How and why height impacts strength

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At 6’4″, I’m tall. I started lifting weights with other guys at 13 years old. When you’re tall, it takes about 8 seconds to realize long limbs don’t help you standout in the weight room.

As a tall person, rummage through the exercise science world a bit and you invariably run into,

As a reminder, force is made of how much mass an object has, and how quickly we accelerate the object. Provided a taller and shorter person lift the same weight at the same acceleration, because a taller person needs to move a barbell further than the shorter person, they have to do more work. Thus, it’s harder for a taller person to lift as much as a shorter person.

That’s often the end of the discussion, but it never jived with my weight room experience. Particularly in college when I was playing football, the taller lifters tended to lift together. Yes, it was harder for us, but it seemed significantly harder.

A guy who was only a few inches shorter seemingly was wayyyyy stronger than he should have been, just based on those few inches.

Here’s what I mean. Say we have two lifters:

• Shazam is 6’2″, 1.88 meters
• Ferguson is 5’9″, 1.75 meters

Alright, now let’s say they’re both lifting 100 kilograms. To keep it simple, we’ll ignore limb lengths and simply use their height as the distance they’re lifting. We’ll say they’re lifting at 10 meters per second^2.

• Work = mass * acceleration * distance
  • Shazam’s work = 100 * 10 * 1.88 = 1880
  • Ferguson’s work = 100 * 10 * 1.75 = 1750
• 1880 / 1750 = Shazam is doing 7.4% more work

Generalizing, if we’re talking a bench press, if Ferguson’s max is 400 pounds, then Shazam’s max should be 370 lbs.

It just never worked out that way. Unless the taller dude was way heavier, it always felt more like a 30% difference, if not more (tall guy could only bench 300 lbs).

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What we all already know- size matters

I found the men’s 2016 olympic weightlifting rankings.

-> I’m often biased to males with these types of articles. That’s only because men have been doing the activity longer, almost always have a much larger sample size, and drug use is more consistent.

There were thousands of them.

-> I wanted to use powerlifters to make this more pure strength oriented as olympic weightlifting necessitates much more speed, but finding powerlifter heights is impossible. Weightlifting is much more popular, where it’s easier to find info on the participants.

I arranged the lifters by total, finding the top ~50 respective heights.

Next, I divided strength by weight, and found those top 50 heights (roughly).

That is, I found the heights of a bunch of guys who are strong in absolute terms -the most amount of weight lifted- and guys who are strong in relative terms -the most amount of weight lifted relative to how much a guy weighs.

The reason relative strength is important is because taller guy’s often make up for their height by being heavier. We wanted to cancel that factor out. That is, does how tall you are affect how strong you can be, no matter your weight?

All the data:

First, height vs absolute strength:

This might be initially surprising. What we see is as height goes up, so does strength! But this is misleading. Like we went over, the tall guy’s are making up for their height by getting heavier. Sometimes, demonstrably heavier.

When we account for bodyweight:

The exact opposite is found. Get taller? Get weaker.

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How much weaker?

Let’s look at these two lifters:

• Orange = 1.97 meters tall and 3.01 strength / weight
• Pink = 1.5 meters tall and 5.0 strength / weight

Thinking about our work formula again,

• Our orange lifter is 31% taller, so we could expect them to be 31% weaker, relative strength wise
  • (they have to cover a 31% greater distance)
• However, 5 / 3.01 = 1.66.

Our shorter lifter is 66% stronger!

“That’s only one guy.”

Arranged by height:

• If we average the height of the top 50 guys we get 1.81 meters.
• If we average the height of the second 50 guys we get 1.61 meters.
  • Based solely on height, that work difference is 12.4%. (The first 50 taller guys have to do 12.4% more work for the same lift.)
• If we average the strength to weight of the first 50 guys we get 3.64.
• If we average the strength to weight of the second 50 guys we get 4.78.
  • The second 50 guys are on average 31.4% stronger.

I think at this point it’s obvious there is something besides straight mechanical work going on here. For instance, why are the second 50 guys ~20% weaker than physics tells us???

