The Confusing History of Strength Co-Efficients

Kevin Phengthavone 415lbs squat black and white

Undoubtedly we’ve all been faced with the question, who is stronger? As a teenager it emerged when those weighing 150 lbs. or less sought to square up to their heavier brethren. Was it more impressive bench pressing 200 lbs. at 150 or 280 lbs. at 200 lbs. bodyweight? While our adolescent selves often solved this problem by calling the other side fat or skinny, we were nevertheless ignorant of this perennial problem. Can strength across bodyweights be compared? For powerlifters or weightlifters currently reading this post, the words Wilks or Sinclair has undoubtedly passed through your lips. For the unaware, the answer is yes, albeit with some reservations.

Since the 1930s a series of formulas have been used to with the express intention of discovering who is the strongest lifter across all weight classes. Varying in their level of nuance, the strength coefficients, as they’re termed, have given a scientific air to locker room debates about the strongest lifter. Perhaps more significantly, they’re also used in competition to determine the overall winner. With that in mind today’s post seeks to examine the history of strength coefficients, beginning in the 1930s and continuing to the present day. As will become clear, the evolution of the strength coefficients used largely echoes the growing professionalism of weightlifting and powerlifting more generally.

From Showmen to Strongmen: The Need for Strength Coefficients

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As detailed previously on this site, the origins for our present interest in all things weightlifting can be traced back to the late nineteenth and early twentieth-century. It was during this period that ‘physical culture‘ as a catch all term for weight training activities first captured the public imagination, much to the delight of iron addicts for the next several decades. Now importantly, physical culture’s popularity stemmed primarily from a steady stream of strongmen and women found within the Vaudeville and Circus. Thus the early strongmen and women made their fame not through competition, although this was undoubtedly used, but rather through theatrical performances and shows. Where competition did exist between lifters, there was little guarantee that standardised weights would be used or that lifters would play fair.

While weightlifting as a sport was part of the inaugural Olympics in 1896, support for the practice within the Olympic world was patchy at best. Where competitive weightlifting thrived was in regional, national and occasionally transnational competitions. The only problem was that lifts varied across competitions. The reason I’m labouring this point is to stress the fact that in the early days of weight lifting, the need for a standardised formula to determine the strongest lifter paled in significance with the need to actually establish a set of guidelines for lifters to fairly compete against one another. Sure conversations about who was the strongest physical culture arose, but they were answered with reference to feats of strength as opposed to mathematical formula.

Things began to change however in the early 1930s. By then standardised forms of weightlifting had emerged. Access to barbells and gymnasiums was plentiful compared to the 1900s although by no means widespread and gym goers finally had a set of standardised weightlifting rules and lifts to turn towards. Since the 1920 Olympic Games, a set guideline for weight classes and standardised lifts had been established. Competitors would no longer be lumped into one class, no would lifts change from competition to competition. Stability, an often mythical idea in the fitness community, had finally arrived and with it, the opportunity for individuals to compare lifters across weight classes.

It’s at this point that the first strength coefficient emerged.

The Hoffman Formula

BobHoffman

Now admittedly, I should have guessed who was going to be the first major player in this story. Bob Hoffman, the owner of York Barbell, a patron of US weightlifting and the inventor of a fish based protein (yes that last one was so very real), is credited with creating the first strength coefficient for Olympic weightlifters. According to Lyle H. Schwartz, whom we shall be returning to, Hoffman’s formula was simple but effective in accounting for disparities across weight categories:

Imagine two balloons in the shape of a lifter, one larger than the other. If we can match the big one by blowing air into the smaller, all dimensions growing in the same proportion, then the original two balloons can be said to be similar. Body weight in similar objects increases as the cube of any length (for example height), while strength presumably depends on how big the muscles are and that increases as the square of a linear dimension….

Put another way, we can account for different weight classes by dividing a lifter’s total by his bodyweight taken to the 2/3 power. Perhaps an example from Hoffman would prove useful at this point. Writing in 1958 on John Davis, Hoffman commentated

Back in 1942, Davis lifting as a heavyweight for the first time, WEIGHING ONLY 200, officially pressed 322(!) in winning the National title at the Arena in Philadelphia. This lift would give John a formula rating of 218.63, the world’s highest at that time

To make things easier for gym goers, Hoffman provided tables for individuals to make quick calculations. According to Schwartz the ritual was pretty straightforward

Take the lifter’s total, find a number in the Hoffman table corresponding to the lifter’s bodyweight, multiply the two together, and you get a “corrected” total. The lifter in any contest with the highest corrected total is the “best

Owing one suspects to the ease of Hoffman’s calculations and also the man’s own standing within the Iron Game, Hoffman’s coefficients were without modification for several decades. This was the case for Hoffman’s first love, olympic weightlifting, and also powerlifting, which as previously noted, emerged as a competitive sport in its own right in the United States during the 1960s. In time Hoffman’s formula was amended in the 1970s to become the Hoffman/Paul formula, the origins of which can be found here.

