Predicting One Repetition Maximum from Repetitions to Fatigue (RTF) testing using Prediction Equations

2.5 Predicting One Repetition Maximum from Repetitions to Fatigue (RTF) testing using Prediction Equations

In determining the one repetition maximum, the best method would of course be the most direct method – lift a weight that can only be lifted one time (Baechle and Earle 2008). As established above, the one repetition maximum test is the gold standard, and has been found reliable as well as safe across a variety of population groups (Levinger et al. 2009, Ritti-Dias et al. 2011, Tiggemann et al. 2011, Heyward and Gibson 2014).

Some issues are raised though regarding one repetition maximum testing. Changes in maximum strength occur regularly, which implies regular testing is necessary (Mayhew et al. 2011, Banyard et al. 2017). However, performing a one repetition maximum test may be time consuming, which is possibly impractical, for example in a team setting, or with untrained individuals for whom several familiarization sessions are required to ensure accuracy and reliability (Benton et al. 2009). Furthermore, as discussed above, it may also lead to muscle soreness, as well as a limited ability to exercise due to the temporary deterioration of muscle function (Braith et al. 1993, Niewiadomski et al. 2008). Therefore, it is evident that undertaking a one repetition maximum test frequently may take away valuable training time (Banyard et al. 2017).

One method to alleviate concern of the previously mentioned issues surrounding the one repetition maximum test, is to use a prediction equation to estimate the one repetition maximum (Heyward and Gibson 2014). This can be done in two ways, namely by choosing a pre-determined number of repetitions (e.g. 3) and then during the testing increasing the weight each attempt until only that number of repetitions can be done, or alternatively by choosing a pre-determined weight and lifting it until no more repetitions can be done (Baechle and Earle 2008). Once a maximum load for the pre-determined amount of repetitions has been determined, or the maximal repetitions at a pre-determined load have been determined, that load or repetition number is then applied to a chosen prediction equation to predict that participant’s one repetition maximum (Mayhew et al. 2008).

The benefits of using a prediction equation based on repetitions to fatigue are firstly that a lighter load is used for the testing, meaning that participants who lack the technical ability, or are not accustomed to using maximum weights may feel less intimidated (Mayhew et al. 2008, Tanner and Gore 2012).  Furthermore, as only a few sets are needed, more time can be used for training, because less time is needed for testing, and also less muscle soreness occurs (Braith et al. 1993, Dohoney et al. 2002, González-Badillo et al. 2011, LeSuer et al. 1997, Mayhew et al. 2008, Reynolds et al. 2006). Over the years, several one repetition maximum prediction equations have been developed (Fleck and Kraemer 2014). Table 3 provides an overview of the more popular prediction equations.

Table 3 – Overview of common RTF Prediction Equations
Author (Year)	Prediction Equation
Abadie (1999)	1RM = 7.24 + (1.05 x Wt)
Adams (1998)	1RM (kg) = RepWt/(1 –0.02 RTF)
Berger (1970)	1RM (kg) = RepWt/(1.0261 –0.00262 RTF)
Brown (1992)	1RM (kg) = (Reps 3 0.0338 + 0.9849) 3 RepWt
Bryzcki (1993)	1RM (kg) = RepWt/(1.0278 –0.0278 RTF)
Cummings and Finn (1998)	1RM (kg) = 1.175 RepWt + 0.839 Reps –4.29787
Dohoney et al. (2002)	4-6RM: 1RM (kg) = -24.62 + (1.12 x Wt) + (5.09 x reps) 7-10RM: 1RM (kg) = -1.89 + (1.16 x Wt) + (1.68 x reps)
Epley (1985)	1RM (kg) = ((0.033 x reps) x RepWt) + RepWt
Kemmler et al. (2008)	1RM (kg) = RepWt (0.988 + 0.0104 RTF + 0.0019 RTF2–0.0000584 RTF3)
Lander (1994)	1RM (kg) = RepWt/(1.013 –0.0267123 RTF)
Lombardi (1989)	1RM (kg) = RTF0.13 RepWt
Mayhew et al. (1992)	1RM (kg) = RepWt/(0.522 + 0.419 e–0.055 RTF)
O’Connor (1989)	1RM (kg) = 0.025 (RepWt 3 RTF) + RepWt
Reynolds et al. (2006)	1RM (kg) = RepWt/(0.5551 e–0.0723 RTF + 0.4847)
Tucker (2006)	1RM (kg) = 1.139 RepWt + 0.352 Reps + 0.243
Wathen (1994)	1RM (kg) = RepWt/(0.488 + 0.538 e–0.075 RTF)
Welday (1988)	1RM (kg) = (RTF 3 0.0333) RepWt + RepWt
From Mayhew et al., 2008  1RM= one repetition maximum. (kg)= kilograms. RepWt= Repetition Weight, the load used. RTF= repetitions to failure.

Table 4 – Overview of compared prediction equations
Author (Year)	Participants	Submaximal Intensity	Prediction Equations Compared
Mayhew et al. (2008)	103	60%, 90%	Adams, Berger, Brown, Brzycki, Cummings and Finn, Kemmler et al., Lander, Lombardi, Mayhew et al., O’Connor et al., Reynolds et al., Tucker et al, Wathan, Welday.
Mayhew et al. (2011)	146	65%, 90%	Desgorces et al., Lombardi, Mayhew et al., Wathen
LeSuer et al. (1997)	67	<10 RTF	Brzycki, Epley, Lander, Lombardi, Mayhew et al., O’Connor et al., and Wathan
Reynolds et al. (2006)	70	5, 10, 20 reps	Reynolds et al., Abadie, Brzycki, Epley, Lander, O’Connor, Lombardi, Mayhew et al.
Kemmler et al. (2006)	70	3-5, 6-10, 11-15, 16-20 reps	Brzycki, Epley, Lombardi, Mayhew et al., O’Conner et al., Wathen, Kemmler, Lauber, Wasserman et al. (KLW)
Brechue and Mayhew (2009)	58	60%, 70%, 80%, 90%	Brzycki, Lander, Mayhew et al., Wathen, Welday
Desgorces et al. (2010)	110	20%, 40%, 60%, 75%, 85%	Degorces et al., Epley, Mayhew et al.

