Recap of the Theory

In this article and the one before it, I develop a way to measure competitiveness in solo sports such as powerlifting, weightlifting, swimming, speed skating, and track events. In these articles, I explain and test three hypotheses:

The results of solo sport competitions (and powerlifting in particular) should be statistically normally distributed. If they are, the distributions should change in certain ways in response to changes in the population of competitors and changes in the competitions’ rules. If the distributions react in the expected ways, we can say that certain statistical distributions indicate relatively more or less competitiveness in the sport. We can then use those distributions to determine what actions the governing bodies could take to improve competitiveness.

In the last article, I said that we could use the idea of the normal curve to assess competitiveness in powerlifting and other individual sports. “Competitiveness” means that participants in a competition have more equal chances to win. When a sport is perfectly competitive, which we will probably never observe in real life, every competitor is equally likely to win. In a perfectly competitive case, the only thing that determines the winner of a competition is random chance.

In the last article, I described the results in an individual sport competition being the result of four factors: human genetic potential, training, technology, and random chance. Then I talked about ways the sports’ governing bodies can manipulate the rules to make their results more competitive:

banning equipment or technology;

banning worse competitors (using qualifying totals or times); and

separating competitors that are really in different populations (weight classes or other similar distinctions).

I said that, by looking at the statistics and distribution (and making a graph) of the results of many competitions, we could compare a sport to itself over time to see the results of these rules changes and the progress of the sport as it becomes more or less competitive.

To make this work, I assume that results of competitions are normally distributed: that is, most observations will be close to the average, and the farther you get from the average (the more standard deviations you are away from the average), the fewer observations there will be. Specifically, I said that the results would match the normal curve.

Using a “strength standards” table, I estimated what a normal curve would look like for the sport of powerlifting. I assumed that the average “advanced” 93kg-class powerlifter, who has trained for several years and is serious about competition, would be able to total 588kg in the three powerlifting lifts (squat, bench press, deadlift). I also assumed that, based on the strength standards table, fewer than 1% of these lifters would be truly elite, able to total more than 658kg.

So for the normal curve of “advanced” 93kg lifters, the average would be 588, and I assumed the standard deviation would be 28kg. Although I later said this was probably too low, it was useful for discussion. The example curve with these parameters looked like this:

Three things can shift this whole curve to the right:

More people with better genetics entering the sport;

The discovery and diffusion of new training techniques;

The discovery and diffusion of new technologies.

When these things happen, it briefly creates a situation where there are really two populations hiding in the data: the competitors benefiting from the better genetics/training/tech, and the ones who are not. Over time, as the innovations come to dominate the sport, the entire curve shifts to the right, and once again there’s just one normal curve to describe the whole population.

The sport’s governing body can affect this curve, and directly affect competitiveness in the sport, by changing the rules at tournaments and meets. In powerlifting, for example:

Equipment/tech bans cut off the right-hand tail of the distribution. They set the upper limit on total lifts and prevent perceived unfair advantages.

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. However, they can’t deal with outliers who resemble the other lifters but have some natural advantage that the weight class or other distinction can’t account for.

Testing the Theory with Real Data

In this article, I compare some of the theoretical distributions from the previous article with ones that I’ve drawn from real data, testing hypotheses 1 and 2 from above. If they fit, I will have a statistical approach to formally assess individual-sport competitiveness (hypothesis 3 from above). Some additional statistics will be used at that point.

Is there a Normal Distribution of Lifters?

The foundation of the approach I’m proposing was: “The results of solo sport competitions (and powertlifting in particular) should be normally distributed.”

My research finds that, for powerlifting, this is the case. In the graph below, I’ve plotted out over 1600 men’s powerlifting totals, taken from 48 real powerlifting competitions between 2012 and 2015. The data are taken from all levels of competition that report results to the national and international federations: local and state meets, the USAPL Raw National Championships, and the IPF World Championships. This represents a range of competitors, from “intermediate” (training a few months and doing a test-run at a meet) to “elite” (among the 1% best lifters, internationally competitive).

Below is a graph showing the results from the men’s 93kg class. A couple of data notes:

Totals are only for raw (unequipped) lifts.

Disqualified totals, where a lifter did not successfully complete at least one of each of the three lifts, are excluded.