New Coefficients on the Block

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That the Hoffman formula was revised during the early 1970s was pivotal in the emergence of new and most would say improved formulas. Across Olympic Weightlifting and Powerlifting, a series of new formulas emerged, each challenging Hoffman’s previous 2/3 power rule. Thus the 1970s saw the birth of the Sinclar formula, still used and routinely revised for Olympic Weightlifting. In powerlifting, several new formulas emerged, some of which are discussed here, but supremacy quickly went to the Schwartz  formula for men and the Malone formula for women.

As explained by Schwartz in a highly readable account, the development of the Schwartz formula for powerlifters stemmed from a glaring problem with both the old and new Hoffman coefficients. Aside from potentially favouring heavier athletes, the Hoffman formula struggled to make fair comparisons in the bench press. I have to admit that at the very least, the Schwartz formula seems easier to understand, at least for my simple mind. According to Schwartz

Since powerlifting was still a young sport in the early 1970’s there was uneven development in the three lifts on the part of most self-trained athletes. I compen- sated for such unevenness by creating artificial “best” totals by adding together the current records in the indi- vidual lifts. A “best” total would have been achieved by that ideal lifter who could match the best performances to date in all three powerlifts. Then I fitted these data to an artificial curve and picked off numbers from the curve for each bodyweight. To use the Schwartz Formula, a person would use my table of numbers and correct just as was done in weightlifting. And it worked. Lifters of all sizes could now be compared.

A similar formula was used for female powerlifters, devised by Pat Malone, to great success during the 1970s.

The Current Formulas

While the Schwartz formula was a huge step forward for powerlifting, it was still problematic. Hoffman’s coefficients favoured heavier athletes and were out of step with the 3 lifts of powerlifting. Schwartz on the other hand was accused of favouring lighter lifters. A change was in the air and it came in 1996.

It was during this time that Robert Wilks, the CEO of Australian powerlifting devised the now ubiquitous Wilks coefficient used across powerlifting meets. At this point I’m completely lost on the mathematics but for interested parties I’ve taken the liberty of pasting Taylorstrength’s excellent explanation of the Wilks formula and its advantages

The coefficient is:

________500_________
a+bx+cx2+dx3+ex4+fx5

x being the body weight of the lifter in kilograms

Values for men are:                               Values for women are:

a=-216.0475144                                     a=594.31747775582

b=16.2606339                                         b=-27.23842536447

c=-0.002388645                                     c=0.82112226871

d=-0.00113732                                       d=-0.00930733913

e=7.01863E-06                                        e=4.731582E-05

f=-1.291E-08                                            f=-9.054E-08

 

The Wilks formula is not, however, based on published data and has yet to be extensively critically evaluated. Vanderburgh PM, decided to examine how valid and accurate the Wilks formula was in practical terms. This was performed by;

  1. Examining residuals bias to verify that the adjusted score does, in fact, lead to no systematic bias based on body mass and;
  2. By applying a more theoretically supportable allometric model to the same data and comparing the fit with the Wilks approach.

Subjects were the current (1999) men’s and women’s world record holders as well as the top two performers for each event in the IPF’s 1996 and 1997 World Championships (a total of 30 men and 27 women for each lift).

Results of data analysis regarding the Wilks formula indicated that:

  1. There was no bias for men’s or women’s BP (Bench Press) and TOT (Total);
  2. There was a favourable bias toward intermediate weight class lifters in the women’s SQ (Squat), with no bias for men’s SQ; and
  3. There was a linear unfavourable bias toward heavier men and women in the DL (Dead Lift). Furthermore, the allometric approach indicated a bias against light and heavy men and women which may be considered acceptable given that half as many lifters are found in the lightest and heaviest weight classes as in the intermediate weight classes.

The conclusion drawn was that when used for BP and TOT only, the Wilks formula appears to be a valid method to adjust powerlifting scores by body mass.

Both the Wilks (powerlifting) and Sinclair (Olympic Weightlifting) formulas are now subject to constant scrutiny and have undergone revisions at various points since their inception. There may still be problems, but it appears to be the best we’ve got.

Wrapping Up

Strength coefficients have come a long way since their early inception under Bob Hoffman. Over time they’ve become more nuanced, more sports specific and to my mind, far more complicated.

Nevertheless for those involved in strength sports, coefficients can make or break a lifter’s meet. I for one, am thankful that my bodybuilding style training means that I can put coefficients firmly to one side for the time being.

As always… Happy Lifting!

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