Too Weak to Read? tl;dr



Note: This series is written primarily for the good-but-strange people at reddit.com/r/weakpots and /r/powerlifting. Please forgive the breeziness of the language. If I ever develop it far enough to publish, I’ll tone it down to something approximating seriousness.

I want to compare “competitive balance” in individual sports like lifting, running, swimming, and speed skating. This has been done for team sports but not individual sports yet.

Results from individual sports competitions should have a statistical distribution (curve) that reflects four factors: human genetic potential, training, technology, and random chance.

The shape of this curve and how it changes over time show the “maturity” and competitiveness of the sport. It also shows how rules changes such as qualifying totals or equipment bans change competitiveness.

If we agree what the curve of a competitive sport looks like, we should be able to tell how close any sport is to that point, and compare it to another sport. Governing bodies (like the International Powerlifting Federation) can use this information to make decisions about qualifying totals, classes, bans, and other rule changes. But… I don’t know what statistical measure to use yet, so for now it’s just an intuitive comparison.



Defining Competitiveness in Individual Sports

What I mean by “competitive balance” is the same definition that’s used for team sports: At a given point in time, no competitor is inherently more likely to win a competition than any other competitor.This gives us information about how fair the sport is, and frankly how interesting it is to watch. If we know ahead of time who is going to win each competition, there’s nothing really interesting about it, unless there’s the novelty of seeing how long one person remains dominant.

In a perfectly competitive powerlifting scenario, there are no Sergey Fedosienkos, who will automatically win every time they step on the platform. (Between 2007 and 2015, Sergey competed in the 59kg division seven times, and won seven times). If the sport is competitive (rather than perfectly competitive), Sergey will win some or most of the time, but sometimes he’ll get beaten by others.

As long as there is one participant who consistently dominates a weight class, then that powerlifting weight class is not yet really competitive. When many or most participants have an equal shot to win a competition, the weight class is more competitive. If all participants are equally likely, the weight class would be perfectly competitive – though this is almost certainly never going to happen in the real world.

I think that by doing some statistical analysis of recent competition results, we can get a sense for how competitive the sport is, and decide whether some changes might be needed to make it more competitive (if that’s desirable). For the purposes of developing this theory, I’m proposing four factors that determine the winner of a given individual sports competition:

Genetic Potential: How naturally big/tall/strong/fast are you? For powerlifting, what are your leverages like? Are you Fedosienko? Training: How much time have you put into making the most of your genetic potential? Do you use better training methods than other people, or just dick around forever? Technology: Are you using equipment or drugs that give you a competitive advantage? Random chance: Anything unrelated to the other three that is evenly “distributed” between competitors. We all (basically) have an equal chance of feeling really good or really lousy when we set up for a lift. If you and I have equal combinations of genetics, training and technology, then the winner will be whichever of us has a better set of random factors at the time of competition.

The more competitive a sport is, the more results are determined by random chance. When a sport is perfectly competitive, the only thing that determines the winner of a competition is random chance.

Note that the goal of training is to minimize the role of random chance. You want to squeeze as much as you can out of your genetics through training, and add as much as you can through legal technology, to get consistently good results. When you compete, you’re hoping your genetics + training + random factors beat the other guys’ training + random factors.

Before we look at how these factors affect and describe powerlifting, let’s brush up on some statistics.

A Little Bit of Statistics: The Normal Curve and a Random Sample



Slightly technical math-y section, but be courageous and read on:

When you go out and collect information about a thing, that’s called an observation of a unit. For example, the height of a person is an observation about that unit. When you collect the same information about a lot of randomly-chosen units, that’s called a “random sample” of all of the units that exist, or the “population.” So if you measure the height of 100 people you randomly select, you’ve taken a “random sample” of the height of the entire population of people.

A “normal distribution” means you expect most observations in the population to be at or near the average for the whole population. As you get farther and farther away from the average, you expect to see fewer and fewer observations. If the measurement (height) is “normally distributed” in the population of all people, then a random sample of height should be normally distributed too. A graph of these randomly-sampled observations should have a certain shape: the normal curve.