It needs to be remembered that these equations are only an estimate of a one repetition maximum, and therefore contain a measure of error (Fleck and Kraemer 2014). For example, in the 14 prediction equations compared by Mayhew et al. (2008) (Table 3, 4), the measure of error in the bench press exercise for college women pre-training ranged from a mean percentage of -24% +9.4 (Berger equation) to 26.7% +101.7 (Brzycki equation), and post training ranged from -23.9% +9.3 (Berger equation) to 29.3% +60.0 (Brzycki equation). In the same investigation, when using no more than ten repetitions to fatigue to predict one repetition maximum, the pre-training measure of error ranged from a mean percentage of -17.4% +7.2 (Berger equation) to 3.9% +8.6 (Tucker et al. equation), and post training ranged from -17.7% +7.4 (Berger equation) to 1.7% +8.7 (Wathen equation). Most prediction equations were formulated using certain repetition ranges or loads, population groups, or exercises, so their accuracy is dependent on the exercise, number of repetitions, gender, and training status (Banyard et al. 2017). Therefore, if wanting to use a prediction equation to determine one repetition maximum, it is absolutely necessary to first determine that the equation is indeed applicable to the population group and exercise under investigation (Mayhew et al. 2008, Desgorces et al. 2010).

With regard to the exercise, this review will predominantly focus on prediction equation literature pertaining to the bench press exercise.

An inverse relationship exists between the number of repetitions that can be performed in an exercise, and the load used for that exercise (Fleck and Kraemer 2014). Predicting one repetition maximum via an equation is based on this relationship, which is assumed to be linear (Brechue and Mayhew 2009). However, the relationship is more curvilinear, with the largest decrease in the percentage of a one repetition maximum being between one and two repetitions of maximum (LeSuer et al. 1997, Brechue and Mayhew 2009). A wide range of repetitions has been tested in the literature, with between two and ten repetitions to failure being recommended for more accurate prediction of one repetition maximum when using prediction equations, though some equations have been applied to up to 20 repetitions to fatigue (Mayhew et al. 2008). Reynolds et al. (2006) submit that linear prediction equations are preferred for tests using less than ten repetitions, and non-linear prediction equations be used for tests using more than ten repetitions.

2.5.1 Use of Prediction Equation in Non-Athlete Populations

Mayhew et al. (2011) compared four prediction equations using a group untrained men and women, to determine the accuracy of predicting one repetition maximum in the bench press exercise, at either 65% intensity or 90% intensity of an established one repetition maximum. The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3. At both pre-training testing prior to a 12 week resistance training program, as well as at post-training testing, most of the prediction equations underestimated the one repetition maximum in the 65% group where a large amount of repetitions were performed (up to 22), with the exception of the Wathen equation which produced non-significant differences. However, in the 90% group the one repetition maximum load was overestimated. The Desgorces et al. equation produced the most accurate predictions, i.e. within 5% of the actual one repetition maximum, both pre- and post-training. Though with accuracy at 39% pre-training testing and 54% post-training testing respectively, one could still question the value of its accuracy for use in a resistance training program (Mayhew et al. 2011).

This stands somewhat in contrast to Mayhew et al. (2008) where it was suggested the prediction equations overestimate one repetition maximum when more repetitions (over 10) are performed. This study compared 14 prediction equations to determine one repetition maximum in the bench press in a mixed group of trained and untrained women. The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3.  The participants underwent testing at 60% and 90% of an established one repetition maximum both before and after a 12 week resistance training program. The predicted 1RM of nine prediction equations was not significantly different from the actual 1RM in pre- and post-training testing when accounting for all repetition ranges. When focused on repetitions of up to ten, nine of the equation predictions were not significantly different from the actual 1RM in pre-training testing. The O’Conner et al. equation had the highest accuracy, with 67% not being significantly different from the actual one repetition maximum. The predicted 1RM of the Brzycki and Lander equations were not highly correlated to the actual one repetition maximum in the pre-training testing. With regard to post training, Adams, Brzycki, Cummings and Finn, Lombardi, and O’Connor et al. provided the highest accuracy in predicting one repetition maximum, at approximately 58% each. The equations of Mayhew et al., Wathen, and Welday were also not significantly different from the actual one repetition maximum.

LeSuer et al. (1997), using untrained college participants, compared seven prediction equations. The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3. The investigators found that only the Mayhew et al. and Wathan equation predictions did not differ significantly from the one repetition maximum. The other five prediction equations significantly underestimated one repetition maximum by up to 6%.

Reynolds et al. (2006), using a mixed group of participants, compared 8 prediction equations, one of which was their own. The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3. They found that their prediction equation, the Brzycki equation, and the O’Connor et al. equation, were the most accurate in the bench press exercise, with the Lombardi and Mayhew et al. equations being the least accurate.

