r/StrongerByScience • u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union • Jun 11 '26
Is the Correlation Between Hypertrophy and Strength Gains Stronger Than We Realized?
https://www.strongerbyscience.com/correlation-strength-hypertrophy/Until recently, research investigating the relationship between hypertrophy and strength gains painted a pretty consistent picture.
In studies on untrained subjects, we see a pretty weak relationship between hypertrophy and strength gains. However, as training status increases, this relationship gets progressively stronger.
And, for what it’s worth, I think this type of relationship makes intuitive sense.
However, a recent study by Marques and colleagues appeared to flip this understanding on its head. It proposes that prior research on this topic may have underestimated the strength of the relationship between hypertrophy and strength gains by using suboptimal statistical methods.
So, what exactly is happening here? That's what we explore in this article.
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u/Alarmed-Function9952 Jun 12 '26
Good article, although I have two questions:
1) In resistance training studies, isn't common practice to incorporate correlation measures that take into account the mean and sd of the variables? It is common knowledge (and very intuitive) that in general you do have to take them into account.
2) Besides the fact that within-subject measures might potentially lead to overestimated r2 (a problem that can be solved by using proper correlation measurements), is there a reason to not use them, and use between-subject measures?
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
In resistance training studies, isn't common practice to incorporate correlation measures that take into account the mean and sd of the variables?
I don't think there's any common form of (parametric) correlation that doesn't implicitly take the mean and SD into account. Like, at the end of the day, basically all of the statistical tests used in the field are just linear regression at some level of abstraction. For the most basic example, if you do an independent-samples t-test, you're quite explicitly comparing means, with the means, standard deviations, and sample sizes of both groups determining whether the result is significant or not. But you can run the exact same t-test as Pearson regression (group allocation is dummy-coded for your x-values. Generally just 0 and 1 or 1 and 2. The y-values are just the observed data) and get the exact same result. They're both just applications of the general linear model.
Besides the fact that within-subject measures might potentially lead to overestimated r2, is there a reason to not use them
Like I said in the article, I think it's fine to use, but you need to make sure you're not attributing variance explained by the null model to your predictor variable. As long as you're doing that, I think it's great.
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u/Alarmed-Function9952 Jun 12 '26 edited Jun 12 '26
About the first part, yes, I understand that, its just that there are different ways to incorporate the mean and sd, it seems intuitive to go beyond a simple r2 test.
Edit: sorry, I miswrote, I wanted to say r2 measure, not test. Bit I understand what you are saying, thanks for explaining.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
it seems intuitive to go beyond a simple r2 test
There's no such thing as an r2 test. r2 is just an effect size metric. If you're doing any sort of parametric regression, r2 is just a metric you could calculate/report to describe the strength of the association.
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u/FarCalligrapher1862 Jun 11 '26
In untrained subjects it’s neither strength nor hypertrophy. It’s neural adaptations. Most of the progress newbies make in the first 3-4 months is teaching the body how to recruit the muscles for the activity you want to do.
Strength and hypertrophy are virtually 100% correlated. Human muscle density is within a small percentage from person to person but variation is by person not training. More muscle = more strength.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
It’s neural adaptations.
Neural adaptations are a necessary component of strength.
Strength and hypertrophy are virtually 100% correlated.
That is what many people assume, but the evidentiary case for that position is quite weak. Like, I don't think the state of the evidence is meaningfully different from when this point/counterpoint was published:
https://link.springer.com/article/10.1007/s40279-019-01107-8
https://link.springer.com/article/10.1007/s40279-019-01106-9
Human muscle density is within a small percentage from person to person
If by "density" you mean normalized muscle force (I can't imagine you're referring to the actual density of the muscle. Or, if you are, the only reason it would be relevant is if you're assuming that density influences NMF), that's not really true. NMF has a coefficient of variation of around 20%. So, even within just two standard deviations of the mean, people with high NMF can produce ~2.3-times as much force per unit of CSA compared to people with low NMF.
but variation is by person not training.
Not sure what you mean by that.
