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How to Use Math to Master Your Physical Strength

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As of this writing, I’m twelve weeks into Tactical Barbell’s signature progression. I’ve done eight weeks of aerobic base building, and this is week four of “Operator Black” for those who know. I’ll write more about the books, program, and my results in the future. For now, know that fitness programming has been on my mind a lot.

If you aren’t familiar, Tactical Barbell is a family of books, primarily authored by K. Black. The program focuses on the needs of military and law enforcement, who typically require a balance of strength and endurance. Being the data nerd that I am, I took the workout program templates and created a series of spreadsheets that effectively plan every workout I’m going to do for the next year. I’m not going to share it with you, as that’s really the point of buying the books, but while working with the numbers I couldn’t help but wonder how such programs come to be.

Origin Stories

When you start reading enough literature about weightlifting, you’ll eventually come across many references to athletic trainers in the Soviet Union during the 1960s through 1980s. Names like Arkady Vorobyev, Boris Sheiko, Yuri Verkhoshansky, and more pop up throughout.

During the Cold War, the Olympic Games were a proxy for which nation could “do it better.” In the 1950’s, the Soviet Union set out to dethrone the United States in Olympic Weightlifting contests. They were extremely successful, dominating the sport for decades- with many Eastern European countries today still winning gold.

That wasn’t an accident, as the Soviet Union drew from its large population and dedicated researchers to studying every last aspect of strength and fitness. They analyzed thousands of training logs, sessions, and victories to devise a program to systematize winning. In comparison, the United States is still decades behind on the research.

Many popular power lifting and fitness programs we see today, including Tactical Barbell, 5/3/1, StrongFirst, and others draw from the body of knowledge developed by the Soviet Union in this period.

One name I’ve seen a lot lately is Alexander Sergeyevitch Prilepin, a Soviet weightlifting coach from 1975 to 1985. He created a chart, colloquially known as Prilepin’s Chart, and this is where I want to start.

% of 1 RM Reps Per Set Optimal Reps Range of Reps
55% - 65% 3-6 24 18-30
70% - 80% 3-6 18 12-24
80% - 90% 2-4 15 10-20
90%+ 1-2 15 4-10

Reading Prilepin’s Chart

Fair warning, we’re about to nerd out with some math.

The chart itself looks straight forward, but I want to make sure you understand the context before moving on to implementing it. There’s a few elements here that result from Soviet weightlifting training methodology. The idea behind the chart is that you use it over and over again for each lift, so it’s not the entire workout per se, but each unique exercise within a workout.

The percentage of 1 repetition maximum (% of 1 RM) is a measure of how much effort you are exerting, otherwise known as intensity level. This is important because a cornerstone of Soviet-style training was regular practice at submaximal intensity. What does that mean?

The Soviets were famous for rarely training near their maximum strength. Instead, they regularly trained at lower ranges around 70% to 85%, which left them with enough energy to come back and do it again the next day. It also gave them ample opportunity to practice the lifting technique to perfection.

The reps per set is an illustration of the average number of repetitions an athlete would do for a given intensity level. Other resources I found mention that Soviet trainers usually programmed between 1/3 and 2/3 of an athlete’s maximum for a given weight. For example, if you could lift 100 lbs with perfect form for 10 repetitions maximum in a single set, then 1/3 to 2/3 for your actual workout sets would translate to 3 to 6 repetitions. Prilepin’s chart simply summarizes the practice.

The optimal reps column describes the typical balance point between work and fatigue for these high level athletes in a single workout for that movement. The range of reps shows the upper and lower bounds for the workout. From these columns, you establish the number of required sets to reach the number of repetitions while keeping the number of reps per set within the bounds of the second column.

For example, if the desired number of reps is 18, and your working sets should stay between 3 and 6 reps, then you would be performing 3 to 6 sets with a few minutes rest in between.

Building a Strength Program

Prilepin’s chart has problems for you and I when it comes to programming. First, it was focused on world class athletes training for the Olympics and other events. This audience was also likely using steroids. The volume and intensity here might be too much for most people. If you plan on using this then I think it’s prudent to start at the lower end of the rep ranges. Consider the “Optimal Reps” number to be the upper bound.

Secondly, this chart is for a single workout for a single lift. It says nothing about accumulated fatigue and recovery requirements over the course of a week of workouts.