However, in Kemmler et al. (2006), in a study of postmenopausal women to determine the accuracy of seven prediction equations, the authors found that all seven prediction equations adequately predicted one repetition maximum from across a wide range of repetitions to failure (3-20 repetitions). The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3. One proposed reason for the difference in the findings between this study and other studies which found variance in the accuracy of prediction equations, is attributed to the homogenous nature of the participants in terms of “sex, age, menopausal status, medication, and illness affecting muscle and bone metabolism and the specific nature of training during the previous 25 months” (Kemmler et al. 2006). Apart from the homogenous nature of the participants, that a machine chest press exercise, and not a free weight bench press exercise was used, may also have affected the findings, as machine weight exercises require a smaller contribution from synergistic musculature (Iglesias et al. 2010).

2.5.2 Use of Prediction Equation in Athlete Populations

Although the training status of the participants in the above mentioned studies varied from untrained to trained, they consisted of non-athletes. Some researchers undertook to investigate the accuracy of prediction equations for the bench press exercise in athletic populations (Brechue and Mayhew 2009, Desgorces et al. 2010, Mann et al. 2015).

In Brechue and Mayhew (2009), five prediction equations were compared for the bench press exercise both pre- and post-training intervention. The list of prediction equations investigated are in Table 4. The prediction equations are provided in Table 3. The Wathen and Welday equations predicted the one repetition maximum with the best overall accuracy. Pre-training, at intensities of 60% and 70%, the Lander and Brzycki equations had the least accuracy, significantly over-predicting one repetition maximum. All the equations were significantly different from the one repetition maximum at 80% intensity. Except for the Mayhew et al. equation, all the equation predictions were not significantly different from the one repetition maximum when tested at 90% intensity. After the intervention, all predictions were similar at 70% and higher intensity testing.

In Desgorces et al. (2010), athletes from four sporting backgrounds (racket/ball games, powerlifting, swimming, rowing) were divided into two groups, namely a high strength group (racket/ball games, powerlifting), and a high endurance group (swimming, rowing). The accuracy of three equations was compared. It was found that while the Desgorces et al. equation provided the best accuracy, the Epley equation performed the poorest overall.

It has been reported that the sport or activity one regularly participates in can have an influence on the prediction equation outcome when lower intensities of one repetition maximum percentage are used. For example, Desgorces et al. (2010) reported that endurance sport athletes were able to do more repetitions when the intensity was lower than 75% of 1RM, compared to strength athletes. Conversely, strength athletes were able to lift more times compared to endurance athletes at higher percentages of 1RM. Above 75% of 1RM however, the differences between the groups were less pronounced.

2.5.3 Variables influencing the accuracy of Prediction Equations

As seen above, the participants training status seems to pay a significant role in the accuracy of the prediction equations. For example, the Brzycki equation performed poorly in the pre-training testing in Mayhew et al. (2008), but was amongst the most accurate after the 12 week resistance training program intervention. Therefore, it can be surmised that as training increases a person’s maximum strength, and with it also changes the relationship between maximum and sub-maximum strength, the ability of prediction equations to accurately predict one repetition maximum may change too (Dohoney et al. 2002, Mann et al. 2015). Mayhew et al. (2011) found that at lower percentages of 1RM, the amount of repetitions to failure were similar between participants having lower (or untrained) and higher (or trained) levels of strength. However, at a higher percentage of 1RM (90%), it was discovered that participants with lower levels of strength were able to perform more repetitions to failure compared to participants with higher strength levels (Mayhew et al. 2011). A similar conclusion for the bench press exercise was reached by Shimano et al. (2006), who compared a group of trained and untrained men, and found that while repetitions to fatigue were similar between both groups at 60% and 80% of the one repetition maximum, at 90%, the untrained group performed more repetitions than the trained group. Dohoney et al. (2002) reason that that the stronger a participant is, the more a prediction equation will underestimate their one repetition maximum, so a prediction equation applicable to their training level should be used to improve accuracy.

Gender, on the other hand, does not seem to play as large a role as expected. Mayhew et al. (2011) found that the results of the prediction equations were similar between genders. Reynolds et al. (2006), also found that gender did not improve the ability of prediction equations to predict one repetition maximum more accurately.  They concluded that gender is either unrelated to 1RM strength, or conversely related to strength to such a degree that it is automatically accounted for in submaximal testing (Reynolds et al. 2006).

Overall, the literature generally suggests that that the accuracy of a prediction equations improves when higher percentages of 1RM, and with it lower amount of repetitions, are used to predict one repetition maximum (Fleck and Kraemer 2014, Mayhew et al. 2008, Dohoney et al. 2002, Pereira and Gomes 2003). In terms of repetitions, the general consensus is that up to ten repetitions will provide sufficient accuracy to estimate one repetition maximum (LeSuer et al. 1997, Pereira and Gomes 2003).  However, Dohoney et al. (2002) compared prediction accuracy of four to six repetitions against eight to ten repetitions to fatigue, and concluded that while both provided useful levels of accuracy, four to six repetitions served as a better predictor of one repetition maximum.  Reynolds et al. (2006) reached a similar conclusion when comparing five and ten repetitions, finding that while both did not differ significantly from one repetition maximum, using 5RM improved accuracy. Therefore, while using up to ten repetitions is still useful, the best accuracy is ensured when repetitions of between two and five, or intensity above 85% of one repetition maximum is used (Brechue and Mayhew 2009). As mentioned above though, in Shimano et al. (2006), while there was no significant difference in the amount of repetitions performed at 60% or 80% intensity between the untrained and trained group, the untrained group was able to perform more repetitions at 90% intensity. This again shows that while overall the accuracy of prediction equations is improved the closer to one repetition maximum the lifts are performed, one still needs to ensure that the correct prediction equation is used for the population group under investigation.