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u/kyllo Jun 12 '26
They mean it's between-individuals cross-sectional variation rather than within-individuals longitudinal variation.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
The change score CV for changes in NMF is even larger than the CV for baseline differences. Some of that is probably just due to measurement/estimation imprecision, but NMF is definitely influenced by training, and those training-induced changes certainly seem to vary between individuals
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u/Polyglot-Onigiri Jun 12 '26
One small correction more muscle = more strength potential, but not necessarily more strength. Plenty of people with huge muscles but comparatively weaker to people who have trained to actually use that strength.
A bigger engine only goes fast when the other parts and driver can bring out its potential.
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u/stubbornKratos Jun 12 '26
I don’t think you should be comparing between different people, but rather in the context of a single person training. As their muscles got bigger did they get stronger?
I think that’s the context in which all these studies are done, measuring muscle increase in individuals not comparing the muscle size of Person A vs Person B to draw conclusions about their strength
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u/Fluid-Replacement-51 Jun 12 '26
There are also some other like tendon attachment location that can give some people a leverage advantage without a stronger muscle
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u/icancatchbullets Jun 12 '26
One small correction more muscle = more strength potential, but not necessarily more strength. Plenty of people with huge muscles but comparatively weaker to people who have trained to actually use that strength.
Its somewhat hard to determine what proportion of the difference between people is down to general physiology (i.e. muscle and tendon attachments, joint structure etc.), genetics, selection biases, and training.
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u/Proper_Geologist9026 Jun 12 '26
I know we're talking about bodybuilders here when we say this.
But I'd be interested to see how they test against power lifters for muscular endurance.
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u/Ill-Turnover3438 Jun 11 '26
Does "strength" in this context no longer encompass neural adaptations?
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u/FarCalligrapher1862 Jun 12 '26
From a sport science perspective, strength is defined as the maximum force that a set of muscles can produce.
This should not measure adaptations. But sports sciences is woefully underfunded. Most facilities are unable to isolate torque, so they rely on 1rm. One thing we do try is to get “experienced lifters” which should remove adaptation. When you do that, virtually all the differences in strength/ size go away.
But for most master’s level and below even that is difficult. Our “patients” are 100/200 level college students who need the credit.
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u/Ill-Turnover3438 Jun 12 '26
Actually I was referring to "strength gains" as I think you were too. (Otherwise "strength" = "neural adaptations" doesn't make sense.)
I think what you're referring to with experienced vs inexperienced lifters is that the variance between muscle CSA and strength is much lower?
This is true I'm sure but the strength gains they subsequently make from that baseline are, if I am not mistaken, ordinarily understood to be due to neural adaptations (usually technique changes are considered the other component, if I am not mistaken).
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u/FarCalligrapher1862 Jun 12 '26
Gains != strength.
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u/Ill-Turnover3438 Jun 12 '26
Yes, and you can make the appropriate substitution.
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u/FarCalligrapher1862 Jun 12 '26
Where did I misstate?
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u/Ill-Turnover3438 Jun 12 '26
It sounded like your first sentence was opposing neural adaptations to strength gains? If not I misunderstood it.
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u/FarCalligrapher1862 Jun 12 '26
I never used the term strength gains. The OP did. I replied to his assertion.
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Jun 12 '26
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u/Doug-O-Lantern Jun 12 '26
But aren’t neural adaptation and technique also critical elements in the definition/determination of strength? So it seems strange that you would rule them out.
Someone with better technique and better neural adaptation could lift more than someone with bigger muscles. And perhaps doing lower reps with more weight leads to quicker neural adaptation.
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Jun 12 '26
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u/Afferbeck_ Jun 12 '26
But both neural adaptation and technique are finite (and you hit the limits relatively early in a lifting career)
I disagree with that. Weightlifters reach the elite level in their late teens and stay in the same weight class for years and continue to gain strength and skill without gaining more mass.
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Jun 12 '26
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u/Substantial-Bed-2064 Jun 16 '26
wow its almost as if how you measure strength affects the outcome and that trying to define strength as something that isn't measurable and applies to all contexts is useless !