Here’s an example, using heights. We believe that in the population (all people), height is a normally-distributed characteristic. If we randomly select 100 people, both men and women, and make a graph of their heights, this is what we would expect to see:

There are three important things to notice about this graph:

The average height of all people is 67.5 inches (171.5 cm for you communists out there). I’ve drawn a red line to show the average. The curve is highest here because it has the most observations: more people will be this height than any other height. The standard deviation (s.d.) is 3.75 inches. Standard deviation is a way to measure how much variation there is in the measure. An important thing to remember is we expect 68% of the population to fall within +/- one standard deviation around the average. This means that the height of 68% of the population should be within the blue-shaded area, from 63.75 inches to 71.25 inches. Only about 15% of people will be shorter than 63.75 inches, and only about 15% of people will be taller than 71.25 inches. There are very few people who are very short or very tall. We call these people “outliers.” The more standard deviations you go above or below the average, the lower the curve, and the smaller a percentage of the population falls into that group. When you are at 56.25 inches (the left side of the graph, less than 4.7 feet tall), you are 3 s.d.’s below the average. We expect only about one-tenth of one percent of people to be this short, and the same percentage of people should be taller than 78.75 inches (six and a half feet tall). These distant parts of the curve are the “outlier regions.”

That’s all the statistics you’ll need to know for the rest of the article. You can breathe now!

The Normal Curve and the Untrained Powerlifting Population

Let’s pretend that you woke up this morning and decided to invent the brand-new sport of powerlifting. Congratulations! The rules of this sport are that everyone performs three lifts (squat, bench press, and deadlift), and whoever has the highest total weight across those three lifts wins.

The sport didn’t exist before today. People might have been doing Olympic lifting or strongman competitions or just dicking around, but until now no one has ever trained, thought about, or competed in the three specific powerlifting lifts.

On this Day 1 of the sport, you decide to have a competition to see who the best powerlifters are. You run outside and grab the first 100 random men you see off the street. Let’s assume they’re all men that fall within what would be the 93kg (205 lb) weight class, if you had established weight classes yet.

(We’ll come back to the problem of weight classes at the end of the article.)

Because no one has ever trained specifically for the sport before, we would consider this a random sample of the untrained population of potential powerlifters. We assume that this population is normal. Because you chose a random sample, some of these men will be really weak; some will be really strong; most will be average.

If all 100 of these men perform the three powerlifting lifts, we would expect their totals to be normally distributed too! Using a table of “strength standards” we can figure out approximate averages and standard deviations for the population. Here is a version of the table in freedom units. (note that the original chart, no longer available, showed average lifts for intermediate lifters that are 20kg higher than the ones used here).

According to the chart, the average untrained 93kg man should be able to do at least the following one-rep maxes:

Squat: 57.3 kg / 126.3 lb

Bench: 62.1kg / 136.9 lb

Deadlift: 71.6kg / 157.9 lb

In other words, the average 93kg guy you pulled in from the street should be able to hit a total of 191kg (421.1 lb) for his one-rep maxes in three lifts.

Of course, not everyone in the untrained population is going to be able to do that. Some people will really be weak (hi there, readers!) and barely total 170kg (374.7lb). Some people are just naturally strong and will total 210kg (463lb) or more.

Obviously, no one will total zero (unless they’re disqualified or die gloriously on the platform). There’s probably some realistic limit to the weakest lift. Let’s say everyone can total at least 170kg. In that case, your normal curve looks like this:

It represents, visually, what we just said above. The mean (average) that any of the untrained, 93kg male lifters can total is 191kg, and the graph is truncated (cut off) at 170, because everyone can lift at least 170. And way over on the right are a very few freakishly strong people who are several standard deviations above the average. They can walk up and total 220 or 230kgs on their first day. These are the ones who will win the first-ever powerlifting tournament.

This curve shows the distribution of results on Day 1 of powerlifting. At this point in the development of the sport, no one has trained and no one has the benefit of technology. So it’s pretty clear that the untrained normal curve, which is truncated on the left side without the influence of any rules or restrictions, fits when results are determined ONLY by genetics and random chance.