Third, the chart is about power-focused Olympic lifts like the snatch or clean and jerk. These are “quick lifts,” and aren’t quite the same mechanics as power lifts like squat, press, and deadlift.

Calculating Workout Intensity

In 2005, Hristo Hristov wrote a paper about turning Prilepin’s chart into a practical programming tool. He called it the Intensity and Number of Lifts (INOL). In short, for a single workout the INOL value of a lift is the number of repetitions for a particular intensity divided by 100 minus the intensity.

Let’s put that in real terms, using the squat as an example. Let’s say my current 1 rep maximum for the back squat is 300 lbs. I’m programming a workout using 75% intensity, 225 lbs, and will perform 5 sets of 6 reps. That’s 30 reps total at that intensity.

Dividing 30 (my total reps) by 25 (which is 100 minus 75), gets me an INOL value of 1.2 for the workout. This value doesn’t really tell me anything just yet. Hristov included a chart to show relative effort of a given workout for a given lift. Now that you’ve seen the math, here’s the easy button: Elitefts put together a chart with all of the values already calculated.

From this, you can see that my calculated workout INOL of 1.2 would be in the “tough” category and I need to be careful about doing it too often. If you run the numbers from Prilepin’s chart, you’ll find that his “optimum” rep number for each intensity works well within this construct. This might be fine for a single workout, but how does it work for accumulated workouts over a week?

Hristov also included a weekly INOL chart. If we add up each of the individual workout INOL values performed over seven days, we get the weekly value.

From this, we would interpret that performing three workouts of my squat workout would be pushing it. 1.2 for three workouts gives me a value of 3.6, whereas doing it only twice per week would produce a result of 2.4. My takeaway is that I would be better off reducing squats to only two workouts per week or reducing the INOL value of a single workout by either cutting back the repetitions or intensity.

Going a Little Deeper

Before zooming back out to show a whole workout program worth of this, let’s spend just a little more time with these INOL values and how you can manipulate them.

The example I gave was performing a single workout consisting of 5 sets of 6 reps at 75% intensity. Hristov actually discussed this a bit in his paper by pointing out that the basic total reps divided by intensity can be misleading, because whether you do 5 sets of 6 or 6 sets of 5 gives you the same result. Another way to approach it is by calculating the INOL on a per-set basis and then adding it together.

Again, let’s illustrate. Assume you want to hit 18 total reps at 75% intensity. That gives a workout INOL value of 0.72, which is right in the green zone. You have the choice of either doing 3 sets of 6, or 6 sets of 3.

Either answer is correct, but the lifter will probably find 6 sets of 3 to be easier because of the reduced work between each rest period. This might be fine if this was the only exercise done during the workout, but all of that rest means performing the complete exercise will take a lot of time. Assuming a 2 minute rest period between each set, the 3×6 exercise is done in about 5 minutes total, not including any warmup sets, while the 6×3 workout would take about 12 minutes.

For time and efficiency reasons, we must find a balance of effort to rest.

Waved Intensity

Realize that you don’t have to stick at the same intensity and rep scheme from workout to workout or even set to set. A program like 5/3/1 might have you perform three sets with different intensity and repetition schemes between each one. Here’s an example from a 5/3/1 workout on Week 3

Here’s another example from 5/3/1 week 2, where you keep a consistent number of reps but vary the intensity.

Both of these workouts fall into the green “optimum” zone of Hristov’s single exercise chart. The last step would be adding together each individual INOL workout value for a given exercise over a seven day period.

If we used the two 5/3/1 examples above, assume you did the week 2 workout twice and the week 3 workout once within a 7-day period (i.e. you did the week 2 workout on Tuesday and Friday, followed by the Week 3 workout on Monday).

In a 7-day period, that results in a weekly INOL value of 2.0 (0.6 + 0.6 + 0.8). Again, right on the money for optimum performance with a single exercise with a little room to add warmup sets or squeeze a few reps in.

The challenge now becomes, what happens if we want to train multiple exercises?

Prilepin and INOL Shortcomings

Before moving on to the next piece and tying it all together, I want to make sure I talk about two important shortfalls of this approach.

The first issue is that the original Prilepin chart only dealt with fast Olympic lifts, and there is a mismatch of training styles and intensities.

To come up with a cleaner suggestion, the Daniel McKee at StratFit did some statistical work on Prilepin’s principles and INOL to come up with a newer “corrected” chart that’s more useful to the average person.