Prior to 2015, USAPL was using different weight classes. I’ve converted the lifter’s real weights to the current weight class, but weight cuts and other attempts to get into or out of the old classes may have influenced totals for each real weight.

There may be some copy-paste errors in the data, but I’ve tried to quality-check it as thoroughly as possible.

The graph below shows two lines: the green line shows the actual distribution of the data. The red line shows a normal curve that has been fitted to the data.

It’s clear that the actual distribution, the green line, is very close to the shape of an actual normal curve (the red line). I am fairly confident that with more data (perhaps 2000 or 2500 lifts in the database) it would be even closer to normal.

We can also describe this distribution with a few key statistics. We’ll use these to compare this distribution with other distributions later.

The mean (average) weight lifted was 604kg;

(average) weight lifted was 604kg; The standard deviation was 97kg. This means that 68% of 93kg male lifters had totals within 97kg of the mean, or between 507kg and 701kg.

was 97kg. This means that 68% of 93kg male lifters had totals within 97kg of the mean, or between 507kg and 701kg. The skewness (asymmetry) was 0.075, which is considered very small, as the normal distribution has a skewness of 0. This means the “tail” on the right side of the mean is a little (but not much) bigger than the tail on the left.

(asymmetry) was 0.075, which is considered very small, as the normal distribution has a skewness of 0. This means the “tail” on the right side of the mean is a little (but not much) bigger than the tail on the left. The kurtosis (“tailedness”) was 2.67. The normal distribution has a kurtosis of 3, which means this distribution has slightly fewer of its observations in the tails than a normal distribution.

How Do Curves from the Real Data Compare to Theoretical Data?

In the last article, I used a “strength standards” table that is, unfortunately, no longer available. (The original link in my earlier article has been edited to one that works; however, the averages from the new table would be 20 kgs higher than the last article shows.) Here is a link to the new tables at strengthlevel.com, which is based on user-inputted data.

According to the user-reported data on strengthlevel, here are the mean (average) total lifts for a 93kg man across squat, bench, and deadlift. We’ll call these our “population” data. Next to these, in the table below, you can see the “sample” data I compiled from the lifting events. For intermediate totals I used any lift recorded at a state/local meet (though of course some competitors there will really be advanced or elite). For advanced totals I used lifts from the USAPL Raw Nationals. For elite totals I used lifts from the IPF World Championships. The “n” in parentheses indicates the number of totals that are averaged to create the sample total.

Level Self-Reported Population Average Competition Results Sample Average (n) Intermediate / State-Local Meets 441 549 (172 lifters) Advanced / USAPL Raw National Meets 543 635 (103 lifters) Elite / IPF Worlds 643 712 (59 lifters)

What we see in this table is that the definition of “intermediate” at the population level does not fit the profile of those who enter competitions. Trying to define “intermediate” in the sample as all those who compete in sub-national competition yields an average total nearly 25% higher than what is observed in the population as a whole. So, unsurprisingly, those who choose to compete probably represent the sub-population that has trained longer and harder than the powerlifting population as a whole.

Because of this, I eliminate the intermediate level and combine the national- and international-level competitors into one elite group. Now the comparison looks like this:

Level Population Average Sample Average (n) Advanced /Sub-national competitors 543 549 (172 lifters) Elite / USAPL Raw Nationals, IPF Worlds 643 663 (162 lifters)

While the means are not identical, we can feel confident that the sample I’ve drawn from real competition data represents a good snapshot of the real lifting ability of the population of advanced to elite powerlifters.

Having established that the sub-population of competitors is normally distributed, and that it is likely the population of powerlifters is probably also normally distributed, now I can directly model how rule changes affect competitiveness. Because I am using only one weight class (93kg) and the same set of equipment bans (only “raw” lifters) , it is easy to show how changes to one kind of rule affect the average results. Other than self-selection, the difference between each level of competition is only the qualifying total needed.

Since there is some right-hand boundary on the distribution that represents the (currently unknown) upper limit on human strength, by definition higher qualifying totals (being a left-hand boundary on the distribution) must yield more competitive results. Because of this, I can compare the statistics (mean, standard deviation, skewness, and kurtosis) between three different competitive levels to see what happens as the rules exclude weaker lifters and force the field to be more competitive.