As a side note, it should be mentioned that when attempting to predict the one repetition maximum using a prediction equation, caution should be exercised when allowing a participant to choose the load themselves, as some will choose a lighter load, and with it perform more repetitions, possibly skewing the results of the prediction equation (Mayhew et al. 2008). This is another reason to choose a load that can only be done up to 10 repetitions to fatigue.

It has been suggested that the reason for the variances in results between populations and prediction equations for the same exercise, or even within the same strength level groups, may be that most of the studies mentioned did not account for the tempo, or velocity, of the movement in the bench press exercise (Pereira and Gomes 2003, Shimano et al. 2006). Unless the time within which the concentric, eccentric, and recovery phase of a repetition is accounted for, while the load used may be the same between participants, the time spent under tension will be different, and with that the possible repetitions to fatigue (Reynolds et al. 2006). Pereira and Gomes (2003), reviewed predictions of one repetition maximum, and concluded that while different velocities resulted in different loads used for prediction equations using between eight to ten repetitions, discovered that only a handful amount of studies actually accounted for the velocity of the repetitions. Studies have suggested that the faster a repetition is performed, the more repetitions can be performed, which will change the number of total repetitions to fatigue, and with it the accuracy of a prediction equation (Ferrari et al. 2017). Ferrari et al. (2017) concluded that, when velocity was accounted for, there were no significant differences between the trained and untrained group, regardless of the percentage of one repetition maximum used (namely 60%, 75%, and 90%).

2.5.4 Safety concerns regarding Repetitions to Failure when using Prediction Equations

As mentioned above, one reason some prefer to use prediction equations based on repetitions to maximum, instead of doing a one repetition maximum test, is safety (Heyward and Gibson 2014). Unlike one repetition maximum tests, using repetitions to failure to predict 1RM produces either less, or no muscle soreness, nor limits the participant’s ability to exercise posttest (Dohoney et al. 2002).

With regard to injuries, despite belief to the contrary, little evidence exists that one repetition maximum testing is more dangerous than when using repetitions to maximum (Mayhew et al. 2008). While the concern behind one repetition maximum testing is the heavy load that is being attempted could lead to injury if the participant fails to lift it, an argument can also be made for the danger of using repetitions to failure, namely that lifting mechanics change as a person fatigues, and with that there is an increase in the potential for a muscle strain or joint injury due to the awkward position the participant may end up in (Mayhew et al. 2008).

Despite an improved accuracy of prediction equations when using lower repetitions, a strong chance of error in the prediction of a one repetition maximum still exists, as seen above. Taken together with the inherent safety of one repetition maximum testing if done according to proper guidelines under professional supervision as mentioned before, a coach or trainer needs to question the purpose behind the testing and then decided upon the most appropriate method. If accuracy of the one repetition maximum load is essential for programming and training of an athlete, specifically strength athletes, using submaximal loads to predict the one repetition maximum might not be appropriate, for if the prediction equation either over-estimates, or under-estimates the repetition maximum strength, any  loads used from the estimation in the athlete’s programming may provide either insufficient, or too much stress for the intended purpose of the program (Pereira and Gomes 2003, Mayhew et al. 2008). If however the coach or trainer understands the limits of prediction equations, and applies them appropriately to the population and exercise under investigation, it can be a useful tool. (Fleck and Kraemer 2014).

2.6 Predicting One Repetition Maximum from the Load Velocity Relationship

2.6.1 Introduction

As presented above, one repetition maximum has traditionally been established either via the direct testing method, or indirectly through use of prediction equations and charts based upon repetitions to fatigue (Baechle and Earle 2008, Fleck and Kraemer 2014, Balsalobre-Fernández et al. 2017).

As also presented above, using the traditional methods is not without its pitfalls. Considerations against the direct method include its possibly increased risk of injuries in some populations, its effect on muscle soreness and temporary inability to exercise effectively soon after, and possibility of overtraining if used too often (Dohoney et al. 2002, Shaw et al. 1995, Balsalobre-Fernández et al. 2017). Therefore, it is suggested that the direct method is best suited for use prior to the commencement of a new training program, to determine the intensities to be used in the program; or after it, to determine the effects of the training program, and also whether the participant has improved in strength (Dohoney et al. 2002, Shaw et al. 1995).

Using prediction equations based on repetitions done to fatigue is also not without drawbacks, as presented above. While it does produce minimal muscle soreness, and also less stress due to use of a lighter load than the direct method, it does nonetheless still create a fatiguing effect on the participant, and also includes possible safety concerns as, although the loads used are lighter, injury may occur due to the changes in mechanics from the repetition fatigue (Mayhew et al. 2008). Furthermore, in choosing a prediction equation, the investigator needs to ensure that they are using the correct prediction equation, taking into account the participant population, their level of training, the exercise selected, and also the amount of repetitions used, failing which the accuracy of the prediction can be quite compromised (Jidovtseff et al. 2011). Lastly, movement velocity and load are closely related, and it has been shown that for the same load, a faster velocity can result in more repetitions accomplished, which may also affect the accuracy of prediction equations, as they don’t take movement velocity into account (Sakamoto and Sinclair 2006).

