## Monday, 26 October 2015

### World Records in Weightlifting and Powerlifting

A few weeks ago, I looked at world records in running and swimming, to see what information I could get out of them and what I could learn about human athletic performance. In this post, I'll look at world records in weightlifting and powerlifting, and see what there is to see. Before I write this, I have a general sense of what the data will look like,  I know that bigger people tend to be stronger and men tend to be stronger than women,  but I don't yet know what nuances will emerge. The overarching question is: can we learn about an extremely complicated system, a human being, from simple data, like how much they can lift?

When I do this analysis, I make the assumption, as before, that the current world is close to the pinnacle of human achievement, and that slight improvements in a given record will not change the trends that much. This is not as true for powerlifting as it is for running.

The difference between weightlifting and powerlifting is that powerlifters lift more weight and weightlifting requires more power. Powerlifting involves the squat, bench press, and deadlift, and weightlifting involves the snatch and the clean and jerk, two ways of lifting a weight from the ground to overhead. Weightlifting used to involve the clean and press as well, but it was removed because people started leaning really far back to make the lift easier and it became impossible to judge.

 From left to right: Squat, bench press, deadlift, clean and jerk, snatch.

Powerlifting data was taken from the website PowerliftingWatch.com, which is generally well updated. It's important to note that I focus on "raw" records, meaning they don't use supportive equipment, which can vastly increase the amount of weight lifted. I don't particularly care whether they were on drugs or not; I want to know the limits of human achievement. Weightlifting data was taken from Wikipedia, with the caveat that the records were annulled in the 1990s when the weight classes were redistributed, and not all the old ones have been beaten. In the case of the "superheavyweight" category, I use the weight of the record holder rather than of the weightclass.

The naive trend we expect is based on the square-cube law: if you make a person bigger by some factor x, their weight will increase as $x^3$ but their strength only as $x^2$, so the increase in strength with respect to weight should be roughly the two-thirds power. In an article I wrote on scaling laws, I showed that men's deadlift records did follow this prediction until the athletes start getting fattier. This ignores many biomechanical effects, for example the benefits or disadvantages of having longer limbs when performing a lift.

Let's first look at the world record data for powerlifting.
 Powerlifting world records.
First, we confirm what was expected: bigger athletes are stronger, and men are stronger than women. There is a trend evident in the squat and deadlift that is the same between sexes: the record increases with weight and reaches a plateau. This plateau occurs when there is a transition weight where the athletes stop getting more muscular as they get heavier, and start getting fattier. This occurs at about 242 pounds for men and 165 pounds for women. It's interesting that this plateau trend is not really evident in the bench press data; it is roughly a smooth increase (the men have an outlier at 242 lb). Why are heavy bench pressers immune to fattiness? Perhaps the reduction in bar-travel distance due to a fattier chest helps, perhaps it's due to the existence of bench-only competitions that avoid the fatigue of squatting before benching. I don't know.

 Champions in the second-heaviest and heaviest weightlifting categories.

I have often heard that women have comparatively stronger lower bodies than men. Is this supported by the data? If we average the female:male ratios across all coincident weights for the three lifts, they are roughly the same for the squat and the deadlift, about 0.71 ± 0.02, whereas the bench press is a lower 0.65 ± 0.01 .

There are two fairly extreme outliers evident in the squat data: the lightest man, Andrzej Stanaszek, is about four feet tall and has considerably different biomechanics; the heaviest woman, April Mathis, is just much better than any other female raw powerlifter. Excluding Andrzej and April, there is a downward trend present in the squat ratio data: large men get better at squatting compared to large women; I believe that this is because the adiposity transition occurs at a lower weight for women.
 Squat ratios.
I tried to measure a "legginess quotient" by dividing the squat records by the bench press records, but there isn't much of a trend. The average ratio is 1.27 for women and and 1.26 for men.

When I try to compare trends between different lifts across weight classes, or between sexes, I come to the conclusion that the assumption upon which I base this analysis is violated: the "raw" powerlifting records do not serve as a proxy for the pinnacle of human performance, and there is significant person-to-person variability that skews the data. This is in part based on my choice to focus on "raw" records, which typically have fewer competitors. To smooth out the stats, I will look at the records for the raw "total," which is the sum of the three lifts. This at least will allow me to more easily compare apples to apples, because each data point is just one person. It would be good to compare all three lifts for each record total, but the data isn't in a neat little package.

 Powerlifting Totals, in linear and logarithmic axes. The superimposed lines are the 2/3 power law. Also I screwed up the colours.
These trends look less scattered than each of the individual lift records. Doing my favourite thing and fitting a power law to the data, excluding the heaviest category, we get a scaling exponent of 0.58±0.05 for men and 0.7 ± 0.1 for women. The naive expectation is 0.66. Another way to look at this by dividing out by body weight, and looking at how many times their own weight they lifted. This generally decreases, for reasons I mentioned above. We also see how good April Mathis is, that she rises significantly above this decreasing trend.

 How many times their body weight they lifted.
When we look at weightlifting, things get a bit clearer. There are no longer fluctuations about the trend due to small numbers or sub-maximal performance. Only the largest athletes fall below the general trend due to fattiness. As a Canadian living in the US, I will now switch from pounds to kilograms as I switch from powerlifting to weightlifting.
 Weightlifting record data. The men's snatch champion is a really big dude.
Something interesting is that for weightlifting, the women tend to get stronger-er with weight compared to men. For both the clean and jerk and the snatch, men's records increase with roughly the square-root of weight, whereas for women it's the .65 and .75 power respectively, which I did not expect and can't currently explain. There is a weak downward trend in the sex ratios, but nothing to get too analytical about. Looking at the ratio of snatch to clean and jerk, there is generally no trend with respect to weight, but the ratio is 0.829 ±0.007 for men and 0.801±0.007 for women, a small but statistically significant difference. I do not know the physiological reason behind this, but it strikes me as the opposite of the powerlifting sex ratio trend.

I would say that we did not learn anything too-too interesting from looking at this data. The records are handwavingly near the prediction of the square-cube law, and the adiposity transition is quite visible when that law fails. Probably the most interesting things I learned were that the bench press sex ratio is lower than the squat and deadlift ratios, and the snatch:jerk ratio is higher for men than for women, both by a small but significant amount. Generally, I think the sport of raw powerlifting has not developed enough to make firm conclusions about a lot of these trends.