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Explanations

Volume vs area

This is the most studied element. Muscle strength correlates well with cross sectional area. Body mass correlates well with body volume.

• Area is length * distance.
• Volume is length * distance * depth

If we view muscle as a rectangular tub, then as the tub increases its dimensions, volume goes up quicker. For example,

• Area starts at 2 * 2 = 4
• Volume starts at 2 * 2 * 2 = 8

If we increase the length, width and depth by 1,

• Area = 3 * 3 = 9
• Volume = 3 * 3 * 3 = 27

Volume is going up faster than area. The area went up roughly double, where volume more than tripled.

Thus, because area relates to strength and volume to body mass, body mass goes up quicker than strength. This is known as allometric scaling. Greg Nuckols wrote a good piece about this,

-Who’s the most impressive powerlifter?

He mentions allometric scaling does not hold up well for super heavyweights (in powerlifting). He and others have related this to body fat. Idea being heavier weight classes get to a point where they are not increasing body fat proportionally with muscle. If they were 8% body fat at 80kg, and 90kg, and 100kg…but then they’re say, 12% at 120 kg, that throws the expectation off.

However, Greg uses a really small sample size (10) with powerlifters.

-> To be fair, Greg was primarily looking at the record holders, and trying to extrapolate that to allometric scaling. But small sample size nonetheless.

In our weightlifting sample allometric scaling doesn’t completely flatten out the data,

And it’s still awfully related to strength to weight ratio,

Allometric scaling also doesn’t directly measure the impact of height, yet we’ve seen height is very related to total strength.

In the below sample of NFL players (from this post) we can see as players get heavier, they get fatter:

However, while strong, the relationship weakens when we look at height vs weight:

In other words, something about being taller is causing a decrease in relative strength, but it might not be solely body fat, because the relationship between height and body fat is strong, but it’s not like the correlation is 1:

Unfortunately, I don’t have the body fat percentage of a hundred weightlifters, but I imagine the relationship would be similar.  Particularly considering the height and weight relationship is so analogous:

And while sometimes conventional allometric scaling works very well,

–A comparison of absolute, ratio and allometric scaling methods for normalizing strength in elite american football players

sometimes it doesn’t. Others have pushed back saying allometric scaling isn’t as simple as only looking at area vs volume,

-Allometric modeling does not determine a dimensionless power function ratio for maximal muscular function

In that study, they discuss issues once getting above only 90 kg. (Far from a super heavyweight.) Where once above that mass, the effect of mass is increased more than you’d expect by the area and volume logic. 90kg isn’t very big. If you’re a tall dude with practically any muscle, you’re going to be that heavy or more. It’s possible what many have been automatically reverting to an explanation of body fat is also part of body height- what we’re fully attributing to weight may also be partially explained by height.

-> One theme of the studies I’ve seen is with football players and powerlifters, allometric scaling looks to work better than with weightlifters. One reason I could see that is the height differential with football players and powerlifters isn’t going to be as great as with weightlifters.

In weight lifting, you have guys from just below five feet to just over 6’5″. Anecdotal, but my experience with football and powerlifters says they don’t vary that much. (You don’t see five foot football players or 6’5″ powerlifters.) So because the heights are closer together, you don’t see the impact of height as much.

Thus…

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Two other factors?

Mechanical work clearly doesn’t explain everything. Biological scaling gets us far, but perhaps not all the way. Really, we haven’t mentioned anything yet directly explaining the physiology of height. We’ve indirectly gotten at it by examining weight, but surely height could have its own explanation, no?

Here are two ways I could see explaining the rest:

• Nerve conduction time
• Blood supply

Nerves can only conduct so fast; blood can only travel so quickly.

If you’re 10 inches taller, that’s 10 inches more a signal has to travel down a nerve. (20 inches more if you include getting a signal back!)

Same goes for blood. If the heart gets a signal it needs to pump more or increase blood pressure,

1. As we already said, that signal takes longer to get there
2. The heart has to pump that extra blood / pressure further

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Overall, we have some solid theory why we DON’T see tall people doing particularly well in events based on

1. Moving their own bodyweight
2. Speed

You see LONG people, that is, long limbs, but you can have 6’4″ limbs on a 5’8″ body.

