[Mark Langley is a Senior at North Carolina Central University and is currently enrolled in the Athletic Lab Coach Apprenticseship Program]

Scaling between intensity and volume is fairly easy. There are even formulas to determine what weight is appropriate to use for 3 repetitions versus 6 repetitions versus 10. Most people just make an arbitrary guess based on what they think the weight should scale to for more or less reps and generally speaking, that’s more reliable than using any one of the available formulas for converting 1 rep max to any number of repetitions, especially beyond the 10RM range.

Likewise, when we start scaling weight across individuals you can “eyeball” the weight, or use any number of methods to scale or make a judgement using the same yard stick, scientifically. The system is far from perfect, but it does provide a common reference point we can evaluate performance.

**Ratio Scaling**

One way to instantly make anyone with Napolean Syndrome happy is by using the ratio scale. This simply uses the weight lifted divided by body weight. In this case, a 75 kg person that squats 187.5 kg has close to 2.5 times strength to body weight. Meanwhile, a 105 kg person squatting 210 kg has an absolute strength measurement above the first person, but is only 2 times as strong relative to their body weight.

Generally speaking, the rationale makes sense, but the science shows it tends to favor lighter weights.^{1} Body mass and strength is not a 1 for 1 correlation. In general, it might be helpful when trying to get a quick gauge of performance by two individuals of similar weight, but at the same time, strength to weight ratios will differ according to what exercise is being compared. A bench press ratio of strength to weight will likely be lower than a squat ratio. Likewise, you could expect that a swimmer weighing 65 kg will likely have a lower ratio than a powerlifter since one sport favors pushing movements more than the other. It’s important to note that in all measures of scaling, whatever method of measuring relative strength is not comprehensive. Meaning, a calculated relative strength in the squat can only be compared to other measures of relative strength in the squat – not a bench press, deadlift, or anything else.

**Allometric Scaling**

### The General Concept

Another method commonly used is allometric scaling. This accepts that 1 kg of body mass does not always equal some fixed fraction of strength. The generally accepted method of allometric scaling is using strength and dividing it by body mass, which is raised to the power of 0.67 (although plausible ranges depending on multiple influences can make that exponent anywhere from 0.45 to 0.97). ^{2}

At this point, understanding the relationship of allometrically scaled strength to involving body composition, limb length, muscle cross-section area, muscle fiber composition, height, age, and gender seems somewhat murky. Although there seems to be an intuitive relationship, the research can only establish a relationship for some of these factors.^{3}

### Wilkes, Sinclair, and Coefficients: accounting for age and gender

The Wilkes coefficient and Sinclair equation are often used in Olympic Weightlifting and Powerlifting. This methods use the same inputs: body mass and mass lifted. This is also very sport specific. So much so, the Sinclair formula is updated every year. The Natural Athlete Strength Association distinguishes itself by focusing on natural athlete population pools – those that have been drug tested to standardize scores. Theoretically, they can be used in other settings with a large enough population to give somewhat a gauge of comparison. They are well conceived and validated, with a few caveats.^{4}

The formula are fairly involved, but one can easily find an app for the iPhone or Android to calculate these factors on the fly. Likewise, the calculations can be simplified by performing a shorthand calculation and multiplying it by a coefficient prescribed by a corresponding table. Coefficients are also presented to represent relative strength for the 16-22 year old category of lifter, as well as the masters category starting at age 40 onto 80 (using the Schwartz coefficient, 90 using the McCulloch). ^{5}

### Normative Data

Short of scaling though, there is a method of comparison where we’re comparing apples to apples, so to speak. The problem with different scales of relative strength is even though they are based on massed observation, they generally assume a general relationship that is regressive, where the extremes of the spectrum fall off and become marginal. Normative data tells us, in very concise and understandable terms, that individuals in a particular sport or field (or sometimes age, depending what table you’re looking at), are able to maximally perform at an average of X weight. ^{6}

Unfortunately, much of this data is presented using either a raw weight (usually pounds) or a ratio scale of strength and weight. Likewise, there’s usually a table defining recreational fitness populations. The short comings of this are the parameters measured and the context of the data. If you’re really hung up on whether or not you are in the top 2% of recreational lifters in bicep curls, there might not be a table of norms for you to follow. Likewise, you might not care how your performance on the leg press is because you test maximal or submaximal strength using the squat. In terms of context, many of these tables of norms are fairly old. Many date back to the 1980’s and 90’s.

## Conclusion

In general, there is some utility in knowing as well as not knowing how well you stack up against the rest. Having that unknown range of what is normal to lift could also be encouraging, making you strive forward without a specific top limit.

Generally, it is never in bad practice to see the results of your training last week or month or year, and goal set for improvement. Rather than relative to some fixed coefficient or fuzzy math, how much stronger, faster, more powerful, etc are you since the last time you did it? Or maybe your goal is athleticism over the life span. In which case, the questions should be how strong/powerful/fast are you relative to how you were in your 20’s or 30’s? That might not even have a number. You might not have done front squats, done Fran, or performed a clean and jerk at that point in your life. Goal setting and achievement are important. In the end, we strive to be better every day. If a string of numbers do that for us, maybe it’s helpful.

**References**

- Jacobson B, Thompson B, Conchola E, Glass R. A Comparison of Absolute , Ratio and Allometric Scaling Methods for Normalizing Strength in Elite American Football Players.
*J Athl Enhanc*. 2013;2(2):1-5. doi:10.4172/2324-9080.1000110. - Folland J, Mc Cauley T, Williams A. Allometric scaling of strength measurements to body size.
*Eur J Appl Physiol*. 2008;102(6):739-745. doi:10.1007/s00421-007-0654-x. - Kerksick CM, Mayhew JL, Grimstvedt, Megan Greenwood, Mike Rasmussen CJ, Kreider RB. Factors That Contribute to and Account for Strength and Work Capacity in a Large Cohort of Recreationally Trained Adult Healthy Men With High- and Low-Strength Levels.
*J Strength Cond Res*. 2014;28(5):1246-1254. - Vanderburgh P, Batterham A. Validation of the Wilks powerlifting formula.
*Med Sci Sports Exerc*. 1999;31(12):1869-1875. doi:10.1097/00005768-199912000-00027. - Lindqvist K. Powerlifting Relative Strength Calculator. 2006. http://tsampa.org/training/scripts/relative_strength/.
- National Strength & Conditioning Association.
*NSCA’s Guide to Tests and Assessments*. (Miller T, ed.). Champaign, IL: Human Kinetics; 2012.