Law of Repetitive Motion and Strength Training

I first heard about the so-called law of repetitive motion via Eric Cressey as far back as 2009, who claimed that it could teach us the key to preventing injury in strength training. The word ‘law’ in regards to strength training or bodybuilding always causes my bullshit meter to ping, so I took it upon myself to investigate this ‘law’ further.

Law of repetitive motion is an equation developed by Dr. Michael P. Leahy, who is the founder of Active Release Techniques (ART). This is an equation describing the interaction between various parameters of human motion: I=NF/AR where:

I = Insult or injury to the tissues
N = Number of reps
F = Force (as a percentage of maximum strength)
A = Amplitude
R = Relaxation period* (lets just say rest)

* Leahy differentiated between “rest” and “relaxation” but it is an impractical distinction at best for resistance training or strength training. A total release of tension between reps is not a realistic scenario. And if “relaxation” is taken to mean all the time spent not actually training, and even doing myofascial release work, then the equation would be impossible to apply except as a thinking exercise.

I doubt that Leahy was thinking of 400 pound back squats when he came up with this equation so its right of title as a universal law should certainly be questioned. It will break down depending on the type of movement (I’ll get into that a bit later). One glaring problem, right off the bat, is that it ignores interset rest which greatly influences tissue recovery. Most trainees keep a fairly constant rate of repetition. That is the “rest between reps” is held fairly constant. Even small deviations in rate (or frequency) will tend to even out over time. But what does the equation say?

The equation translates: Tissue injury or insult is equal to the number of reps times the force applied divided by amplitude times relaxation period. This means that the greater the reps and force the greater the insult to the tissues. The greater the amplitude and rest the lower the insult to the tissues. Most trainees will get most of that. Except for amplitude. What the heck is that?

You may have heard trainers and coaches talk about movement amplitude without much explanation. I often talk about amplitude as being one of those performance characteristics that determine the outcome of a training regimen and one of the factors indicating reductions or improvement in performance. The bulk of this article must focus on amplitude because it is the most complex of all the factors in the equation.

You might know a physics definition or even several different ways of looking at wave amplitudes. The best way to describe what amplitude is, to me, is to invoke a guitar string. Think of the resting position of the string as the “zero point”. Now you pluck the string by pulling on it a certain distance and letting go. The string vibrates back and forth in a wave. The peak of that wave goes back to the point which is the distance you originally pulled it, but never beyond that point. The distance between that peak and the original zero point is the amplitude. This is the most common and basic way (I think) of looking at amplitude.

The definition of amplitude changes depending on the system (e.g. sound wave, spring, pendulum, etc.) and what to measure is a personal choice but usually, the distance is measured from the middle to the extremes. And the unit of measurement could change depending on the conditions. This is important in human movement since some movements would be more correctly measured as an angle rather than a distance.

In the above image of a wave diagram γ is the amplitude. See that it fits, more or less, my description. By the way, λ is the wavelength. The important thing to see is that amplitude is basically a distance measurement. It is important not to take this thinking too far because if you try to relate human movement to wave amplitude things get messy. The time it takes for one repetition becomes a “period” and a repetition itself becomes a cycle. We don’t want that to muddle our thinking although there are a number of “strength scientists” around who would have no problem applying this type of jargon to strength training.

So, amplitude is, for human movement, range of motion, change in position, or even displacement of the implement in a resistance exercise. All three could work. The important thing to know is that it is most useful to measure amplitude as the extent of movement or displacement from a mean to the extreme range of a repetitive movement. A little imagination and you’ll see that this leaves a lot open for interpretation. It gets tricky and that is why such pat little equations, although superficially useful, can never be universally applied. There are different types of amplitude where movement is concerned:

There is external amplitude which is the range of movement of the entire body relative to some external benchmark such as the ground or an apparatus such as a gymnastic apparatus. Then there is internal amplitude which is the range of motion of individual body segments or joints or their movement relative to each other. ¹Alter, Michael J. “Ch. 19: Functional Aspects of Stretching and Flexibility.” Science of Flexibility. Champaign, IL: Human Kinetics, 2004. 257. Print.

A very typical scenario during the progression of the squat, whether back squat, front squat, etc. is that while the load on the bar increases relatively quickly for a period of time the amplitude decreases. Amplitude is a very easy concept to understand in this case. The mean is the upright, standing or ready position. The amplitude is the total distance the bar moves from that starting point. The deeper the squat the greater the amplitude. This is only external amplitude though and ignores the movement of individual joints and body segments. This means that even if external amplitude remains apparently constant, the range of motion may be borrowed from inappropriate joints.