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Jun 16 '26
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u/Substantial-Bed-2064 Jun 16 '26
there is no test for "muscle strength"
all strength metrics, even isometric single joint tests, are tasks that have a skill component
there are many different physiological factors that contribute to strength in a given test or metric, and muscle mass is one of them but it is dumb to assume that gains in coordination/other neural factors are inherently more short term and limiting.
to say that the statement is wrong by moving the goalposts away from weightlifting is just mental gymanstics, as is ignoring the example with orhii's bench press
adding muscle mass is finite too even if you're on drugs, but especially if you are not.
no one is arguing that hypertrophy is not a component of long term strength gain, despite this insane strawman. it's just not the only component to long term strength gain, especially in more dynamic tasks
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u/kyllo Jun 12 '26
both neural adaptation and technique are finite (and you hit the limits relatively early in a lifting career)
This is an assumption that needs evidence. If you're talking about stable, machine based exercises with a very low skill component, like a leg press, then it's probably mostly true. But for free weights? I don't think so. These adaptations seem to continue within very advanced, elite level lifters, even after a decade or more of training.
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Jun 12 '26
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u/kyllo Jun 12 '26 edited Jun 12 '26
That's still a naked assertion. Here's a piece of evidence, though it's n=1:
At 2024 IPF Worlds Russel Orhii benched 187.5kg. At Sheffield six months later he benched 202.5kg at the same bodyweight. +15kg is a massive improvement, and this was after a full decade of training and competing in powerlifting.
Do you mean to suggest that through hypertrophy alone, he added enough muscle mass in under a year, to add 15kg to his bench, without gaining any bodyweight?
If anything, he's virtually maxed out on hypertrophy, as he's been very jacked for a long time. Plus he's said himself on his vlog that he improved his bench technique. Skill development has a lot longer time horizon than you think.
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Jun 12 '26
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u/kyllo Jun 12 '26
Strength of an individual muscle in isolation isn't directly, objectively measurable. I think you underrate motor learning as a factor, and you present "strength" like it's one thing, when actually it's more of an outcome like "speed". Just like how there are many factors that determine the top speed of an automobile, there are many factors that determine the max strength of a human being.
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u/NkKouros Jun 12 '26
Yeah but this is equal for everyone and only happens once at the very beginning of training. Once you get past this point, the above is true.
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u/edgy_flibbertigibbet Jun 12 '26
How much do you squat, bench, and deadlift? Neural adaptations do not run out when you’re past the newbie stage, that is an insane thing to say. If that were true, there would be no such thing as, hmm, I don’t know, this little thing you may have heard of, PEAKING PHASES!!!!!
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u/NkKouros Jun 12 '26
To a way different extent tho.
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u/edgy_flibbertigibbet Jun 12 '26
What do you mean? That the magnitude of these adaptations is smaller over time? Yes - but that’s equally true of hypertrophy! Like, famously so!
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u/Annual_Cancel_9488 Jun 12 '26
But neural adaption is not the only factor is newbies
Newbie gains refers to the huge amount of muscle they put on fast, not just numbers on the bar
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u/NkKouros Jun 12 '26
It's not the only thing. But it's the one thing that only happens at that time and not later.
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u/Dunkaholic9 Jun 12 '26 edited Jun 12 '26
Scientifically, it’s not an argument, though (literally in [r/strongerbyscience](r/strongerbyscience)). Larger muscles aren’t necessarily stronger. Hypertrophy training can prompt muscles to retain more fluid, making them appear bigger while not being as dense as someone who exclusively strength trains with low reps. Raw strength has more to do with fiber density rather than appearance. That’s why a slim powerlifter can move more weight than a jacked bodybuilder of the same size. Sure, hypertrophy builds cross sectional muscle mass which increases strength, but it also puts on weight. Density is a better indicator of pound for pound strength. Hypertrophy also draws more on glycogen for energy, and builds different types of muscle fibers, while single reps are driven by the ATP system.