Secondly, you might have noticed that I haven’t mentioned anything above 6 repetitions in a set. Neither did Prilepin. Some styles of lifting, like hypertrophy training, call for rep ranges of 8, 10, 20, and beyond. This updated chart helps by eschewing the standard 2 to 6 reps and leaving it as a total number of reps in a workout and an optimum number of sets.

This format scales with the intensity, and the numbers work well for any kind of training.

  • 60% intensity is good for about 4 sets of 12 reps (very common bodybuilding range)
  • 80% intensity is ideal for about 4 sets of 5 (common powerlifting practice)
  • 95% intensity calls for 4 sets of 1 rep

You’ll have to do some rounding, but this chart does help guide you in the right direction.


Training Maxes and Accumulating Fatigue

Two more notes before getting on to a practical example. I use a 90% training max in my planning. I first learned this from 5/3/1, and it means that I don’t use my actual 1 RM is for a given lift when writing down what I intend to do. Instead, I base everything on 90% of my 1 RM. This gives me a margin of error that my “tested” 1 RM might have been with bad form, or I’m tired, and any other number of factors. Even if I plan to lift 100% of my “training max” it’s still only 90% of my actual max.

Working down the line, when I plan to lift 80% or 90% of my training max, the actual numbers are 73.7% and 84.2%. I tell you this because when I calculate my workout INOL numbers, I’m using these actual percentages and not the “planned” percentages.

For a workout where I planned to do 4 sets of 5 reps at 85% intensity, my actual intensity is 78.9%, so my INOL number works out to 20 (4 multiplied by 5) divided by 21.1 (100 minus 78.9), or 0.95.

Secondly, Hristov’s chart provides INOL values for a week. When combining workouts over several weeks, I average the values. To see if I’m pushing too hard or need to up the challenge.

If I have a particularly challenging week, then I plan to follow it up with an easier week to keep the average where I want it.

So how do I know what to use as my actual 1 RM? I do two things. First, I test it from time to time by working up to a heavy enough weight that I can safely do no more than two or three reps with good form. Then I take that weight and the number of reps and put it into a calculator. This tells me my estimated 1 RM. This might not be the most accurate, but since I use a training max, the margin of error is fine.

Secondly, and far more common, after every 4 to 6 weeks of lifting, I just add weight to my estimated 1 RM. Typically that’s 5 lbs to any upper body movement and 10 lbs to any lower body movement. I then base my training max and all other lifts off of this new number. After six months or so, I might test it again to see where I’m at.

Strength Programming

There are a lot of great strength programs out there from people who have trained thousands of athletes and developed solid systems for getting there. I happily point you towards Starting Strength, 5/3/1, Tactical Barbell, and others. When you read enough of these, you notice themes and that’s what I’m getting to.

What I’m writing here is just an example of how you might approach this process if you choose to do it yourself.

Exercise Selection

Most of us don’t have a huge amount of time to spend in the gym per week. We simply cannot budget two or three hours per day to focus on everything. We must find the biggest bang for our buck. That comes from compound lifts that involve multiple joints and muscles.

The human body exerts force in five basic movements. Horizontal pushing, horizontal pulling, vertical pushing, vertical pulling, and hinging. Our “bang for the buck” comes from training these movement patterns.

Outlift had a great article on the exercise selection topic that I shared around the Discord server. The walked through the selection process and ended up with the five following lifts:

  • Front squat
  • Bench press
  • Deadlift
  • Overhead press
  • Chin-up

They also outline alternatives for each if you aren’t yet able to execute each one with correct form. For example, using goblet squats in place of front squats or pushups in place of bench press. This list is a good starting point, but I’m not here to prescribe a workout to you- only illustrate how this list might be used.


Planning the Workouts

It’s not practical to all of these lifts in a single day. With sufficient rest periods, such a workout would take hours. By the time you got to the end, you would be exhausted. Instead, we much choose one of two paths.

The first option is to split the five movements into two different workouts done on different days. This is the format of Starting Strength, 5/3/1, and Tactical Barbell’s “Zulu” program.

The second option is to simply cut out two exercises and lean heavily into the other three. For example, you could argue that getting significantly stronger with the bench press has positive effect on shoulder strength as well, so the need to additionally focus on overhead press isn’t there. The same happens with deadlift, where a combination of chin ups and back squats train most of the same muscle groups so deadlift might be unnecessary.

Under the second option, you might choose to rotate exercises periodically. For example, swap bench press and overhead press every six weeks.