So it not only matters “how deep” one goes, but what point is measured! Even a squat with good and constant amplitude could be very stressful to certain tissues. For instance, if only the bar travel is measured and the apparent depth is actually due to lumbar flexion rather than a deep knee bend using full range of motion in the hips, knees, and ankles, wouldn’t this have a different impact on the injury potential the equation seeks to measure? So amplitude is NOT just one measurement and what we measure matters. We have to assume the internal amplitude is held constant, which is likely not the case.

Since the distance the bar travels in our scenario does not remain constant (assuming internal amplitude does) the amplitude does not remain constant. Since amplitude is part of performance then performance does not remain constant. A simple fact that is largely ignored by most trainers.

Applying the “law of repetitive motion” to this works fairly well as a general guideline as we can see that the force applied is going up and the amplitude is going down. So the tissue stress theoretically goes up (again, internal amp being constant) And despite the very large forces involved the law should predict that resistance training, when performed with full range of motion and sensible volume, is less injurious to tissues than activities such as running.

In reality, however, it does not make sense to group resistance training under the same “law” as high impact activities. Plyometrics, for instance, can involve forces even greater than strength training. Even simple jumping movements, such as jumping jacks, can impart ground reaction forces (GRF’s) of 3 to 5 times body weight.²McKay H, Tsang G, Heinonen A, MacKelvie K, Sanderson D, Khan KM 2005 Ground reaction forces associated with an effective elementary school based jumping intervention. Br J Sports Med 39:10–14   Depth jumps must surely impart the greatest GRF’s of any plyometric drill. How does amplitude affect these forces?

Looking at the amplitude of a depth jump would yield different conclusions. A depth jump is a plyometric exercise where the trainee stands on a box of a certain height and performs a vertical jump with a controlled landing while flexing the hips, knees, and ankles but controlling the torso. This is followed by an immediate vertical jump from the floor as high as possible.

The height of the box would be one possible measure of amplitude. The distance the shoulders move may be another. A higher box during plyometric depth jump increases the load on the body (which is extreme to begin with) and thus the potential for injury. The extra force must be attenuated during landing by increasing the amplitude of flexion involved. This increase in amplitude would by no means lessen the injury impact to skeletal tissues. During a plyometric movement, there is only a certain range of amplitude that is useful because too much amplitude increases the force the athlete must overcome in order to reverse the movement. Too much force and the amortization phase is increased which may defeat the purpose of the exercise since the phase between the eccentric and the concentric must be kept short to take advantage of the stretch-shortening cycle. Suddenly the law of repetitive motion isn’t looking so good. All movement isn’t the same. Human movement is too complex. We cannot apply one simple little equation.  By the way, the recommended range of height for depth jumps is 16 to 42″ with the average being 30 to 32 inches.³Baechle, Thomas R., and Roger W. Earle. Essentials of Strength Training and Conditioning. Champaign, Il. [etc.: Human Kinetics, 2000.

Regardless, we can still say that the amplitude of joint movement must be kept high or maintained in order to 1.) perform the movement correctly and with skill and 2.) decrease the chances of injury. Knowing this we can also keep in mind a few other parameters which influence movement amplitude:

Mobility and Flexibility

It is generally held that mobility must be constantly maintained to ensure that movements can be performed fluidly and with full range of motion of the various joints. If the equation means that higher amplitude causes lower injury risk, then this would seem to be in agreement with general notions concerning mobility. While there is some question as to this, for resistance training it may be useful to possess a degree of mobility that is slightly greater than that which is required by the movement or lift. In other words, what Bompa referred to as a “flexibility reserve” ⁴Bompa, Tudor O., and Tudor O. Bompa. “Ch. 13: Speed Flexibility and Coordination Training.” Periodization: Theory and Methodology of Training. Champaign, IL: Human Kinetics, 1999. 375. Print. However, I emphasize the word “slight” here. There is no need for hyper-mobility and for most this takes the form of an over-indulgence in either flexibility training such as static stretching or the prolonged indulgence in various contortions that have no relation to human performance such as in some yoga practices. There is also no reliable evidence that such a reserve actually decreases injury risk or that a lack of it is predictive of injury.

Time of Day

Range of motion can vary depending on the time of day. This is especially true of lumbar range of motion with this effect being more marked in flexion range of motion than extension. The lumbar flexion range of motion increases throughout the day from morning to afternoon.⁵Ensink FB, Saur PM, Frese K, Seeger D, Hildebrandt J: Lumbar range of motion: influence of time of day and individual factors on measurements. Spine 1996 , 21:1339-1343 And, in general, most people are more flexible in the afternoon than in the morning.