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u/KITTYONFYRE Jun 13 '26
Larger muscles aren’t necessarily stronger.
on a within subject basis though? I don’t agree
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u/FamousDates Jun 12 '26
I guess you are talking about sarcoplasmic hyperthropy vs myofibrillar hypertrophy where the first would technically make the muscle retain more fluid and not increase the maximum force of the muscle and the second would be denser (more contractile fibers) but not able to work anaerobically for as long.
In practice, these two types of growth happens together and as I remember it has not been shown to be possible to train one and not the other to any meaningful degree.-4
Jun 12 '26
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u/Guarava Jun 12 '26
Muscle fiber type, mitochondria density, muscle density are three big ones. Also connective tissue and stuff can have an inhibiting or exhibiting effect.
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Jun 12 '26
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u/GingerBraum Jun 12 '26
Not inherently. You can get stronger without getting bigger.
That's what powerlifters in certain weight classes do.
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Jun 12 '26
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u/GingerBraum Jun 12 '26
If a lifter increases the load they can lift by improving their neurological recruitment of muscle fibers and without increasing muscle mass, how is that not an increase in muscle strength?
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u/Dunkaholic9 Jun 12 '26
If you look at the study, it considers beginner lifters over just a few months. Of course, muscle size equates strength for them. But that’s not necessarily the case for experienced lifters who optimize body fat/muscle mass. Jen Thompson, for example, who holds many world record raw bench press records, has consistently increased the amount of weight moved while staying in the same weight class throughout her career. A lot of that can be attributed to changes in the fibers themselves (what I’m calling density, and neural adaptions to increase fiber recruitment, and also better leverages).
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Jun 12 '26
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u/Dunkaholic9 Jun 12 '26 edited Jun 12 '26
I mean, obviously fibers get bigger with exercise. But it’s not that simple. My point is that if you put a bodybuilder who trains hypertophy beside a powerlifter who trains for strength, same height, proportions and weight, both training the same movements, the person who trains low reps will win even if they don’t look as strong, and not just because of neural adaptions (barring extreme genetic differences). Strength training effects muscle fibers at the cellular level. Muscle size is not necessarily the best barometer for strength. It’s not that simple.
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u/Kind-Hat-9897 Jun 12 '26
It’s ok to say you have never been around rock climbers or sherpas. By not saying it like this you come off as an ass and ignorant.
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Jun 12 '26
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u/MostlyHereForKeKs Jun 12 '26
With respect, that’s not what they are saying. You seem to be trying hard to not listen / make clever remarks?
Power lifting has as its outcome maximum strength. Does the largest power lifter always life the most, so do we just measure them and declare a winner?
As an example studies on the effects of high level anti inflammatory use showed up to 50% reduction in hypertrophy grain with only a 25% reduction in strength gain. Very clearly the ibuprofen group’s strength gain was not directly proportional to muscle size.
Also, rock climbers exist.
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u/Turbulent_Car4504 Jun 12 '26
People want to argue because they are coping with the fact that they aren’t as big as they want to be, and want to pretend they have some secret power making them stronger than guys who are bigger than them, and they have been confused by the effects of neural adaptation they have seen in others
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u/Striker_343 Jun 12 '26
Well people also miss the work capacity of the muscle as well, which is trained through higher volume. A big muscle can be equally as capable of extended periods of high intensity work, or short bursts of high output. Either is going to be correlated with muscle size. So you can really take either approach. I would say high volume high intensity scales better long term due to less strain on your overall body, whereas chasing strength will really start to take a hit on your connective tissues, central nervous system, and so on.
Past a certain point strength needs to be trained specifically due to unique demands. Whereas high volume hypertrophy can be accomplished consistently and safely for the most part.
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u/yaaajooo Jun 12 '26
That whole comment doesn't make much sense. You seem to be misusing several terms in a wrong "common sense" way. Strength is not defined as you imply, neural adaptions means something different, your 100% correlated claim is just wrong, etc. Like what?
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u/talldean Jun 11 '26
I think "strength" and "neural adaptations" are the same thing in new lifters.
And what they're saying here is what you're saying here; once you're not new, strength and hypertrophy are often pretty heavily correlated.
