d = 0.143).
All 1RM predictions were significantly different (p < 0.001) to the 1RM for all trials (Figure 3). Compared with the 1RM, there was considerable individual variation for the 90% (−5.5 to 27.8%), 80% (−12.3 to 29.4%), and 60% (−5.5 to 47.6%) 1RM predictions (Figure 3). Interestingly, the Pearson correlations for the predicted 1RMs up to 90% (r = 0.93), 80% (r = 0.87), and 60% (r = 0.78) were practically perfect or very high as seen in Figure 5C. However, comparison of these correlations using Fisher's r-to-z transformation revealed that all 3 correlations were significantly different (p < 0.001) from the 1RM. In addition, the SEE revealed large absolute errors (10.6, 12.9, 17.2 kg) and moderate-to-poor CVs (7.4, 9.1, 12.8%) for the 90, 80, and 60% 1RM predictions, respectively (Figures 5A and 5B). The effect size (d) for the magnitude of 1RM predictions ranged from 0.71 to 1.04, as seen in Figure 5D, indicating all 1RM predictions were moderately different to the 1RM.
The main finding of the present study was that in strength-trained subjects, the load–velocity relationship was not reliable and valid enough to accurately predict maximal strength for the free-weight back squat exercise over 3 trials, which did not support our hypothesis. Essentially, the V1RM used in the load–velocity relationship to predict 1RM was too variable (CV = 22.5%) between sessions. However, as expected, the load–velocity relationship was more accurate when lifts were performed at higher loads that more closely approached the actual 1RM, yet the predictions were still significantly different from the 1RM. The concept of greater accuracy at higher loads is well documented in the 1RM prediction literature (25). For example, Mayhew et al. (22) reported the accuracy of repetition to failure methods of 1RM prediction were enhanced when higher loads were lifted. However, the need to obtain velocities at intensities that are close to 1RM for accurate sessional 1RM predictions defeats the rationale of employing the load–velocity relationship method because its suggested purpose is to accurately predict 1RM and avoid frequent maximal testing (18). As a result, this study suggests that if the V1RM is applied in the linear regression equation to predict maximal 1RM, the load–velocity relationship cannot accurately predict daily or training session specific 1RM for the free-weight back squat exercise.
The present study revealed that subjects who could lift at least 150% of their body mass were reliable at the back squat 1RM assessment as noted by the practically perfect correlation (ICC = 0.99), low measurement error (SEM = 2.9 kg; CV = 2.1%), and small individual variation (−5.6 to 4.8%) between trials. Interestingly, the 1RM reliability data in our study were similar to the correlation (ICC = 0.97), measurement error (SEM = 2.5 kg), and individual variation (−6.7 to 9.1%) between trials reported by Comfort and McMahon (7). However, our investigation revealed that all predicted 1RMs were less reliable than the actual 1RM, evidenced by greater differences in the reliability analyses including the correlation (ICC) and measurement error (SEM and CV). If the load–velocity relationship were to be considered as a valid method to modify sessional training loads, the 1RM predictions would need to mimic the reliability statistics of the actual 1RM. Most notably, 1RM predictions would need to have practically perfect correlation, trivial effect size, small error of measurement and low CV, but these were not observed in the present study.
Importantly, comparisons of the validity correlation data using Fisher's r-to-z transformation analysis revealed all predicted 1RMs significantly overestimated (p ≤ 0.05) the actual 1RM. Therefore, the load–velocity relationship was unable to accurately predict maximal strength for the free-weight back squat exercise. This was further evidenced by large errors (SEE = 10.6–17.2 kg), moderate-to-poor CVs (7.4–12.8%), and moderate effect sizes (d = 0.74–1.09). Consequently, if the load–velocity relationship cannot accurately predict a stable 1RM across 3 trials, then it is unlikely to predict sessional training loads according to daily readiness. Interestingly, slightly lower correlations and higher measurement errors (SEE) were observed in the present investigation compared with the findings of 2 other 1RM prediction studies (3,17).
Jidovtseff et al. (17) combined the data from 3 studies, culminating in 112 subjects (including 22 female) of recreational training status (1RM to body mass ratio = 0.85) performing concentric-only bench press 1RM on a Smith machine. They then examined the linear regression equations, made from 3 or 4 sets performed up to 80, 90, or 95% 1RM, and analyzed the relationship between bench press 1RM and the load at zero velocity. They found an almost perfect correlation (r = 0.98), yet noted a moderate measurement error (SEE = 7%). Similarly, Bosquet et al. (3) examined the validity of the force–velocity relationship (employing an undisclosed algorithm) to predict bench press 1RM. They had 27 subjects (5 female) of recreational training status (1RM to body mass ration = 0.87) perform the bench press 1RM on a Smith machine with a 4-second pause between eccentric and concentric phases. One repetition maximum predictions were taken from an average of 4 trials that were performed until power decreased (approximately 48% of 1RM) during 2 consecutive loads. They reported a practically perfect correlation (r = 0.93), which aligned closely with the correlations found in the present study, and a measurement error of 9% (SEE). Although helpful, the practical usefulness of the findings from the 2 aforementioned studies is perhaps limited.