The most oft-cited data are observations by Osolin in 1971 which reported that range of motion was lowest in the morning and greatest between 10 and 11 Am and 4 and 5 PM. However, subsequent observations have amplitude being greatest at different periods and most tests were done on specific body regions. The peak “suppleness” of your lumbar region may occur at a different time of day than your hamstrings. It would be extremely difficult to find good data but it is safe to say that your range of motion will increase throughout the day and begin to dip again after about 4 PM, which some wiggles in between. The stiffness we all feel in the morning is not just a feeling but indicates much less range of motion than occurs slowly throughout the rest of the day. Diurnal variations in movement amplitude lend credence to the advice that one should train always at the same time of day, when possible. And this of course would apply to training specifically for mobility as well.

Law of Repetitive Motion and Resistance Training

A number of writers have attempted to meld the law of repetitive motion with resistance training. What the law brings to the student of strength training is the understanding that training injuries are more likely to result from cumulative trauma brought about by high volume weight training with low amplitude. This is a valuable lesson since many trainers and trainees alike tend to assign heavy weight low volume resistance training to a higher risk category than high volume, moderate intensity training. While the acute risk of very heavy loads is greater, the chronic risk of high volume training, as exemplified by the bodybuilding body part split, is much greater and most injuries are the result of chronic tissue overload.

However, such a formula can be nothing more than a basic guideline when it comes to resistance training. Such a formula taken as “law” could lull a trainee into a false sense of security. It is much more applicable to continuous cyclic movements such as running than to the repetitive movements of resistance training. It is also important to realize that the body’s tissues do not only adapt to movement but also to static postures and positions held habitually for long periods of time.

Strength Training vs Bodybuilding

Now, what I haven’t done yet, is really analyze this in terms of maximal low rep strength training versus high rep resistance training, such as bodybuilding. Before, I said that the law predicts that moderate strength training with good range of motion, etc. (fairly consistent amplitude) would have less potential for injury, and that taken at face value, that makes sense.

But the part of the formula that translates to an increase in the potential for injury is force and reps. For lifting weights, force is the load on the bar. Many are going to assume that when force goes up, injury potential goes up, and therefore heavy weight lifting or near-maximal training has just as much potential for injury as high rep training. Well, if you think that, you’re not understanding the formula, and indeed, this is not what we find in actual practice.

See, according to the formula, if the force, or load on the bar, increases, regardless of whether the reps stay the same, the potential for injury increases. Conversely, if the reps increase, and the force stays the same, the potential increases. But, in a given time period, as the force increases, the reps go down and thus the REST, increases. In the same time period, if the reps go up, the rest decreases. Assuming amplitude is held constant, or near-constant, this predicts that, yep, force alone does NOT equal more potential for injury.

Let’s say we have 10 minutes to finish a set of squats. Let’s say our force starts at 100 (that’s 100 pounds) and our reps start as one. Just being conservative, we put our rest at 9.5 And Amplitude, we call that 1, because, it doesn’t change during one rep. Solve for I and you get about 10.5. That’s meaningless in itself but it seems low, right?

So, what if we raise the reps to a typical number, 24. Say, 4 sets of 6. I’m going to say that puts our rest at about 9. I’m going to take a leap and say amplitude is held constant at 1. Solve for I. That is 266. Our injury potential just skyrocketed.

Let’s reverse is and keep the reps at ONE rep, but raise the force to 400. Amplitude is, of course, held constant because it is one rep. And rest is at least 9 minutes. The math is easy. I goes down to 44. Even a few more heavy reps will not cause an injury potential as high as our 24 reps. However, in this scenario, the time does not change and may seem overly long. However, as long as we assume the same time-period, long or short, we will get the same relative results. The only way to cause different results is to perform out heavy singles in a very short time period, even shorter than the time we would perform 24 reps in a typical bodybuilding session.

Although I still think the formula is a simplistic and even a bit silly attempt to quantify injury potential, I can’t help but smile because it predicts what I’ve been saying for years. And it shows what the typical trainee is missing. Obviously, we don’t usually perform just one single, but as we raise the weight, we also raise the rest or relaxation period. The risk of catastrophic failure always goes up with weight but these failures happen a lot less than chronic injuries from high rep low rest training for hypertrophy, etc.

Yet, trainees are constantly told to never rest more than 90 seconds or some number like that. If certain “coaches” think that maximum training causes more injuries, and they are prescribing virtually the same amount of rest for higher force as for higher reps, well, the math is there, isn’t it? This is not to say that I never do a heavy lifting session with ‘short’ rest periods, just usually longer than what I use for bodybuilding sessions, even during the same workout.

Of course, I would not rely on a formula to tell me that. As I explained, the formula cannot really be held as a law because we cannot really have one good number for the controlling factors. But it does coincide with most of the strength training worlds experience and observations, and with what injury data we have, and therefore the conclusion we have reached through inductive reasoning.