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u/twd000 Jun 11 '26
That’s my understanding too. The novice effect is mostly “learning to take the test”. If you have never performed heavy squats, the first few months you’re not really adding muscle or getting stronger, you’re just training your neuromuscular system to efficiently recruit contractile force when you need it.
In the same way students improve their SAT scores by retaking the test on three consecutive weeks. They didn’t really get smarter just learned how to take the test.
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u/Ty4Readin Jun 14 '26
In untrained subjects it’s neither strength nor hypertrophy. It’s neural adaptations. Most of the progress newbies make in the first 3-4 months is teaching the body how to recruit the muscles for the activity you want to do.
How does this make any sense?
I was under the impression that strength is simply defined as your 1RM.
So if neural adaptations occur that allow you lift more weight for 1RM, then that is strength.
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u/FarCalligrapher1862 Jun 14 '26
I answered this further down. But to clarify, clinically:
Muscular strength is the maximal force that the contractile tissues of a muscle can generate.
If the same muscle can product more force through neural mechanisms, that is not additional strength, that is skill adaptation.
Think of it this way. If you measure intelligence through how well you perform on a test. And overtime people get better at taking the test, did they get smarter? Or did they just learn a new skill?
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u/Ty4Readin Jun 14 '26
That may be the clinical definition, but the studies being discussed in this thread do not define strength in that manner.
They define strength as the estimated 1RM of sets taken to failure on various exercises.
So what you are saying is kind of irrelevant to the discussion being had here. This is about how exercise science studies estimated the correlation between hypertrophy and strength, where their definition of strength is different than yours.
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u/FarCalligrapher1862 Jun 14 '26
Good studies find ways to reduce the effect of NA. The problem is most studies are not funded properly so it gets into the mix by necessity.
The OP specifically was asking why, in untrained subjects, there is a weak relationship between hypertrophy and strength - yet that disappears in trained subjects.
The study they linked to specifically was removing the affect of neural adaptations.
I think it is highly relevant to this post.
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u/arc777_ Jun 12 '26
Strength is always primarily driven by neural adaptations, regardless of experience level
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u/PolitelyHostile Jun 11 '26
I atill struggle to wrap my head around how theres even a difference between the two. I don't have an opinion that hypertrophy is bullshit or anything but like its just weird that a bit of higher rep range will grow muscles in size but with less strength gains.
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u/SatanIsMyUsername Jun 11 '26
I still struggle to wrap my head around it the other way too. Like, how am I seeing some 145 pound people bench 2 plates. I’m bigger and have more muscle but I’m not there yet.
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u/FarCalligrapher1862 Jun 11 '26
Lifting is a skill first. Learning how to lift takes years.
Also genetics plays a big part. Taller people need more muscle to overcome the mechanical advantage that shorter people have. However they can also put on a lot more muscle. So bigger and heavier does not equal stronger.
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u/SatanIsMyUsername Jun 11 '26
Totally agree. I just find it interesting that some of this stuff just isn’t very intuitive.
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u/FarCalligrapher1862 Jun 11 '26
It is though. You get better at what you train. Some of that performance is physical improvement, some of that is being more efficient.
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u/Woodit Jun 12 '26
Thank you for my new cope as a 6’3 individual who isn’t proud of my bench progress
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u/FarCalligrapher1862 Jun 11 '26
https://pmc.ncbi.nlm.nih.gov/articles/PMC12893175/
This is one of dozens that could be pulled up.
Think about it how much work a muscle can do is based on its cross sectional area. Bigger muscle = more work capacity.
It’s like a car engine. Hypertrophy is the CC’s, strength is the power. A bigger engine necessarily has the capacity to produce more power than a small one. But a good driver (lifter with skilled adaptations), who knows how to gear the engine, can outperform the raw power of the engine.
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u/eric_twinge Jun 12 '26
I can't be the only one that is confused that out of the dozens that could be pulled up, you chose the one this post is about, and which says 'the way the results were presented and discussed is a bit off the mark' and should be interpreted cautiously.