For example, the kinetic and kinematic data collected from exercises performed on a Smith machine are specific to that particular machine given the conceivable variation in barbell mass, angle of bar path, and frictional forces between equipment. Moreover, even though pause and concentric-only contractions minimize measurement error in concentric movement velocity (24), 1RM predictions using the pause or concentric-only method provide limited ecological validity, as they do not reflect a true free-weight 1RM technique (no pause between eccentric and concentric phases), which uses the SSC. Strength-training exercises incorporating the SSC are popular among athletes and are known to produce greater force than concentric-only contractions (1). Consequently, exercises incorporating the SSC can result in greater enhancement of performance tasks such as running and jumping. Therefore, to ensure ecological validity, if training with exercises using the SSC, the 1RM assessment (used to program relative intensities) must also incorporate the SSC. Furthermore, the pause or concentric-only 1RM assessment would likely produce a lower 1RM load than a free-weight 1RM assessment. Consequently, it is likely that the training adaptations would be compromised if one were to prescribe training intensity, for an exercise using the SSC, based off a pause or concentric-only 1RM assessment.
Another major finding in the present study was the greater individual variability of predicted 1RM when fewer sets were used for the estimation. This is in agreement with the findings of Jidovtseff et al. (17) who suggested that differences between the lightest and heaviest loads used for prediction should exceed 0.5 m·s−1. Moreover, the large variability between trials of the V1RM also enhanced the measurement error in the predicted 1RMs for the free-weight back squat. In contrast, another study found that the V1RM was reliable for the 1RM back squat when a 4-second pause was incorporated between the eccentric and concentric phase (8). Although rest/pause or concentric-only assessments may not provide perfect ecological validity for exercises incorporating the SSC, they have been shown to provide reliable movement velocities at submaximal and maximal intensities (8,11). It is well established that if maximum effort is provided on the concentric phase of a lift, the associated movement velocity will decrease as fatigue ensues (27). Therefore, isoinertial assessments using a pause or concentric-only method maybe beneficial as a fatigue monitoring tool by quantifying changes in mean concentric velocity for a given relative load.
When examining the findings of the present study, the lack of ability to accurately and reliably predict 1RM on a daily basis with the use of velocity measures calls into question the theoretical model presented by Jovanovic and Flanagan (18). Specifically, Jovanovic and Flanagan (18) suggested that the use of daily predictions of maximal strength could be made from the measurement of barbell velocity and training loads could then be adjusted based upon the predicted maximums to account for the athlete's current fatigue status. However, the present study clearly shows that in a recovered state, the prediction of 1RM is highly variable when using velocity and results in a systematic overestimation of the actual 1RM (Figure 6). As such, it is highly likely that when athletes are fatigued, further variability will be noted. Therefore, based upon the present study, it is not recommended to use 1RM predictions as a tool for adjusting training loads to account for fatigue status. However, it is likely that sound periodization methods, such as incorporating heavy and light training days, will appropriately account for the changing status of the athlete. For example, traditional periodization literature recommends adjusting training loads by 5–10% across the training week to account for accumulative fatigue (2). Interestingly, this classic recommendation for modulating intensity between heavy and light resistance training days would account for the 2.1% CV noted in the present study and allow for adjustments in training load according to daily fatigue.
Crucially, the findings of the present study regarding the 1RM prediction method (calculated by entering the V1RM into a linear regression equation) are limited to the free-weight back squat exercise performed to full depth with a relatively homogenous strength-trained population. Moreover, even though we acknowledge this method was not accurate enough to predict 1RM, it does not necessarily mean that all approaches using the load–velocity relationship would fail. Future studies may look to determine whether the accuracy of 1RM predictions in free-weight exercises can be improved by using alternative nonlinear regression models or other variables such as peak concentric or mean propulsive velocity. In addition, it is not well understood whether the accuracy of 1RM predictions is affected by exercise selection, age, gender, or training status.
Based on the results of the present study, it appears that the load–velocity prediction of the free-weight back squat 1RM performed to full depth is moderately reliable and valid but not accurate enough to predict maximal strength on a daily basis. This was primarily because of the poor reliability of the V1RM. Consequently, performing sessional 1RM predictions to track changes in maximal strength and adjust sessional training loads according to daily readiness appears unlikely. However, if training for maximal strength gains, the variation in velocity may not matter providing maximal effort is given through the concentric phase of the lift. Furthermore, fluctuating the training intensity using sound periodization could also account for daily readiness. Although if an individual is performing power-based training where specific velocities are to be achieved, then sessional adjustment of load by monitoring velocity maybe useful.
It is important to note the practical applications that stem from this work, most notably, even though the load–velocity relationship up to 90% of 1RM only provides a moderate estimation of 1RM, it holds similar validity to other predicted 1RM methods. However, for programming purposes, strength-trained individuals are recommended to periodize relative loads from a periodic 1RM assessment and account for daily readiness or envisaged fatigue by systematically modifying volume or intensity in accordance with periodization strategies and athlete monitoring programs. Future studies using free-weight exercises may monitor changes in movement velocity at relative submaximal loads to modify training sessions, but this has yet to be established as a reliable method of monitoring training loads in free-weight exercises.
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