Another issue surrounding traditional testing concerns the fact that a person’s maximum strength varies daily, due to factors such as nutrition, sleep, recovery, lifestyle, and normal biological variability (Jovanovic and Flanagan 2014). This daily variance can be as high as 12-18% over or under the one repetition maximum, meaning the total variance range can be as big as 36% (Jovanovic and Flanagan 2014, Braith et al. 1993). Without being able to accurately determine a person’s strength more regularly, and relying on a one repetition maximum value which may be outdated or incorrect for that time, there is genuine risk in using training loads that either over or under represent the person’s strength level for that day (Jidovtseff et al. 2011, Jovanovic and Flanagan 2014).

A third method of determining one repetition maximum strength has recently become popular, namely using movement velocity measurements (Bazuelo-Ruiz et al. 2015, Balsalobre-Fernández et al. 2017). The use of velocity measurements to predict a one repetition maximum is based on the load velocity relationship, according to which an inverse relationship exists between a load and the velocity with which that load can be moved, namely the higher the load, the slower the velocity with which it can be moved, and the lower the load, the faster the velocity with which it can be moved (Zatsiorsky and Kraemer 2006, Cronin et al. 2003, Balsalobre-Fernández et al. 2017, Jidovtseff et al. 2011).

Based upon this inverse relationship, a close correlation exists between the load being moved, and the velocity of that movement (Jandačka and Beremlijski 2011, Jidovtseff et al. 2011). Based upon this close correlation, by measuring the velocity of the load being moved, it should be possible to accurately determine the one repetition maximum without the need for traditional methods, but rather by moving a submaximal load with maximum velocity, and then using regression equations (Pérez Castilla et al. 2017, Harris et al. 2010, González-Badillo et al. 2011, Jidovtseff et al. 2011). This can be beneficial as one repetition maximum can be determined more frequently due to the lighter loads and fewer repetitions necessary, and even be determined during a training phase to allow for regular and more accurate adjustment of the load to match the intensity percentage of one repetition maximum for that day (Pérez Castilla et al. 2017).

This method was not previously popular largely due to a lack of ability to accurately measure velocity in isoinertial movements commonly used in personal and athletic performance training, such as the bench press exercise (González-Badillo and Sánchez-Medina 2010). The technology that was available was prohibitively expensive for many coaches, trainers, and researchers (Halle et al. 2017). However, with technological improvements and more affordable prices, it has now become more common to use such technology, ranging from advanced video systems, smart phone applications, linear position or velocity transducers, and various types of dynamometers such as accelerometers, including wearable ones such as the PUSH band under investigation (Jidovtseff et al. 2011, Balsalobre-Fernández et al. 2016, Balsalobre-Fernández et al. 2017)

2.6.2 Mean Velocity vs. Mean Propulsive Velocity vs. Peak Velocity

To measure velocity in isoinertial movements such as the bench press exercise, the concentric portion of the movement is measured, i.e. the lifting of the barbell from the bottom position until the arms are fully extended at the top (Sanchez-Medina et al. 2010). The concentric movement starts and ends with zero velocity, with it reaching a peak velocity somewhere in-between (Sanchez-Medina et al. 2010).

It should not be thought that the concentric phase of a movement is purely propulsive, as there is also a significant breaking phase to decelerate the load being lifted (García-Ramos et al. 2017a). The propulsive phase can be described as “that portion of the concentric phase during which the measured acceleration is greater than acceleration due to gravity” (Sánchez-Medina et al. 2013). The breaking phase consists of decelerating the load with a bigger force than that of gravity (Sanchez-Medina et al. 2010). In the breaking phase, there is a negative force being applied against the load to maintain balance (Sanchez-Medina et al. 2010, Banyard et al. 2017).

During the concentric movement, the portion which constitutes the breaking phase is dependent on the load used (Sanchez-Medina et al. 2010). The lighter the load as a percentage of one repetition maximum, the higher the movement velocity will be, which in turn means the longer the breaking phase will be to return the velocity back to zero at the end of the movement (Sánchez-Medina et al. 2013). However, it has been discovered that at loads above 75% to 80% of the one repetition maximum, this breaking phase disappears, and the whole concentric movement can be considered as propulsive (Sanchez-Medina et al. 2010, Sánchez-Medina et al. 2013).

Before going further into the literature surrounding one repetition maximum predictions based on velocity measurements, first the different types of velocity measurements that are used in the literature need to be defined. The main measurements used to measure velocity are mean velocity (MV), mean propulsive velocity (MPV), and peak velocity (PV) (Sánchez-Medina et al. 2013):

Mean Velocity:  this is the average velocity from the beginning to the end of the concentric phase of a movement, and is also referred to as average velocity (Jidovtseff et al. 2011, García-Ramos et al. 2017a).

Mean Propulsive Velocity: this is “average velocity from the start of the concentric phase until the acceleration of the bar is lower than gravity” (García-Ramos et al. 2017a).

Peak Velocity: this is the “maximum instantaneous velocity reached during the concentric phase” (García-Ramos et al. 2017a).

Another term that should be included is Mean Velocity Threshold (MVT), also referred to as one repetition maximum velocity, which is the average velocity of the last successful repetition when performing repetitions to fatigue (Jovanovic and Flanagan 2014).  Izquierdo et al. (2006) tested repetitions to fatigue using intensities of 60%, 65%, 70%, 75%, and 100% of one repetition maximum, and found that regardless of whether only one repetition, or multiple repetitions for the different intensities were performed, the velocity during the last successful repetition remained constant. The mean velocity threshold also does not change when a person’s strength levels have either improved or declined (González-Badillo et al. 2011).

