June 19, 2014

I’m pretty tall. Six-foot three-inches. When I do any type of squat in the gym, people sometimes remark, “Man, that’s a long way down (to hips to knees).” Conventional wisdom says, the taller you are, the more disadvantaged you are at back squatting, because you have more range to cover and more work to do.

Is this true? Sort of.

Recently I collected data on 5,376 CrossFit Open participants, including data on athletes’ one-rep max (1 RM) back squats, heights and weights, to try and see if height does affect one-rep max back squat. And if so, to try and quantify the effect of height on back squat.

Of the 5,376 CrossFit Open participants, 1,067 men self-reported their 1 RM back squat, their height and weight.

The mean 1 RM back squat (for men) was 319.7 lbs, with a standard deviation of 67.2 lbs. This means we’d expect 68% of male CrossFit Open athletes to back squat 252.5-386.9 lbs.

Here is the distribution of 1 RM back squat:

Note that since better athletes are more likely to self-report, the mean is probably higher than a true cross section of CrossFit male athletes.

Nevertheless, we can still look at the effect of height on back squat.

With the data from the 1,067 men, when we run a simple regression of 1 RM back squat verse height, it actually appears that height is ever so slightly beneficial – the taller you are, the more you can 1 RM back squat. The formula is:

**[1 RM back squat (lbs)] = 210.56 + 1.57*[height(in)]**

Here’s the scatter plot and regression line:

Although this correlation is statistically significant, it’s really not practically significant. We’d expect someone who’s 6’0” to lift about 10 more pounds than someone 5’6”, which isn’t much of a difference. So, we can conclude here that when we’re looking at the effect of height on 1 RM back squat, there’s not much of an effect.

However, this correlation is likely confounded by weight. Our taller people weigh more than our shorter people. What we really want to know is, if all our participants weigh the same, how does height affect back squat?

We can control for weight by running a multiple linear regression. When we run a multiple linear regression between 1 RM back squat, height and weight, we can see the independent effect of height. We get a formula of:

**[1 RM back squat (lbs)] = 413.11 – 5.35*[height(in)] + 1.51*[weight(lbs)]**

**So, when weight is controlled for, increasing height is indeed disadvantageous in 1 RM back squat.** This equation is both statistically significant and practically significant. If a 5’6” guy and a 6’0” guy weighed the same (and they had similar strength), we’d expect the 5’6” guy to be able to lift 32.1 more pounds due to his shorter height advantage. Thirty-two pounds is a lot – just about a half standard deviation.

Another way we can control for weight and better visualize the relationship between height and 1 RM back squat is to only calculate a linear regression between height and 1 RM back squat for men of specific weight.

For instance, only looking at men who weigh between 185-189 lbs (n=114), we see once again very clearly that increasing height negatively affects 1 RM back squat. The relationship between 1 RM back squat and height for these men is:

**[1 RM back squat (lbs)] = 860.22 – 7.63*[height(in)]**

And here is what the scatter plot looks like:

In this smaller model, we’d expect a 185 lb 5’6” guy to lift 45.78 more pounds than a 185 lb 6’0” guy. That’s a lot!

So then why does our raw data, weight not controlled for, show that height doesn’t effect 1 RM back squat?

What this data seems to suggest is that people who are taller have big frames that can put on a lot of weight and a lot of muscle. This big frame, added weight and added muscle may cancel out the negative affect of height.

**In conclusion, while height negatively affects 1 RM back squat, height also positively affects weight (and ability to gain muscle?), which may annul the negative affect of height on 1 RM back squat for experienced lifters.** Thus tall experienced weight lifters who have added a lot of weight to their frame probably aren’t at a disadvantage for being tall for 1 RM back squat. Conversely, tall inexperienced weight lifters who don’t have a lot of muscle suffer greatly from being tall for 1 RM back squat.