Strength divided by muscle size still carries a size effect
In short
Muscle strength is multifactorial, and size and strength change by different amounts depending on the resistance-training loading paradigm. This paper applies ratio normalisation and multiple regression to NHANES 1999-2002 data and to the authors' earlier dataset in order to compare them. Its conclusion is that ratio normalisation carries assumptions that are not obvious unless you test them, so strength divided by muscle size cannot be treated as a size-free number.
The standard way to compare people of different sizes is to divide strength by body mass or muscle size. This paper argues the division is not as clean as it looks: ratio normalisation rests on assumptions, and skipping the test leaves a size effect in the supposedly corrected number.
Why divide strength by muscle size at all?
Two reasons. One is attribution: to tell whether a strength gain came from muscle growth or from neural and intramuscular adaptations, you need size held fixed. The other is comparison between individuals, putting people with different amounts of muscle on the same scale.
There is a real reason to bother. As the authors note, size and strength are associated but often change disproportionately under different loading paradigms. Eight weeks of training regularly produces a small change in size next to a large change in strength.
What does the ratio assume?
Comparing strength divided by muscle size assumes strength is directly proportional to size and that the relationship passes through the origin. When real data violate that, the ratio still tilts systematically with body size. You believe you corrected for size and you did not.
The authors demonstrate the point on NHANES 1999-2002 data and on a previous investigation from their own group, running ratio normalisation alongside multiple regression. Regression holds size fixed as a covariate instead of dividing by it, so it survives a relationship that does not pass through zero.
This is a methods paper, not a training trial. No program comes out ahead here. What it does give you is grounds to ask how any relative-strength number was constructed before you trust it.
How Muscle Index handles it
Muscle Index does not divide the Big 3 total by body weight. It multiplies by a fourth-order DOTS polynomial coefficient fitted to real lifter data. The fact that the relationship between a 60 kg lifter and a 100 kg lifter is neither linear nor origin-crossing is already inside the coefficient. Plain division is what produces the familiar bias toward lighter lifters.
For the numbers behind the same problem, see the r=0.92 size-strength correlation is inflated and strength rose 79.5% while only one muscle grew. On where a standard should come from at all, see strength standards belong to the real distribution.
Frequently asked questions
Does dividing strength by body weight or muscle size make a fair comparison?
Not on its own. The division assumes strength is proportional to size with a relationship passing through the origin, and when data violate that, a size-related tilt remains after normalising.
What is used instead of ratio normalisation?
Multiple regression. Muscle size enters the model as a covariate and is held fixed rather than divided out, which works even when the strength-size relationship does not pass through zero.
Why hold muscle size fixed when looking at strength?
To attribute the gain. Whether strength rose because muscle grew or because of neural and intramuscular adaptations can only be separated with size held at a constant value.
Do muscle size and strength always rise together?
No. They are associated but change disproportionately depending on the loading paradigm used, and a small size change alongside a large strength change is common.
How does Muscle Index correct for body weight?
It multiplies the Big 3 total by a fourth-order DOTS polynomial coefficient rather than dividing by body weight. The non-linear relationship between weight and strength is built into the coefficient, which avoids the light-lifter bias of plain division.
Source: PubMed