# Wilks Coefficient

The Wilks Coefficient or Wilks Formula is a coefficient that can be used to measure the strength of a powerlifter against other powerlifters despite the different weights of the lifters. Robert Wilks is the author of the formula.

## Equation

The following equation is used to calculate the Wilks Coefficient. The total weight lifted is multiplied by the Coefficient to find the standard amount lifted normalized across all body weights.

$\textit{Coeff} = \frac{500}{a + bx + cx^2 + dx^3 + ex^4 + fx^5}$

x is the body weight of the lifter in kilograms

Coefficients for men are:
a=-216.0475144 b=16.2606339 c=-0.002388645 d=-0.00113732 e=7.01863E-06 f=-1.291E-08

Coefficients for women are:
a=594.31747775582 b=-27.23842536447 c=0.82112226871 d=-0.00930733913 e=0.00004731582 f=-0.00000009054

## Example

The main function of the Wilks formula is involved in Powerlifting contests. It is used to identify the best lifters across the different bodyweight categories and can also be used to compare male and female lifters as there are formulas for both sexes. First, second and third places on the winner’s podium within their own age, bodyweight and gender classes are awarded to the competitors who lift the most weight respectively. Where two lifters in a class achieve the same combined total lifted weight the lighter lifter is determined the winner.

The Wilks formula comes into play when comparing and determining overall champions across the different categories. The formula can also be used in team and handicap competitions where the team includes lifters of significantly varying bodyweights. The Wilks formula, like its predecessors (the O'Carroll and Schwartz formulas), was set up to address the imbalances whereby lighter lifters tend to have a greater power-to-weight ratio, with lighter lifters tending to lift more weight in relation to their own bodyweight. This occurs for a number of reasons relating to simple physics, the nature of the makeup and limitations of the human skeletal and muscular system as well as the shorter leverages of smaller people.[1] Note the totals section and that lighter lifters below 100 kg bodyweight achieve totals in excess of ten times bodyweight whereas heavier lifters do not. The Wilks system is primarily a handicapping process that provides an adjusted statistical method to compare all lifters of varying classes and groups on an equal standing and makes allowances for the disparities.

According to this setup, a male athlete weighing 320 pounds and lifting a total of 1400 pounds would have a normalized lift weight of 353.0, and a lifter weighing 200 pounds and lifting a total of 1000 pounds would have a normalized lift weight of 288.4. Thus the 320 pound lifter would win this competition. Notably, the lighter lifter is actually stronger for his bodyweight, with a total of 5 times his own weight, while the heavier lifter could only manage 4.375 times his own bodyweight. In this way, the Wilks Coefficient places a greater emphasis on absolute strength, rather than ranking lifters solely based on the relative strength of the lifter compared to bodyweight. This creates an even playing field between light and heavyweight lifters—the lighter lifters tend to have a higher relative strength level in comparison to the heavyweight lifters, who tend to have a greater amount of absolute strength.