Which option is best? There isn’t one answer. Option one lends itself better if you have three to four days per week to dedicate to strength training. Option two might work best if you can only dedicate two or three days per week.

For illustration, let’s assume we’ll do the first option and split our lifts into two different workouts: A and B.

Workout A

  • Bench press
  • Front squat
  • Chin-up

Workout B

  • Overhead press
  • Deadlift

Loading and Scheduling of Workouts

With our two workouts, the next step is deciding how we want to schedule. This workout split lends itself well to either four days per week or three days per week.

With four days it would look something like this:

  • Monday: Workout A
  • Tuesday: Workout B
  • Wednesday: Rest
  • Thursday: Workout A
  • Friday: Workout B
  • Saturday: Rest
  • Sunday: Rest

Repeat this schedule from week to week. You could fit in conditioning work (which I’m not getting into) on Wednesday, Saturday, or in conjunction with a lifting day.

A three-day schedule would rotate over two weeks to look something like this:

  • Monday: Workout A
  • Tuesday: Rest
  • Wednesday: Workout B
  • Thursday: Rest
  • Friday: Workout A
  • Saturday: Rest
  • Sunday: Rest
  • Monday: Workout B
  • Tuesday: Rest
  • Wednesday: Workout A
  • Thursday: Rest
  • Friday: Workout B

With this schedule, you have more room for recovery or inserting conditioning work throughout the week on their own days. Let’s run the numbers on this assuming a flat 80% intensity level for all workouts.

According to our earlier chart, the optimum number of repetitions at 80% is 18. For argument’s sake, let’s include one set of five warmup reps at 65% (INOL .14) and then three work sets of five reps (0.25 INOL each). Combined, that gives us a single exercise INOL of 0.89 per exercise in a workout.

In the first schedule, four days per week, we do each workout twice. That results in 1.78 INOL for the week, which is a bit lower than optimal (optimal being between 2.0 and 3.0). Over two weeks, just for reference, we reach an accumulated value of 3.56 for each workout.

With the second schedule, workout A has a 1.78 INOL in the first week and only 0.89 in the second week. Workout B is the opposite. Over two weeks, combined, each workout accumulates 2.67 INOL.

Now you’re seeing how the frequency of workouts matters. Workout schedule A produces more frequency and you would therefore expect better results. However, on a week-to-week basis, neither schedule is overly demanding.

Manipulating Variables

How could we further manipulate this? One answer is adding additional repetitions. Instead of doing five reps, what if we did six? Three sets of six reps at 80% is an INOL of 0.9, then add the warmup set (0.14), and we’ve made a slightly more challenging workout at 1.04 INOL, but brought our weekly number up to the optimum zone with 2.08.

Alternatively, you could manipulate the number of sets or intensity levels. Three sets of five at 85% does the same thing for us. You could also try changing the intensity level from workout to workout with the same week, such as four sets of six at 75% on one day, and then three sets of five at 85% the next day.

You get the idea. Vary the intensity and repetitions, but keep yourself in the optimum INOL training zone to continue making progress.

So Now What?

If you’re inclined to create your own workout regime, I hope this post gives you the tools you need to get more out of your training. That said, I think a better option is looking at some of the well-known programs I’ve mentioned throughout. These were created by trainers with years of experience training thousands of athletes to success. They followed these same principles to create their programs, and they are all effective.

Regardless of whether you create your own program or choose one I’ve mentioned in this post, the most important thing is consistency and safety. Don’t execute lifts with poor form- you will get injured. Stay consistent on a program for at least eight weeks before ever considering trying something different. Ultimately, it doesn’t matter what program you choose- only that you stick to it.

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Matt

Matt is the primary author and owner of The Everyday Marksman. He's a former military officer turned professional tech sector trainer. He's a lifelong learner, passionate outdoorsman, and steadfast supporter of firearms culture.

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2 Comments
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Clark
Clark
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Interesting stuff!!! Your conclusion looks to be similar to Mark Rippetoe’s. I’ve used his Starting Strength program for years. Not sure if he also read Soviet literature, but has also given strength training a lot of thought. This may explain the similar conclusions. Mark’s biggest difference, however, is rep count and % of max. While you’re nerding out, his book, “Practical Programming for Strength Training” is excellent and explains his reasoning better than I can. What I can say is my results using his “system” have been fantastic as I approach 60. Thanks again for digging into these types of… Read more »

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