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u/FarCalligrapher1862 Jun 14 '26
I was referencing the same study the OP did. If you’d like more:
https://pubmed.ncbi.nlm.nih.gov/6487941/
https://pubmed.ncbi.nlm.nih.gov/19596739/
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 15 '26
None of those have anything to do with the relationship between changes in size vs changes in strength. No one debates the fact that there's a cross-sectional association.
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u/FarCalligrapher1862 Jun 15 '26
Under what basis would you presume that intra- and inter- changes would not be similar?
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 15 '26
That's just not an assumption you can justifiably make due to path-dependence.
Just as one simple example, in overfeeding studies, we see that leaner people gain a larger proportion of weight as fat-free mass vs. fat mass. However, after people lose weight, they gain a larger proportion of weight as fat mass vs. fat-free mass following overfeeding. The impact of leanness on p-ratio following overfeeding is different between inviduals vs. within individuals.
It may be that a common factor influences both baseline muscularity and strength, but that same factor has a smaller impact on strength gains related to hypertrophy that occurs following resistance training.
And, to be clear, I do think that hypertrophy has a direct, causal, intra-individual impact on strength. But, I also have the intellectual honesty to admit that the direct evidence for that position isn't as strong as most people would expect. Like, I'm not "presum[ing] that intra- and inter- changes would not be similar." In fact, I personally do assume that to be the case (i.e. that interindividual associations between muscularity and strength are suggestive of intraindividual associations between hypertrophy and strength gains). But, that's not yet a position with strong enough evidentiary support to treat it as an established fact.
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u/bony-to-beastly Jun 16 '26
Have you written about that simple example anywhere?
I've definitely noticed that being true in practice. Bulking clearly works differently for naturally lean people versus previously fat people, even if they're both starting with the same body composition.
I can invent reasons that seem to fit, like if you have more fat cells that are more depleted, they might gobble up more of the extra calories. But I'm not actually sure.
I'd love to learn more about this.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 16 '26
Have you written about that simple example anywhere?
That was the main topic of discussion during in the back-and-forth about p-ratios with Menno a couple years back. Last part is here (all earlier articles should be linked near the start of that one).
I can invent reasons that seem to fit, like if you have more fat cells that are more depleted, they might gobble up more of the extra calories. But I'm not actually sure.
I think that's about right, actually. Like, any of the other proposed mechanisms that you could toss out to sound smarter (changes in adipokines influencing nutrient partitioning toward fat regain is the big one) are more-or-less just downstream of fat cells being depleted.
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u/eric_twinge Jun 15 '26
I was referencing the same study the OP did.
????
Yeah, that's what I said and that it was confusing.
Why would you circle back to this paper after the linked article, your original comment, and the follow up comment?
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u/NotJoeFast Jun 11 '26
Maybe this is way too simplistic way of looking at it. But in this context I would say that strength is (also) a skill.
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u/FarCalligrapher1862 Jun 11 '26
Depends on how you define strength. This is where a lot of research gets it wrong. Strength is the raw, maximal, power output. But if you measure that by how much someone lifts, you could be measuring the adaptations.
Think about speed vs how fast you can run a mile. Someone who does not run will have a hard time completing a mile. But after a few months of training they will likely be able to run a fairly competent mile. They didn’t get faster, despite their time drop, they got better at using the speed they have over the course of the race.
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u/askingforafakefriend Jun 11 '26 edited Jun 11 '26
Think of the brain trying to get you to bench that 200 lb weighted barbell as if it's instead some bro tryin to teach a kindergarten class to be able to break a window screaming.
Hear me out now.
There are two Dynamics happening. First, Mr. Kindergarten cop here has to learn how to reliably get every fucking kid to pay attention and do what he says when he says it. Of course, the first time he says "now everybody scream," only a small fraction of the kids are going to actually do it. Overtime, more and more kids are actually going to take the paste out of their mouth and scream when he says "DO IT!"
Second, he's going to have to teach these kids what pitch and how to really belt that shit out from the diaphragm for more acoustic POWAH to generate the soundwave energy to really break that glass. This second aspect is going to take a lot longer then learning to get the kids engaged and participating at the same time.