The mean velocity threshold however is specific to each exercise as well as to that exercise’s manner of execution (Izquierdo et al. 2006, Sánchez-Medina et al. 2013, Pérez Castilla et al. 2017). For the bench press exercise, the mean velocity threshold or one repetition maximum velocity is approximately 0.15m/s, though it has ranged from as low as 0.10m/s to 0.23m/s in the literature (Jovanovic and Flanagan 2014, Helms et al. 2017, Jidovtseff et al. 2011). The reason for the variances in the velocity can be ascribed to differences in testing procedures, method execution, and equipment used, or individual variances (Izquierdo et al. 2006, Jovanovic and Flanagan 2014). An overview of one repetition maximum velocity studies can be viewed in Table 5.

Table 5 – Overview of Mean Velocity Threshold for Bench Press
Author(Year)	Equipment	Execution	MVT (m/s)
Helms et al. 2017	Free weight	Pause between Eccentric and Concentric	0.10
Izquierdo et al. 2006	Smith Machine	No Pause between Eccentric and Concentric	0.15
González-Badillo and Sánchez-Medina 2010	Smith Machine	Pause between Eccentric and Concentric	0.16
Garcia-Ramos et al. 2017b	Smith Machine	Pause between Eccentric and Concentric	0.16
Garcia-Ramos et al. 2017b	Smith Machine	No Pause between Eccentric and Concentric	0.17
Sánchez-Medina et al. 2013	Smith Machine	No Pause between Eccentric and Concentric	0.17
Pallarés et al. 2014	Smith Machine	No Pause between Eccentric and Concentric	0.19
Pallarés et al. 2014	Smith Machine	Pause between Eccentric and Concentric	0.22
Jidovtseff et al. 2011	Smith Machine	Pause between Eccentric and Concentric	0.23
MVT= Mean Velocity Threshold, M/s= metres per second

2.6.3 Choosing a Velocity to establish One Repetition Maximum

With the load velocity relationship as a foundation, predicting one repetition maximum through measuring the concentric movement velocity and applying a linear regression or other algorithm has been validated by research, although care should be taken when using this method as often the predicted and actual one repetition maximum values can differ significantly and therefore should not be used interchangeably, despite a high correlation (Bosquet et al. 2010, Jidovtseff et al. 2011, Jovanovic and Flanagan 2014, Banyard et al. 2017). It needs be stated though that as this is a relatively new research area, the amount of studies available, particularly with a focus on the bench press exercise are still limited (Jovanovic and Flanagan 2014, Picerno et al. 2016, García-Ramos et al. 2017a).

As pointed out above, concentric movement velocity can be measured using three methods, namely mean velocity, mean propulsive velocity, and peak velocity (Banyard et al. 2017).

While accurately predicting the one repetition maximum on the basis of the load velocity relationship is dependent on several factors, such as the mathematical method used, the equipment used, the execution method as well as the chosen exercise; the literature is equivocal with regard to which velocity method should be used (Jidovtseff et al. 2011, Banyard et al. 2017).

Some authors, such as Jidovtseff et al. (2011), propose that using mean velocity is to be preferred. In their study, using a linear regression equation, they found a very high correlation between predicted and actual one repetition maximum, though they did however add a proviso that if using this method, at least three to four submaximal measurements should be taken at incremental loads, with at least 0.5m/s difference between the lightest and heaviest increments (Jidovtseff et al. 2011). Intensities from 30% to 95% of one repetition maximum were tested. Picerno et al. (2016) also using the mean velocity method, went as far as to claim that predicted and measured one repetition maximum values may be used interchangeably, based on the very high correlation found in their investigation. Intensities from 50% to 80% of one repetition maximum were tested. To ensure better accuracy in one repetition maximum prediction, it is suggested that loads of at least 80% of one repetition maximum be included in the testing (Jidovtseff et al. 2011, Picerno et al. 2016).

García-Ramos et al. (2017a) investigated the difference in accuracy between mean velocity, mean propulsive velocity, and peak velocity. Using a smith machine, they tested the bench press throw exercise under two execution methods, namely both with and without a pause between the eccentric and concentric movement. While under lower loads the participants were allowed to throw the barbell, under heavier loads the throw was now longer possible, and therefore the execution was that of a regular bench press exercise. It was confirmed that there is a strong and fairly linear load velocity relationship, and found that using mean velocity provided the strongest linearity, as well as the highest accuracy of linear regression equations (García-Ramos et al. 2017a). In terms of strength of linearity and accuracy, mean velocity was followed by mean propulsive velocity, and last by peak velocity (García-Ramos et al. 2017a).

In a follow-up investigation by García-Ramos et al. (2017b), both execution methods (pause and no pause between the eccentric and concentric component of the lift) were investigated in both the bench press throw as well as the regular bench press exercise, using mean velocity as the measurement. The strong and fairly linear load velocity relationship was again confirmed across all variants. However, it was also found that the maximum strength was higher for the no pause compared to the pause method of execution, and the mean velocity was also higher for each percentage of the one repetition maximum. The reason put forward for the difference in strength and mean velocities was the contribution of the eccentric component in the form of the stretch-shortening cycle. Furthermore, stronger participants displayed higher mean velocities at the different intensities measured. Therefore it was suggested that although mean velocity provides a high measure of accuracy, different regression equations need to be used for different execution methods, and that each individual may have their own load velocity profile (García-Ramos et al. 2017b).

Results using mean velocity are not equivocal however. In contrast to Jidovtseff et al. (2011), Bosquet et al. (2010), also using a pause between the eccentric and concentric movement in a Smith machine bench press exercise, determined that while the method is indeed valid, the accuracy of one repetition maximum prediction in this investigation was too low to be of practical value. The difference between the two studies may possibly be attributed to the different mathematical methods used, namely a linear regression in Jidovtseff et al. (2011) versus a proprietary algorithm in Bosquet et al. (2010).