Level Qualifying Total Needed Mean Total Standard Deviation Skewness Kurtosis Sub-national competitions None 549kg (172 lifters) 73 -0.25 3.06 USAPL Raw Nationals 484kg (in 2015; none previously) 635kg (103 lifters) 79 -0.01 2.82 IPF Worlds Winning nationals 712kg (59 lifters) 72 -0.62 3.4

The mean totals change as expected: the sub-national mean is the lowest, the national-level mean is nearly 100kg higher, and the world-level mean is almost 80kg higher again.

The main takeaway from this table, however, shows that the particular qualifying rules for the IPF World Championships permit competitors that probably don’t “belong” there, competitively. This is more easily seen by visually comparing the distributions of the three groups

.

In the first image, the “sub-national” competition totals, the mean total is 549kgs. This is certainly representative of an “advanced” group of lifters, but because there is no qualifying total required, it has a long left tail. Its skewness is -0.25 (where a perfect normal distribution has skew of 0). On the right-hand side, there are no totals higher than 750kgs, which is clearly not enough to win the national/international competitions. (If I included more lifting data, however, we would see a few totals above 750kg. For the most part, lifters have to qualify at sub-national events in order to attend national/international events).

The second image shows the distribution from United States national-level competition, the USAPL Raw National championships. Here, the mean total is 635kg – much higher than sub-nationals – and the skew is almost 0. This distribution is quite close to normal, although you can see the truncation on the left-hand side due to the institution of a qualifying total for 2015. Because lifters had to be able to total at least 484kgs (as of 2015), there are relatively few totals on competition day that came in between 450 and 500kgs.

The IPF Classic (Raw) Worlds, meant to be the best-of-the-best in worldwide powerlifting, do not use any qualifying total. Instead, lifters are invited to participate if they are one of the top three lifters in their national federation – for example, the United States sends places 1, 2 and 3 from the USAPL Raw Nationals.In practice, this means IPF Worlds sees the very strongest lifters – but also sees many powerlifters who are competitive within their countries, but not across countries. While the mean total is 712 kg, the negative skew is comparatively large: -0.62. That long left tail represents competitors who would not have a chance at winning some national competitions, let alone the IPF Worlds.

To put it another way: the mean total at the USAPL national competition was 635kg. The mean at IPF Worlds was 712kg. The standard deviation at IPF Worlds was 72kg, meaning that about 16% of world-level competitors (those who are more than 1 s.d. below the mean, at 640kg or below) would have a below-average total at the U.S. national level. This is also true of the USAPL national competition, where about 16% of lifters who were 1 s.d. below the mean (or 556kg) would be below-average in a sub-national meet.

Both of these suggest that, from the standpoint of competitiveness alone, both the USAPL Raw Nationals and the IPF Worlds could stand to significantly increase their qualifying totals.

This problem has occurred before in other sports. Most famously, this is what led Olympic ski jumping authorities to institute the Eddie “The Eagle” rule, when a lack of competition in the U.K. allowed Eddie Edwards to qualify for the U.K. Olympic ski jumping team without any real hope of a good performance.

In the next section, I will look at what would happen if the IPF did significantly increase the qualifying totals for the World championships.

WHAT HAPPENS IF IPF WORLDS INSTITUTES A QT? (Or – Fixing the Eddie the Eagle Problem)

From the analysis so far, it’s clear that the IPF has room to make their international competition more competitive, and can accomplish this by instituting a qualifying total instead of the current “best lifters from each nation” standard. However, even though we now know this, we have to guess about two things:

If the current distribution – a strong negative skew – is not desirable , what shape would be more desirable? What will the short-term and long-term effects of a QT change be? Is it a good idea to make the change?

The first question is somewhat easier to answer than the second. In the last article, I stipulated that under perfectly competitive conditions every lifter has an equal chance to win every competition. In other words: the QT would be so high that only the best can compete. They would all generally be as strong as each other, and random chance alone would determine who has the highest total each time. If you drew a curve of these (hypothetical) results, you would see that they are NOT normally distributed. Almost all results would be the same, or very close to each other, with a few higher totals indicating lifters who had a “good day” and won their competitions. This (again, hypothetical) curve would look like more like a straight line, with a short right-side tail, than a curve. It would also mean that very, very few lifters were competing – perhaps as few as 5 lifters in each weight class.

