More on the Wilks Formula

Since I get regular requests from various people to please give them the actual "formula" so that they can input it into their programmable calculators to use at meets I have decided to put this as a link on-line where they can access it. I received the following from Dave Bracken who received it from an IPF Committee member and I cannot otherwise vouch for it. Try plugging some actual values in and see if it produces the desired values.

The data used to determine the Wilks coefficient were the totals of all of the first place lifters at all of the world championships since the beginning of the IPF worlds. Men's data for the men's formula and women's data for the women's formulas.

The formula is:

reduced total = total lifted *500/(a+b*x+c*x^2+d*x^3+e*x^4+f*x^5)
 
Where x is the body weight of the lifter in kilograms

The coefficients for men are:

a=-216.0475144
b=16.2606339
c=-0.002388645
d=-0.00113732
e=7.01863E-06
f=-1.291E-08

The coefficients for women are:

a=594.31747775582
b=-27.23842536447
c=0.82112226871
d=-0.00930733913
e=0.00004731582
f=-0.00000009054

Questions and Answers Regarding Wilks and Other Handicapping Systems:

Q: What research and physiology science is there behind these handicapping systems such as the Schwartz, Malone, and Wilks formulae?

***Generally, all that these folk have done is to use various regression methods to fit a curve to the world's records for all bodymass divisions, with no attempt to explain any underlying physiology.

Q: Are there published and peer-reviewed studies that explain the methods used to construct the Wilks system? Where is the evidence that the other systems are biased and that the Wilks corrects them?

***Siff's regressions and those of Sinclair have been published in academic journals.

Q: How can USAPL (USA Powerlifting) meet directors and referees explain coherently to second or third-placing lifters why the Wilks coefficients were used to rank them as they did?

***Robert Wilks was a member of the International Powerlifting Federation at the time the Wilks formula was adopted. The formmula developed of the late Mel Cunningham Siff, a South African professor of civil engineering who had a passionate interest in Olympic weightlifting and other strength sports, had a coefficent of correlation between the actual data and the values of the Siff formula values of better than 99.6 percent which is far better than the other formulae, hence it has led to far fewer conflicts in competition. There is a website which compared our different formulae and here is link to the Siff Formulae.

Q: After one bench-press competition in which I officiated as a referee I was asked by a 150 lifter, who had lifted over twice his body-weight (315 lbs), to explain to him why another lifter weighing 265 who pressed 500 got first place in that competition when in fact that lifter had lifted less than twice his bodyweight. I was at a real loss to explain to him why the Wilks coefficients were such a reliable and reasonable way to compensate for differences in bodyweight.

***The problem here is that the Wilks vales were developed for t-o-t-a-ls and not for individual lifts. Therefore it is even more inappropriate to use any of the systems for ranking anything but what they were determined for - namely TOTALS. Therefore when the Wilks coefficients are applied to single lifts different effects occur. Bench increases most with body weight so when the Wilks coefficients are used to rank bench press meets this greatly favors the heavier lifters. When the Wilks coefficients are used on a single lift deadlift meet it greatly favors the lighter lifters since deadlifts alone do not increase as fast with body weight as total does. It may be appropriate for squats but it probably favors the lighter lifters again if it is applied to single lift squats. A fit to individual lift data is what is needed if individual lifts are compared. (Thanks to Dr. Dave Bracken, an Los Alamos nuclear physicist and world champion powerlifter for this answer!)]

Q: In any case I would like to understand the science and methodology behind the Wilks system . . .

Siff; Now that I have seen the Wilks formulae, I have been able to compare my system with his by applying them to the current men's world records, as tabulated below. What I have done is compute the scores for both of our formulae so that they reflect a percentage of the mean of the world's best performances.

Q: Who are the world's best powerlifters according to the Wilks and Siff body-weight hanicapping formulae?


BMASS     LIFTER	    RECORD   SIFF    SIFF   WILKS   WILKS
	                             Score   Rank   Score   Rank     

 52	  Andrzej Stanaszek  592.5   104.87    3    116.28   10
 56	  Hu Chun-Hsiung     637.5   100.53    7    116.07   11
 60	  Joe Bradley	     707.5   102.17    5    120.68    6
 67.5	  Alexei Sivokin     800.0   102.58    4    123.36    4
 75	  Rick Gaugler	     850.0   100.38    8    121.14    5
 82.5	  Mike Bridges	     952.5   105.90    1    127.62    1
 90	  Mike Bridges	     937.5    99.55    9    119.70    7
100	  Ed Coan	    1035.0   104.90    2    123.32    2
110	  Alexey Gankov	    1002.5    98.10   11    117.99    9
125	  Kirk Kaworski     1045.0    98.36   10    119.10    8	
125+	  Bill Kazmaier*    1100.0   100.66    6*   122.94    3*


Mike Bridges at 82.5 kg division total is the best relative score of all time [RESULTS CORRECTED THANKS TO ALAN GIBSON . . .}

[Note by Andy Anderson: Kazmaier's total is set apart from the others, because Dr. Mel Siff who provided these results, did not know what his bodymass was when he achieved his 1,100 kg total - in his calculations, he estimated 140 kg as his body-mass, which yielded the values above. If that is anywhere close to his actual body-mass, then he would rank as shown.