In a comparison between using the mean velocity method versus the mean propulsive velocity method, while García-Ramos et al. (2017a) found that using mean velocity is more accurate, González-Badillo and Sánchez-Medina (2010) came to the opposite conclusion. As in García-Ramos et al. (2017a), González-Badillo and Sánchez-Medina (2010) also employed the pause method using a Smith machine bench press. They concluded that using mean propulsive velocity is the preferred method, as it is a truer representation of true neuromuscular potential (González-Badillo and Sánchez-Medina 2010). They found that using mean propulsive velocity is more accurate across all intensity ranges, as compared to using mean velocity, especially when loads and intensities are lower. The reason given is that using mean velocity does not take into account the increasing magnitude of the contribution of the breaking phase in the concentric movement the lighter the loads. As already mentioned above, when loads are above 75% to 80%, the whole concentric phase may be considered propulsive, but with loads below that intensity, using mean velocity will give an inaccurate estimation of one repetition maximum (Sanchez-Medina et al. 2010, Sánchez-Medina et al. 2013). Even when a person’s strength level change after a training period, using mean propulsive velocity gave consistent values, unlike when mean velocity was used (González-Badillo and Sánchez-Medina. 2010).

González-Badillo and Sánchez-Medina (2010) concluded that using mean propulsive velocity has sufficient accuracy that only one repetition is needed to help determine the percentage of one repetition maximum being used.

The same conclusion was expounded in another investigation by Sanchez-Medina et al. (2010) using the same method of execution and equipment. Namely, measuring mean propulsive velocity better represents neuromuscular ability, particularly at loads under 75% of one repetition maximum, unlike mean velocity which underestimated neuromuscular ability at loads under 75%, for the same reasons provided by González-Badillo and Sánchez-Medina (2010).

It is argued that one reason to prefer predicting one repetition maximum using the velocity method is indeed because lighter loads can be used, but if loads closer to one repetition maximum are needed for improved accuracy, as is also the case in a repetitions to fatigue method, then this defeats the purpose of using the velocity method (Banyard et al. 2017).

Most research in this area used a Smith machine, as seen above. As the barbell bench press exercise is more commonly used in resistance training programs, Loturco et al. (2017) compared the accuracy of the mean propulsive velocity method to predict one repetition maximum between both the Smith machine and barbell variation of the bench press, with no pause between the eccentric and concentric, which again is more typical of a resistance training program. It was confirmed again that when using mean propulsive velocity, there was a very high level of accuracy (95%) between predicted and actual one repetition maximum values for the Smith machine bench press, as well as the barbell bench press (Loturco et al. 2017).

With regard to using peak velocity to predict one repetition maximum, as mentioned above, García-Ramos et al. (2017a) found that it was the least accurate of the three velocity methods in the Smith machine bench press exercise. One study, Rontu et al. (2010) focused on peak velocity, using the barbell bench press exercise with no pause between the eccentric and concentric parts of the lift, and instead found that the correlation between predicted and actual one repetition maximum was very high. They concluded that this velocity method can be used for prediction purposes based on just one submaximal lift, with the best accuracy being achieved when the load was between 70-80% of actual one repetition maximum (Rontu et al. 2010).

When interpreting research regarding prediction of one repetition maximum using the load velocity relationship, apart from discerning between velocity methods, attention needs to be given to the manner of execution, namely was there a pause between the eccentric and concentric part of the lift (Sakamoto and Sinclair 2006, Jidovtseff et al. 2011). A reason for adding a pause between the eccentric and concentric portion is to eliminate any possible contribution of the eccentric component to the concentric component (Jidovtseff et al. 2011). Without a pause, the effect of the stretch-shortening cycle initiated by the eccentric movement can increase the concentric velocity of the lift, particularly the initial acceleration, which will provide a significantly higher prediction value as well as actual value of the one repetition maximum than if the lift was only concentric (Sakamoto and Sinclair 2006, García-Ramos et al. 2017b). Therefore, different regression equations need to be used for each type of execution (García-Ramos et al. 2017b).

While several variables need to be accounted for when predicting one repetition maximum using the load velocity relationship, namely the mathematical method used, the difference in equipment, the method of execution method, and of course the velocity method; gender however, does not seem to affect the prediction outcomes when using the force velocity relationship (Jidovtseff et al. 2011, Bazuelo-Ruiz et al. 2015).

The question remains which should be the preferred velocity method. Both have been found to be valid and accurate under both similar and different execution methods (using a pause or no pause between the eccentric and concentric phases), and both have provided opposing results (González-Badillo and Sánchez-Medina 2010, Jidovtseff et al. 2011). Jidovtseff et al. (2011) have put forward two reasons for preferring the mean velocity method, firstly that it is a better representation of the full concentric phase, and secondly because it is easier to analyze mathematically due to the linear nature of the load velocity relationship.  On the other hand, mean velocity does not take into account the contribution of the considerable magnitude of the breaking phase the lighter the load is, and also underestimated neuromuscular ability (Sanchez-Medina et al. 2010). However, for strength coaches and personal trainers, using mean propulsive velocity can make mathematical analysis unnecessarily complex (Banyard et al. 2017).