Specialization and Better Genetics

Fast forward five or ten years. Your new sport of powerlifting is attracting new competitors, and these lifters are learning how to get better at lifting. This process will continue basically forever, so understanding what’s happening here is key to understanding how to think about the competitiveness of the sport. As time goes on, four things happen that shape the distribution of competitive results:

People self-select into the sport because they think they’ll be good at it. Competitors and coaches develop better and more effective training methods that help them maximize their genetic potential. New equipment and substances (wraps, suits, shoes, nose tork, steroids) allows competitors to exceed their genetic+training potential. Random chance is still in effect.

In this section we cover the first thing that happens, specialization. This means that people become competitive powerlifters because they expect they can compete. Remember when you went out and grabbed 100 random 93kg men to compete on Day 1? It’s not really reasonable to think that the competitors in a sport are randomly selected. Sorry!

As it develops, the population of powerlifters no longer resembles the population of people as a whole. And it doesn’t even represent the population of athletic people as a whole, since the sport favors certain body types over others.

If you restrict competitive powerlifting to those who choose to be powerlifters, you now draw your sample from a different population, one with better powerlifting genetics. The distribution is the same shape, but everything has moved to the right – that is, everyone is stronger.

If the average total for the untrained population of 93kg AS A WHOLE was 191kg, let’s say the average total for those who would choose powerlifting is closer to 210kg. Everything shifts to the right around that point, shown in the graph below. Also notice that as we get further away from the absolute bottom of human performance (hi again, readers!), the truncation on the left side is less severe. As the average performance gets better, there’s more room for people to do poorly compared to other competitors.

Just like the untrained population as a whole, the genetic freaks way out in the 250+kg tail will win every time they step on the platform.

That is, until people start to innovate…

Innovation: Training and Tech

Genetics isn’t everything in powerlifting, or any other sport, but that’s only because we haven’t hit the limits of current training and technology. Innovations in training techniques help competitors squeeze every last kilo out of their genetic potential, and give them a leg up.

In other words, training harder or smarter can certainly give you a leg up on competitors – but only on those who aren’t training as hard or as smart as you. When one group benefits from great training strategies, and another group doesn’t, your normally-distributed population is really two sub-populations: those who have the advantage of the better training methods, and those who don’t!

This is the same problem you may have noticed in the height example earlier! The average height of all people may be 67.5 inches, but that’s really masking two different sub-populations: men and women. In fact, if we were to look at the two groups separately, we’d see they are really different curves! For men, the average height is 70 inches (5’10”) and the s.d. is 4 inches. For women, the average height is 65 inches (5’5″) and the s.d. is 3.5 inches.

Now, instead of the nice smooth curve of height with an average of 67.5 inches, we actually have two normal curves, with different averages and different widths:

The curve for the women is thinner and taller because their standard deviation is smaller – that is, they’re more clustered around the average. The heights of the men are a little more spread out, so their curve is wider and shorter. Notice that, for example, a 76-inch (6’4″) woman is very unusual, but the men’s curve is much higher there – it’s not that rare!

The same thing happens in powerlifting when one group benefits from an innovation in training, and another group doesn’t. Instead of one uniform population, you’re now really dealing with two different populations. So you wind up with a curve that looks like the yellow curve below, even though what’s really going on is the blue and red curves:

The overall average, including both the untrained and the trained lifters, has now moved up from 210kg in the last graph, to about 300kg here. However, it’s really showing the influence of the two different populations. The blue curve shows the untrained (or the less-well-trained) lifters alone, centered on the expected “untrained” average of 210kg, and truncated at 170kg on the left side. The red curve shows the trained group alone, centered on the total of 391kg (862 lbs).

These expectations, again, come from the “strength standards” table. Intermediate means you’re a recreational lifter and have been training a couple of years. You’re probably starting to compete at this point, but most of these folks are not serious podium threats. The outliers on the right side of the red curve, though, are where we find the advanced lifters and the best-of-the-best, the elites: “less than 1% of the weight-training population will attain this level.” So even in the “trained” group there’s a pretty wide variance.