Usain Bolt is perhaps an exception, at 6’5″. He’s actually a quasi exception- he’s notorious for a bad start, and he really shines towards the endurance part of the 100 meters. (Though endurance runners, like marathoners, skew short.) Others have stuck with him well up to that point:

It would be interesting to know how Bolt is overcoming his height issue. Perhaps he say, has an unusual nerve conduction velocity, allowing his height to not be a detriment. Or, in fact, being taller means having a bigger heart. Maybe Bolt’s heart is big enough to negate the blood traveling factor.

-> Other potential factors:

-Fast twitch ratio

-Muscle density

-Muscle / tendon lengths / attachments

-His surface area to volume ratio (this dictates how easily you can dissipate heat, potentially the reason whites don’t perform as well as blacks in running)

-Intelligence with training (e.g. staying healthy)

-Drugs

That doesn’t mean, even on average, that tall people are doomed in sports. Obviously not. In basketball, it doesn’t matter how quickly you can send a nerve signal if you can only get nine feet in the air. Too short, and you can only weigh so much before getting fat. It doesn’t matter how quickly you accelerate when there’s no mass in your ass. There are also other advantages of long muscles, which we’ll get to in another post.

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Brief tangent

We can see above

1. Predicting performance in sports is easy
2. Predicting performance in sports is impossible

If your criteria for performance is strength to weight ratio, or you’re in a low weight class, it’s easy. You NEED to be short.

If your criteria for performance is absolute weight lifted, it’s easy. You NEED to be heavy, which means you need to be taller.

If you’re trying to predict basketball performance, 6’8″ vs 5’8″? Easy. 6’8″.

When we’re looking at extremes, it’s not that hard.

When we’re looking at the middle, which by definition is most people, it gets much harder.

When you’re 5’8″, even if you have the most fast twitch muscle available, the fastest nerve conduction velocity, in basketball, it’s borderline impossible to overcome your height.

But when you’re assessing 6’5″ vs 6’2″, everything gets way murkier. You might be able to assess height, strength to weight, and nerve conduction velocity, but putting together an algorithm that properly weighs those variables, oh, and probably another 1000 variables we haven’t discovered yet, or just don’t have data on, ain’t easy.

One of the hardest parts of studying taller guys, and thus, the heavier guys, is there are not as many of them. (90% of the population is 6’2″ and under.) What if one reason the smaller guys standout with strength to weight ratio is simply because there is more of them, thus more competition, thus higher totals? After so many years and so many people, coupled with the fact the tall guys have the incentive of being the strongest person in the world (remember, taller = stronger), I find this to be an unlikely explanation, but it has to be on the table.

“[one hypothesis] the 2/3 exponent approach tends to “bias” [against] those in the extreme weight classes is because far more competitors are found in middle weight classes (not surprising as M tends to be normally distributed in the population). As these lifters have more competition, one should not be surprised when middle weight class lifters tend to receive the highest [allometric] scores.  Furthermore, when Batterham and George eliminated the heaviest lifters (those who have no upper limit of M) from their analysis, the resulting exponent for M was 0.68, nearly identical to 2/3.”

A simple index to adjust maximal strength measures by body mass.

What isn’t brought up in that quote though is when eliminating the heaviest lifters, you also eliminate the tallest ones!

This is why sports teams, to this day, have a terribly hard time predicting players. There is a great story in The Undoing Project about Daryl Morey, who is from MIT and has dedicated his life to predicting player success. He works for the Houston Rockets. DeAndre Jordan was a player every team passed on, including Morey, yet who’s become a NBA standout.

Turns out Jordan didn’t like his college coach and hated school.

Yep. That simple. Right coach, doesn’t have to deal with school, boom, now he fits into the predictive model.

We often assess these variables with the caveat “all else being equal,” but all else is never equal.

And even with all the measurables quantified, it’s debatable whether it’s even possible to reasonably predict the human mind.