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 my homepage 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:

I directed several questions to Dr. Mel C. Siff, an exercise physiologist who is extremely knowledgable and who was kind enough to try to answer my questions. What follows are some of his answers to my questions:

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?

***This evidence I have not seen. My regressions and Sinclair's have been published in academic journals, but I have not seen any of the others there. I would also be interested in seeing what data they use and how they have obtained their relationships.

Q: Now that I have qualified as a USAPL State Referee and am becoming involved in the administrative aspects of running a meet, I find it very frustrating that I cannot explain coherently to second or third-placing lifters why the Wilks coefficients were used to rank them as they did.

***I cannot see why his coefficients have been used either. We had constant battles when we used those types of formula back in South Africa, which is one major reason why I developed alternatives. The correlation coefficient between actual data and my formula values is better than 0.996, which is far better than the other formulae, hence it has led to far fewer conflicts in competition. By now, you must have seen that website which compared our different formulae. If not, here are my Formulae.

Q: Last March 13 following a bench-press competition 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.

***Try my equations and let me know what you think. [Another Answer: The Wilks 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 Dave Bracken for this answer!)]

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

***I don't blame you - If you find out that you also prefer my formulae, then, by all means take it further in the powerlifting community. My formulae do not become redundant every time a new record breaks the older ones by a significant amount - that is why I relied on the average of the 6 or 10 best lifts ever achieved in any given division and why I used the actual bodymasses of the lifters instead of the division upper limits (more details are covered in "Supertraining").

[Update provided on May 12, 1999, posted July 2, 1999 -]

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.


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*


Actually, I had anticipated that there would not be any major differences between our results, but there certainly are. Our tables formulae agree that Mike Bridges at 82.5 kg division total is the best relative score of all time, but after that there are some great differences. For example, my formula ranks Ed Coan at 100 kg division total as 2nd . . . [RESULTS CORRECTED THANKS TO ALAN GIBSON . . .}

[Note by Andy Anderson: I used the Siff formula to recalculate Ed Coan's score using his December 1998 USPF total of 2,463 lbs. (1117.5 kgs) at his bodyweight of 108.8 which yielded a Siff score of 109.76 which would have bested the 110 kg. ranking above and which also would have ranked him as BEST LIFTER OF ALL TIME. . . However to be consistent one would have to recalculate all Siff Scores for all ten world first place holders in each weight class drawing on both the current USPF and IPF records.]

I have placed Kazmaier's total apart from the others, because I did not know what his bodymass was when he achieved his 1,100 kg total - in my calculations, I 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.

Since I have not competed in powerlifting for many years, I cannot judge as well as some really serious modern powerlifters - let them check through the comparison tables of our two different formulae and comment on what they think.

Hope that helps.

Kind regards

Mel

Dr Mel C Siff
Denver, USA
mcsiff@aol.com