If you only looked at the yellow curve, you’d miss what’s really going on here. Even though they’re all in the same weight class, the people in the red group are essentially members of a different, better, stronger population. They will almost never lose to the untrained blue folks. If the distribution looks like this, the sport is not truly competitive.

As the sport matures, more research gets done, effective coaches get noticed, and the knowledge of how to train best gets diffused to the general population. If we assume that in a perfectly competitive sport all competitors get equal benefit from training (regardless of the methods or coaching), then this simply shifts the curve to the right, from blue to red. The yellow curve is an “intermediate” phase, a sign that the sport still has room to grow and become more competitive. Knowing when you’re in the blue, yellow or red curve, however, is a challenge for another time.

And another thing about that red curve: when all competitors benefit equally from their training, the winners are still the ones with the best genetics. All we’re doing is shifting the highest totals to the right – that is, all we’re doing is making new world records.

For innovations in technology, it works the same way. When people first discovered lifting suits, it temporarily created a second, higher-performing population of lifters that competed in the same events as those who didn’t wear suits. No matter how much training the un-suited lifters had, their best competitors (the right-hand tail of their curve) would never get totals as high as the best suited competitors.

The same thing happens, undesirably, with those who use steroids. And those who wear squat shoes, or wrist wraps, or lifting belts, or any other assisting gear, whether it’s legal or not in the federation.

Eventually, technology that works will get adopted by all competitors, shifting the curve as a whole to the right. Unless, of course, it gets banned.

How Rules Shape Competitiveness: Bans, Weight Classes, and Qualifiers

Sometimes a federation will notice that a new technology puts those who use it at a completely higher level than those who don’t. It’s almost as though people using that tech come from a stronger population than those who don’t.

If the tech is generally available to all competitors, the fed might say “Hey, this is pretty great, we’re knocking down world records really quickly!” They would then choose to let the tech percolate until it’s the standard in the sport.

This was the case in a sport very similar to powerlifting: speed skating. (Note: not similar). If you watched speed skating during the 1998 Winter Olympics, and who didn’t, you would have heard a ton about “clap skates.” In the 1996-1997 season, the Dutch women’s team adopted these and starting wrecking the international competition. The speed skating federation rolled with it, and by the Olympics every team except North Korea was using them. EVERY World Record was broken in those games. Thanks, clap skates!

Powerlifting seems to have gone in the other direction, splitting up the lifting world into “raw” (or “classic”) and “equipped.” Now, instead of having one big population hiding two different sub-populations, we can see the actual distribution of raw and equipped strength, separately. What the ban on equipment in the Raw division does, essentially, is cut off a lot of the right-hand side of the graph.

Federations can also choose to enact qualifying totals, which are essentially bans on weak competitors. Qualifying totals cut off the left-hand side of a distribution, to make the sport appear more competitive. Let’s consider just the sub-group of lifters who are strong enough to compete nationally. We’ll call these the “advanced” lifters. The “strength standards” tables define advanced as “those who have multi-year training experience with definite goals in the higher levels of competitive athletics.”

According to the tables, an advanced 93kg male lifter should be able to total about 519kg, or 1155 lbs. An “elite” 93kg male, defined as basically the top 1% of the lifting population, should be able to total 658kg, or 1450lbs.

So let’s say the “average” advanced lifter should be halfway between advanced and elite, or 588kg (1296 lbs). If only 1% of the advanced population is elite, though not necessarily true, the distribution of people who can do that might look like this:

The elites are way over on the right side again. Fewer than 1% of the folks in this population are going to hit totals higher than 658kg, and a vanishingly small number will get totals high enough to be competitive internationally (the winner in 2015 had 833kg(!!!)).

You could argue, based on this, that I might have drawn the graph wrong and it should be centered higher or have a larger standard deviation. That’s fine, I’ll draw a new one.

Making up numbers, let’s pretend that the real graph of the advanced-to-elite powerlifters as of 2015 looks like this, with an average at 676 and a standard deviation of 62.8. This would mean that only about 5% of this group of lifters are really strong enough to win the world championship.

