Muscle growth correlated with strength at r=0.92 — the number is inflated
In short
The link between muscle growth and strength gains gets stronger with training experience: weak in complete beginners, explaining up to about 70% of the variance in well-trained lifters. A recent study reported r=0.92 even in beginners, but that figure comes from repeated-measures correlation — a method that produces values around 0.83 on simulated data with no relationship whatsoever.
Nobody disputes that muscle size and strength are related. The argument is about how much, and one recent study shook that number hard.
The picture up to now
Research has painted a consistent picture. In untrained subjects, the relationship between hypertrophy and strength gains is very weak. As training status rises it strengthens progressively, reaching R² values of 0.6–0.7 in well-trained lifters — hypertrophy explaining roughly 70% of the variance in strength gains.
The reason is intuitive. Early strength gains come mostly from technique and motor learning. Across studies on untrained lifters, the averages are a 5% increase in muscle size against a 22% increase in strength. Even if hypertrophy causally contributes, it can only account for a bit under a quarter of what those beginners gained. With experience there is less left to extract from technique, so hypertrophy explains more.
The study that flipped it
Marques and colleagues had 39 untrained men complete 15 weeks of quad-focused training, measuring quadriceps volume by MRI and strength by isometric torque and knee extension 1RM. On average isometric strength rose 21.6%, 1RM rose 28.6%, and quadriceps volume rose 12.7%.
The correlations are the point. Repeated-measures correlation gave r = 0.92 for isometric strength and 0.89 for 1RM. Between-subject associations on the same data were 0.35–0.60. Read one way, hypertrophy explains 80–85% of the variance in strength gains; read the other, 12–35%. Same data, different method, different conclusion.
Why the method changes the answer
Between-subject comparisons carry individual differences with them. Two people with equally sized biceps can respond differently to the same 5% of growth: favourable insertions and high specific tension might turn it into a 20% strength gain, unfavourable ones into 10%. Gather twenty or thirty such people and the group-level relationship looks weak even when it is strong inside each individual. Repeated-measures correlation is an attempt to strip those fixed differences out, and the idea is sound.
Why you should not take the number at face value
Repeated-measures correlation is very sensitive to the coefficient of variation of the change scores. Strength and hypertrophy outcomes typically have change-score standard deviations comparable to the mean change — if a study's average strength gain is 10 kg, the SD tends to fall between 5 and 15 kg. When both outcomes move positively with CVs between 0.5 and 1.5, repeated-measures correlations of 0.65–0.85 can appear with no real association at all.
The author demonstrated this by simulation: two dummy variables increased entirely at random with no interaction between them still produced a repeated-measures r of 0.83. Ordinary Pearson correlation on the same data correctly reported no relationship.
An r of 0.8 from repeated-measures correlation literally means the same thing as an r of 0.8 from Pearson — but it implies something very different about how strongly one variable's change predicts the other's.
In summary
- Hypertrophy probably contributes more to beginners' strength gains than earlier studies suggested.
- But the relationship is nowhere near as strong as r=0.9 usually implies.
- When repeated-measures correlations turn up in papers, do not read them like ordinary correlation coefficients.
How to read your strength score
A relative strength score is a strength measure, calculated from Big 3 one-rep maxes, and this research bears directly on how to interpret it. Early on the score can climb fast while the mirror does not change, because much of that rise is skill rather than muscle — that is normal. Later, moving the score further depends more on muscle. Logging bodyweight alongside your Big 3 over the same period makes it much easier to see which of the two is driving the current climb.
Frequently asked questions
Does bigger muscle always mean more strength?
They are related but not proportional. In beginners, hypertrophy explains little of the variance in strength gains; in well-trained lifters it reaches around 70%. Much of the early gain comes from technique and motor learning.
How much size and strength do beginners gain?
Across studies on untrained lifters the averages are roughly 5% more muscle and 22% more strength. In a recent 15-week lower-body study, quadriceps volume rose 12.7% and knee extension 1RM rose 28.6%.
What does the r=0.92 correlation actually mean?
It came from repeated-measures correlation. Between-subject correlations on the same data were 0.35–0.60, and repeated-measures correlation is sensitive enough to change-score variability that it can return around 0.83 on data with no relationship at all.
Should I train for size or for technique to get stronger?
It depends on your stage. Beginners have the most to gain from movement skill and motor learning; as experience accumulates and technique yields less, muscle growth accounts for a larger share.
Source: Stronger by Science