2.6.4 Need for establishing an Individual Load Velocity Profile

Different individuals have differing strength levels and neuromuscular abilities (González-Badillo et al. 2011, Banyard et al. 2017). Therefore the load velocity relationship between individuals may differ, with each individual having a slightly different mean velocity threshold for the same exercise.  (González-Badillo et al. 2011, García-Ramos et al. 2017b). González-Badillo et al. (2011) found that for the same individual, the correlation between the velocity and chosen percentage of the one repetition maximum was excellent and consistent, regardless of improvements in strength levels. For this reason, it is advised to rather create individual load velocity profiles over a wide range of intensities, including at 100%, with a minimum of  0.5m/s difference between the lightest and heaviest load measured, to increase the accuracy of one repetition maximum prediction for that individual (Jidovtseff et al. 2011, Jovanovic and Flanagan 2014, García-Ramos et al. 2017b).

2.6.5 Conclusion regarding use of Velocity for establishing One Repetition Maximum

Based on all the above, for predicting one repetition maximum via velocity to be accurate, the testing procedures (such as movement execution, loads and repetitions used), and mathematical and velocity methods would need to exactly replicate those of the relevant studies, which may either be impractical or not applicable to the coaching environment (Picerno et al. 2016). Due to all the possible issues and discrepancies mentioned, and that despite having good validity, the accuracy may be insufficient with the predicted and actual one repetition maximum values being too different to be of practical value, and therefore it may be recommended that actual and predicted values should not be used interchangeably (Jovanovic and Flanagan 2014). While the velocity based prediction methods based on the individual’s load velocity profile may be used for monitoring purposes, it would be prudent to nonetheless undertake traditional one repetition maximum tests to ensure the effects of the training program (Jovanovic and Flanagan 2014, Banyard et al. 2017).

2.7 Technologies for measuring velocity

2.7.1 Linear Transducers as the Gold Standard

Different technologies have been created to be able to measure the velocity of a barbell, such as linear transducers, video systems, smart phone applications, and a variety of accelerometers (Harris et al. 2010, García-Ramos et al. 2017b, Balsalobre-Fernández et al. 2017). Traditionally, movement velocity has been measured in laboratory settings using three dimensional motion capture camera systems, which is regarded as a criterion (Kim et al. 2010, Halle et al. 2017, Jandačka and Beremlijski 2011). Markers are placed on criterion locations on a body such as joint centers and orientation axes of limbs, or on equipment itself such as a barbell (Kim et al. 2010). The movement of the markers is then tracked by motion capture video cameras to determine the velocity of the limbs or equipment, the data which is interpreted by the applicable software (Kim et al. 2010, Halle et al. 2017).

However, motion capture systems are prohibitively expensive for most individuals, teams, and even many institutions, and are also difficult to use without receiving training in the system (Halle et al. 2017). Furthermore, although considered a criterion, they are not without errors in movement measurements, such as skin movement during a motion, system error, and marker noise (Kim et al. 2010). They lack portability, and hence can’t be used in the field or training facility (Halle et al. 2017). Therefore there is a need for a more affordable, easy to use, portable criterion that can be used by coaches and researchers alike

With improvements in technology, the linear transducer has emerged as a gold standard, and the criterion against which other new velocity measuring technologies are measured against, due to its precision and reliability in quantifying barbell velocity (Jidovtseff et al. 2011, Garnacho-Castaño et al. 2015, Balsalobre-Fernández et al. 2017, García-Ramos et al. 2017b, Halle et al. 2017, Pérez-Castilla et al. 2017). Linear transducers work by attaching a retractable, measuring cable from a central processing unit to the barbell or similar resistance training item, such as a weight stack in the case of using a machine (Jovanovic and Flanagan 2014, Picerno et al. 2016, Pérez-Castilla et al. 2017). There are two types of linear transducers, namely linear position transducers, and linear velocity transducers (Balsalobre-Fernández et al. 2016). Linear position transducers measure the barbell velocity by measuring the displacement of the cable over time, whereas linear velocity transducers record electrical signals proportional to the velocity with which the cable is moving (Jovanovic and Flanagan 2014, Balsalobre-Fernández et al. 2016). Both measurements are then converted and displayed by the applicable computer software in real time into velocity measured in meters per second (Harris et al. 2010, Pérez-Castilla et al. 2017).

2.7.2 PUSH Wearable Device Literature

At the time of writing, there have been two studies that investigated the validity of the PUSH device, namely Sato et al. (2015), and Balsalobre-Fernández et al. (2016). The criterion used as well as the equipment and exercise selection was different between these two investigations.

Sato et al. (2015) investigated the validity of the PUSH wearable device by comparing it to a three dimensional motion capture system. They tested two upper body free weight exercises, namely a dumbbell arm curl, and a dumbbell shoulder press, over four sets of ten repetitions each. A device was used for each arm to also determine device-device consistency. In the first two sets, ten pound dumbbells were used, and 15 pound dumbbells were used in the last two sets. The investigation found that the PUSH wearable device provided accurate measurements of velocity as compared to the motion capture system, with only fairly small errors. Furthermore, a high correlation was found between both the left and right arm device, signifying that the device may be worn on either arm with equal measurement accuracy.

Balsalobre-Fernández et al. (2016) investigated the validity of the PUSH wearable device by comparing it to the gold standard, namely a linear transducer. In their investigation, a Smith machine back squat movement velocity was measured over 5 incremental loads, ranging from 25 – 85% of one repetition maximum, performing three repetitions at each intensity. Both peak velocity and mean velocity was measured. It was found that there is a very high association as well as very high agreement between the linear transducer and the PUSH wearable device for both velocities. However, a systematic bias was found, with the PUSH wearable device showing lower values when measuring peak velocity, and higher values when measuring mean velocity, compared to the linear transducer.