A distribution that is CLOSER to perfectly competitive than a normal distribution (but still not perfectly competitive) would look something like the graph below – just the very right-most tail of the normally-distributed population of powerlifters. This distribution has a strong positive skew, nearly 1. The majority of lifters are close to each other at the left-hand side of the distribution, and a few competitors with better genetics or better training are consistently dominating the field.

Many highly-competitive individual sports are in this situation, or recently have been, where a handful of athletes (e.g. Kim Walford and Jennifer Thompson in powerlifting, Michael Phelps in swimming, Usain Bolt in running, etc.) can reliably be found on the top of every results table, followed by a tight pack of competitors.

Assuming this is desirable, the IPF could achieve something like this by experimenting with different left-hand cut-off points (qualifying totals) until an appropriate distribution emerges. I did this as an exercise, trying various QTs until I settled on a cut-off of 740kg, about 30kg higher than the old IPF worlds mean lift. The new distribution looks like this:

Using this proposed QT, most world-class 93kg male lifters are much closer to each other than before: about 80% of totals fall between about 740kgs and 790kgs. Another ten percent are between about 790kgs and 820kgs. This means that, under this new proposed QT, about one in ten totals would be above 820kgs, which puts them (more or less) in range of IFP world record totals. (Note: I have had a difficult time finding out what the actual IPF world record is for 93kg. I think it belongs to Jesse Norris, but he also is serving a suspension for a failed drug test, so I’m not sure if it counts).

This exercise shows HOW to make world-class lifting more competitive, but it does not address the question of WHETHER to do so. That is a much more complicated question.

In the previous discussion, I have not really talked about why competitiveness is a good thing. The general idea is that a more competitive sport is a more exciting sport, and a more exciting sport is more likely to attract new competitors, fans, and perhaps advertisers. All of this creates a virtuous cycle of development for the sport, and ensures continued improvement in genetics, technology and training.

It seems possible that a too-aggressive approach to creating competitiveness could choke off this cycle and ultimately harm the sport.

In the IPF world championship example above, a higher QT would cause a trade-off. On the positive side, the lifters who survive the cut-off would be more interesting to watch, as their lifts would be more impressive, and (to some extent) more likely to set world records.

On the negative side, a higher QT would exclude many nations from international competition, at least in the short run. Over the last three years of IPF World Championships, the 93kg weight class has had 47 lifters representing 27 nations. All continents are represented, and large and small countries both appear: the USA, Great Britain, Canada and Russia, of course, but also smaller (by population and economy) nations like Turkmenistan, Bulgaria, the UAE, and New Zealand.

A QT of 740kgs would leave a much less diverse group. In the last three years, lifters from 14 of those 27 countries would not have qualified. This could mean less interest and excitement for powerlifting in those now-excluded countries, which could lead to less development of the sport there, and in turn a lower chance that world-class lifters will begin to emerge from those nations.

By contrast, if the IPF set a less-aggressive QT, this could strike a better balance between providing exciting world-class competitions, and including additional markets for the sport that can help its ongoing development. For example, the QT could be set at 640kg, meaning that national winners would have to be at least as strong as the “average” USA national-level lifter to compete internationally. At this QT level, only four nations would have failed to send a qualified athlete from 2012-2015: Russia, Turkmenistan, the UAE, and Uzbekistan. That might be a more desirable result.

Takeaways from This Article

Powerlifting ability is normally distributed in the population as a whole, and normally distributed among those who compete in powerlifting. Increasing qualifying totals (QTs), by definition, increases competitiveness at a given tournament. Because the competitors are normally distributed, this means a more-competitive distribution looks like the right-hand side of a normal curve: a truncation on the left side, and a medium-to-long right tail (positive skew). This means most lifters are about the same strength, and a few lifters will be dominant over the group. Other solo sports (e.g. weightlifting, speed skating, swimming, sprinting) should also have this kind of distribution if they are competitive. I will test this in the next article. Competitiveness is important because it makes the sport more exciting to watch and participate in, which should help the development of the sport. However, pursuing competitiveness at the expense of inclusion might hurt the development of the sport.