Weightlifter’s Normative

The Question

I once asked my weightlifting coach about a correlation among typical lifts. If I can Deadlift 300lbs, how much should I be able to Back Squat? I’m not talking about Olympic athletes whose records are public and who were as much born to be the best as they have trained to be so. I’m referring to an average human being who decided to play around with a barbell.  My coach was not able to answer my question definitively.  I found a website here and there with scant numbers and lacking citations but, nothing solid.

The Data

There’s a relatively large community of weightlifters who share their achievements publicly: CrossFit. Athletes create profiles such as this one and update them regularly.  I wrote some code to download the profile of every athlete on one of the CrossFit Open rosters, all 132,355 of them.

The Analysis

Back Squat vs. Deadlift

Consider the plot of the athletes’ Back Squat maximum vs. Deadlift maximum (hereafter the terms maximum and one rep max shall be omitted and it shall be understood that all quantities discussed are such).

The plots are made up of 13562, 30284, and 43846 samples respectively. Jitter is added to the data and opacity to the dots so that the plots are easier on the eyes. The jitter is necessary because the weights are multiples of five and if plotted as are create a caustic image; opacity helps to ignore the outliers.

Deadlift and Back Squat are two of the least technical lifts. Correlation between them is therefore likely entirely due to the athletes’ physical characteristics, as opposed to skill. The plot has a few stark features worth noting.

• The correlation is linear.
• The correlation does not depend on gender.
• Amateur athletes are typically able to Back Squat ~ 81% of the Deadlift, the solid line through the middle of the data.
• There appear to be sharp upper and lower bounds for the bulk of the data.
  • The upper bound is — suspiciously exactly — the line y = x.

Both lifts derive vast majority of the power from the legs. The same set of muscles is engaged in the same exact directions. There are, however, key differences.

• Back Squat requires one to lower and raise the bar in a controlled fashion. Athletes lower the bar sans control and sometimes even drop it after a Deadlift, thus dispensing with a significant fraction of the work.
• Athlete’s hip crease must drop below their knee during a Back Squat. It is more difficult to stand up from than position than from the bottom of the Deadlift, where the athlete’s legs aren’t nearly as bent (more on that later).

The points above hint as to the linearity of the correlation — identical muscles pulling in identical directions — and provide some insight into why an athlete can Deadlift more than (s)he can Back Squat — differing range of motion and the amount of work. Let’s now look at the apparent upper and lower bounds.

Deadlift ~ Back Squat

Given an uninjured athlete, there are three explanations for the case of one’s Deadlift and Back Squat approaching one another.

• An athlete is not squatting low enough during the Back Squat, not breaking parallel with the ground. His/her Back Squat maximum is exaggerated and must be lower if the exercise is performed properly.
• An athlete is placing an undue amount of the load on his/her back during the Deadlift, not using enough legs during the drive phase of the exercise. His/her Deadlift can increase with improved form.
• An athlete is taller than the average, requiring him/her to almost go into a full squat to grab the bar for the Deadlift. Shorter athletes are closer to the bar at the start of the exercise and need not drop into a full squat to pick it up. The lower is the squat, the harder it is to stand up from it. Little can be done to increase the Deadlift to Back Squat ratio for taller athletes.

Deadlift ≫ Back Squat

With the same assumptions as previously, there are three explanations for the Deadlift to significantly exceed the Back Squat.

• An athlete is not keeping his/her back erect enough while descending into the bottom of the squat, i.e. face too close to the knees, thus limiting the amount of weight (s)he can raise from that position. His/her Back Squat can increase with improved form.
• An athlete is descending too much during the Back Squat, thus limiting the amount of weight (s)he can lift from that position. His/her Back Squat can increase with improved form.
• An athlete is shorter than the average, allowing him/her to barely bend the knees at all to pick up the bar at the start of the Deadlift and lift significantly more than a comparably-developed, taller athlete.

At the time of writing of this post, Richard Froning‘s Back Squat is 83% of his Deadlift. Julie Foucher‘s ~ 82%.

Clean & Jerk vs. Back Squat

In the order of ascending difficulty, the next lift is the Clean (& Jerk). Consider the plot below (40,191 samples).

Clean & Jerk is a compound lift involving both raw strength, vast majority of which is provided by the same muscles as in the Back Squat and the Deadlift, and skill. Timing, shoulder strength and stability, coordination, which are all but absent from Back Squat and Deadlift, play an important role in Clean & Jerk. Two physically identical athletes max out at two significantly different weights depending upon their skill. The data places an average Clean & Jerk at ~ 69% of the Back Squat.

Whereas Richard Froning fell almost squarely into the average performance on his Deadlift vs. Back Squat, his Clean & Jerk is 78% of his Back Squat. This is so because the Deadlift and Back Squat are more about raw strength than skill. As an experienced weightlifter, Mr. Froning is expected to perform in the above-average skill range for the Clean & Jerk.  Julie Foucher’s Clean & Jerk is 76% of her Back Squat, also above average as expected.

Snatch vs. Clean & Jerk

The Snatch is the most technical lift. Consider its correlation to the Clean & Jerk (38,847 samples).

Requiring even more training and skill, the Snatch averages ~ 76% of the Clean & Jerk. Richard Froning’s ratio is ~ 82%, Julie Foucher’s is 85%; comparable to the modern Olympic weightlifters.

A Note About Olympic Lifts.

For the Clean & Jerk and the Snatch, athletes of above-average skill are expected to be above the average ratios, those of lesser skill are below. If an amateur athlete is significantly below the average ratio on one or both of the lifts, it could signal underdeveloped or insufficiently mobile shoulders and/or lack of coordination.

Conclusion

Table of average relationships between the lifts analyzed, column divided by row.

	Snatch	Clean & Jerk	Back Squat	Deadlift
Snatch	1	1.32	1.92	2.38
Clean & Jerk	0.76	1	1.45	1.77
Back Squat	0.52	0.69	1	1.23
Deadlift	0.42	0.56	0.81	1

Notes

An astute reader will notice that each plot shows less variance than the one before it. The thinning of the correlation is primarily caused by the fact that the athletes attempting more complicated lifts such as the Snatch are typically more skilled and therefore fall within a narrower distribution than novice athletes who primarily train with Deadlifts and Back Squats. This is a common phenomenon. If 100 individuals’ 1mi run time is sampled at random, the spread is likely to lie between 5min and 20min due to the variance in natural predilections and lifestyles. If said individuals receive one year of comparable training, the dispersion will shrink markedly. An extreme example of this effect are Olympic athletes, who often win by mere (milli)seconds and kilograms.

A trained eye may also notice that the intercepts of the plots are not zero. The analysis enforces zero intercepts to simplify the interpretation of the results, which are approximate a priori. Allowing the intercept to be derived from the data does not meaningfully alter the conclusions.

Future Work

These scatter plots represent a fraction of the data. More analysis is coming soon.