From the Fed’s perspective, all the exciting stuff is happening on the right-hand tail, where you have world records being broken and some theoretical freak eventually getting close to 850kg or more. If you’re the USAPL, the one of the governing bodies of powerlifting in the US, you might look at this and say “We don’t want our podiums cluttered up by anyone who isn’t world-class material.” So you lop off anyone who doesn’t total at least 612kg (1349 lbs). Coincidentally, this is the qualifying total the USAPL actually chose. Now the distribution would look like this:

Now – what if you have a couple of Fedosienkos out there? What if, instead of one-tenth of one percent of lifters breaking those World Records, you suddenly have 5 or 10 percent of your competitors in the “outlier” region? If you can rule out training and technology differences, you’re probably looking at a different genetic population.

Think back to the first random sample of 100 93kg men. Imagine if we had just sampled 100 men, regardless of weight. This random sample would have a lot of men who are lighter than that, and a smaller but large number of men who are heavier than that. Generally, we know that larger and heavier people can lift more than smaller and lighter people. (Time to start bulking!).

Instead of being centered at an average of 191kg, since we’ve introduced more lighter lifters into the mix, maybe the average total for all men is 188kg. Now that you have the entire population of men in there, though, the standard deviation is going to be MUCH larger, since the curve has to account for the very weakest, lightest men, and the very strongest, heaviest men.

The same way the graph of the height of all people missed the difference between men and women, combining the lifting totals of all men is going to miss the difference between those who are heavy and those who are light. Sergey Fedosienko is in the lightest class, but he lifts like a man who is 10kg heavier. If he were squished together into one class with all the other lifters, though, even Sergey Fedosienko at 59kg would routinely get crushed by the best lifters from the 74kg and higher groups. The lighter lifters would never have a chance.

For that reason, the Feds impose weight classes. Weight classes are bans on unfair genetics. Though sometimes, as with poor Sergey, you get someone whose genetics or other special circumstances are just off the charts. Because of his genetic lifting advantages, he really is in another population. But, as of now, there aren’t enough lifters with a similar size and shape to spin off into their own class. There isn’t a good way to deal with the Fedosienko problem without either screwing him over or allowing him to continue his uncontested dominance of his class. But at least you can identify those kinds of problems by looking at the curve.

To summarize, before wrapping the whole thing up:

Equipment/tech bans cut off the right-hand tail of the distribution; they essentially help to set the upper limit on total lifts.

Qualifiers (bans on weaker competitors) cut off the left-hand tail, and set the lower limit.

Weight classes try to distinguish between unique genetic populations, but sometimes they can’t deal with outliers.

Getting Towards Better or Perfect Competitiveness

The one thing that I left out of the last graph is that it doesn’t really make sense to have a right-hand tail extending way off in the distance. At some point, we have to assume there is a limit to what genetics and training can do for you, given the currently-legal set of equipment. Without specifically breeding for more Fedosienkos, let’s pick an artificial number and say that the most any 93kg man will ever be able to total is 875kg.

By pushing up the lower limit, you get a tighter and tighter distribution. A tighter distribution means that there is less room for distant outliers that are high above the average. At some theoretical point, WHICH WE HAVE NOT REACHED, every competitor has roughly the same genetic, training, and tech advantages. And THAT means the winner is more likely to be determined by random chance: in other words, the sport would be perfectly competitive.

I’m not sure we can know when we’ve hit that point. But I think, when the sport is fully mature and the federations are aggressively blocking all but the best-of-the-best from international meets, the distribution of world-class competition results would look like this:

In the next article, I’ll use real results from IPF/USAPL competitions, and see how they match up to these theoretical curves. Later, I’ll try to find some math-based way to know how close we are to that point, and compare it to other individual sports (Hello again, speed skating!).

My theory is we don’t actually have to know what the upper bound number is, the strongest any 93kg man can ever be. In fact, we’ll never be sure, because genetics and training and tech will probably always improve. I’m hoping we can just tell where we are by the shape of the curve.

I hope you enjoyed the read! See you next time!