Theory and meaning of the Wilks score?

Question

The Wilks score is used to compare powerlifting scores for lifters of different body weights. A coefficient

                          500
Coeff = -----------------------------------------,
         a + b*x + c*x^2 + d*x^3 + e*x^4 + f*x^5

depending on the body weight "x" of the lifter in kilograms is multiplied by his or her total to arrive at a sort of "standardised" score for comparison. (It appears that it may also be used to compare individual lifts.)

There are specific (sex-dependent) values given in the linked article for a,b,c,d,e,f. Is there any online source explaining the theory behind the Wilks score? The linked Wikipedia article does not explain where the denominator polynomial coefficients (a,b,c,d,e,f) come from and why the formula has the specific form given, and Google wasn't of much help.

The quintic polynomial (a+bx+cx²+dx³+ex⁴+fx⁵) appearing in the denominator has three real roots. The negative root can be ignored as meaningless, and the two positive roots (roughly 13.5kg and 283kg) are presumably to be considered "out of range". Thus, I would guess this formula was obtained by fitting some collection of data. But what data? Alternatively, perhaps there is a theoretical model explaining these coefficients? (The only, admittedly crude, model I can think of is a multiplier very roughly like x^-(2/3), which doesn't resemble the form given for Wilks, though the curves do have roughly the same overall shape on a sensible body-weight interval.) There must be some published literature on this, but I could not find it.

Answer 1

I sadly cannot find any resources explaining the coefficients.

My best guess is that it is interpolated using a large amount of data from official powerlifting events, and fitted using some "best fit" approach like the Method of Least Squares. This would explain where the coefficients come from.

The roots of the quintic polynomial would of course cause an indeterminate value due to division by zero, but being that they require a person's bodyweight to be either negative, or extremely low/high, they need not be worried about.

The only decent resource is could find was this study which just seems to validate that the formula causes very little bias one way or the other.

Answer 2

There doesn't appear to be anything out there that exactly meets your requirements eg. in, Who is Strongest? Adjusting Lifting Performance for Differences in Body Weight, Dan Cleather, MA, ASCC, CSCS it states:

despite the wide use of the Wilks formula, it has never been fully supported by published data. An alternative method for comparing the powerlifting performances of athletes of different body weight was proposed by Mel Siff

which the paper goes on to explain. But there is a paper that appears to validate the Wilks formula: Validation of the Wilks powerlifting formula. Vanderburgh PM1, Batterham AM.

Answer 3

All studies what I have found (mentioned in other answers) are using only the world records to validate the Wilks formula. What does not really make sense for the purpose how it is used today (for comparison of ordinary lifters at competitions).

See the following post about this issue: http://physicalpreparedness.com/wilks-validation/ In this post is validation of the Wilks formula with big amount of records of raw powerlifters from recent years.

According to statistical tests in this post, it seems that Wilks normalization is kind of alright, but slightly not optimal.