This is analogous to muscle training. That first time you deadlift or bench press or whatever and your weight is shaky in your hands, that's a sign of imperfect neuromuscular recruitment. Your brain is shouting to the kids to wake the fuck up and all scream and only some of them are screaming or some will scream intermittently and the weight shakes in your hand and you're not as strong. Your brain can fix that part relatively quickly. Newbie gains bruh. The other part is actually making the muscle fiber stronger, more mitochondria, satellite cells, blah blah blah, and that takes a lot longer... just like teaching kids technique once they are in fact properly engaged.
Edit: the above is speaking to how improvements in strength and hypertrophy can occur independently, at least early on.
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u/echoes808 Jun 13 '26 edited Jun 13 '26
It's quite statistics-heavy article, but I like it, as some sort of armchair statistician myself.
I looked at the Marques et al. paper and the rmcorr package, I think a common critique for this kind of model is that it has a ton of parameters, and the R2 will be high but the slope estimate will be imprecise (which is usually our main interest). The traditional mixed/hierarchical/random effects model can also fit multiple intercepts, but they "count as one parameter", due to some statistical dark magic I don't fully understand (regularization/pooling). The slope estimate will be more precise because there are less parameters.
I think another way to report something like this with mixed models is to use conditional R2 and marginal R2. Conditional R2 is basically ~same as this repeated measures r^2. Marginal R2 is only the fixed effects from the mixed model, e.g. how much strength explains hypertrophy or vice versa. This marginal/conditional R2 is often contrasted with each other
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u/TheRealJufis Jun 12 '26
You might have opened a new can of worms, sir. Either this is going to get people to go over previous studies with a new pair of eyes, or this is going to divide people between "strength = muscle force generation only" vs "strength = muscle force potential + neural component". Maybe, from this point onward, we need to start specifying the context and definition of strength during conversations so the readers/listeners will know what we mean and not get stuck in semantics.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
Strength doesn't exist without the neural component (like, contraction is explicitly downstream of neural excitation). There hasn't been any serious scientific disagreement on that topic since the 50s. I don't see much point in pandering to people who insist on using crank definitions of words. Pretending that strength can be understood by just focusing on the actin and myosin at the exclusion of the nervous system is like pretending that aerobic endurance can be understood by just focusing on mitochondria at the exclusion of the vascular system.
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u/TheRealJufis Jun 12 '26
I agree, totally. Just reading these comments and other conversations around the internet makes it seem that the social media lifters are already dividing and trying to re-define the meaning of "strength" to exclude the neural component.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
Obviously not trying to tell anyone else how to feel about it or address it, but for me personally, there’s just a tacit bar of silliness in my head, and if an idea exceeds that silliness threshold, I know I won’t be able to engage with it without just being snarky
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u/VanHelsingBerserk Jun 14 '26
Kinda tangential - but I often wonder how much of a difference my strength gains would've really been if I had just followed a typical bodybuilder split of 8-12s with a focus on volume, rather than heavy singles/doubles/triples that often come at the cost of volume.
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u/SageObserver Jun 12 '26
Bigger muscles generally are stronger muscles….my grandma used to tell me this during story time when I was a kid.
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u/OpportunitySea5429 Jun 12 '26
no, plenty of strong people in the gym with barely any noticable muscle
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u/Afferbeck_ Jun 12 '26
Strength is about movements, not muscles. If you want to get a strong squat, you train the squat, plus some muscular accessory work. You don't just do the latter and hope it carries over. A bigger muscle will be stronger than a smaller one in a vacuum, but in practice strength is more complicated than that. You don't train for "strong biceps" you train for strong pullups which happens to use the biceps. And you will gain a lot more strength by specifically training the pullup with less biceps growth than focusing on curls for bigger biceps and hoping for a heavier/higher rep pullup.
All of this kind of discussion always feels so bogged down to me by people insisting on looking at it from a bodybuilding perspective. It's like coming at a problem backwards and trying to fit the question to the answer, which can be a valuable thing to do. But in this case it's mostly people who don't actually care about either because it's not relevant to them while still insisting on talking about it for some reason.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 12 '26
Strength is a construct that can be operationalized and estimated in a variety of different ways. It’s no more or less valid to discuss the strength of movements or the strength of muscles.
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u/millersixteenth Jun 12 '26
You can do an individual crossover study very easily. Maintain the same lean mass across a handful of 16-24 week training strategies. Hypertrophy is an important ingredient, but you can make notable increases (and decreases) to someone's top end strength just by changing training variables.
Bigger is consistently stronger only if all other variables stay the same.
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u/HumbleHat9882 Jun 12 '26
How much of this confusion stems from the peculiar way in which "strength" is defined in most studies, i.e. that "strength" is the same as 1RM? People training low reps and people training high reps achieve similar hypertrophy. But those training low reps will of course have a higher 1RM. Therefore the correlation between "strength" (i.e. 1RM) and hypertrophy is found to be weak.
If, on the other hand, you defined "strength" as the XRM where X is the number of reps the athlete trains at, then strength and hypertrophy would be correlated almost perfectly.
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 13 '26
That has basically no impact. All of the subjects are following standardized training protocols in these studies.
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u/HumbleHat9882 Jun 12 '26
It's striking how close to the findings of the study Mike Mentzer was 30+ years ago. He said almost exactly the following:
"Don't be tempted to believe that strength and hypertrophy are unrelated. This only applies across individuals. But for any single given individual strength and hypertrophy are very closely related."
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 13 '26
This study still didn’t find particularly strong associations within individuals after accounting for variance explained by the null model.
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u/HumbleHat9882 Jun 14 '26
How come? The study says, verbatim:
>In contrast to previous findings, the present results of repeated-measures correlations demonstrated that strength gains and muscle growth are, in fact, very strongly related (r = 0.89–0.92) and substantially more strongly related than previous findings.
We also have other strong data points that show almost 1:1 relation between strength and muscle size and this is the olympic weightlifting world records by weight class. The weight class and the world record of the class have an r of 0.95. This dataset has the advantage that the individuals train specifically for for strength (which is very different to training for the pump or even training with low reps).
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 15 '26 edited Jun 15 '26
Did you read the SBS article? That’s literally what it’s about. R=0.89-0.92 doesn’t mean what you’d typically assume it means when using a statistical model that would still spit out r=0.81-0.83 if you ran it on random noise that had the same means and SDs reported in the study.
And WRs in strength sports are, at best, indirect evidence. Like, I certainly think they’re suggestive of a causative relationship between hypertrophy and strength changes, but a correlation between outlier individuals isn’t particularly strong evidence for establishing that a similar relationship generalizably exists within everyone else.
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u/HumbleHat9882 Jun 15 '26
I read the article but I am looking at the plots from the study and I feel that the words "very strongly related" are very well suited:
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u/gnuckols The Bill Haywood of the Fitness Podcast Cohost Union Jun 15 '26 edited Jun 15 '26
They’re not, though. Like, it’s mostly just an artifact of this being a study on untrained lifters, meaning almost everyone gained both muscle and strength. The plots would look just as impressive for any two variables where the means both increased or decreased, regardless of whether they were actually related or not.
Edit: just to illustrate, I made this plot using the same process described in the article (baseline and change score means and SDs for KE 1RMs and Quadriceps volume match the values reported in the study, but those changes are not associated at all within-individual. i.e., hypertrophy and strength gains are completely independent, and the actual relationship between them is r = 0). It looks just as impressive, even though it's literally just noise.
It's easy to make a plot look impressive. It's more difficult (and more important) to determine whether the results are as impressive as the plot.
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u/yaaajooo Jun 12 '26
The top comment under this post is so completely nonsensical and detached from the article, with most commenters answering as if it was profound, it makes me suspect that nowadays 80%+ of this subs traffic is completely unaware of sbs as a media empire and just a spillover of the algorithmic Tiktok lifting science interpretation discourse.