Jupyter notebook to fit a reciprocal polynomial on Wilks coefficients
The Wilks coefficients are used to compare the weights lifted by athletes of different body weights. The weight lifted is multiplied by the coefficient corresponding to the body weight. The higher the product, the better the athlete has performed. All weights need to be expressed in kilogram.
Unfortunately, the creator of the formula, Robert Wilks, CEO of Powerlifting Australia, hasn't published the formula on which the coefficients are based on. Only two tables of coefficients are available, one for men, one for women.
The code in this Jupyter notebook extracts the coefficients from those tables (see the files wilks-men.tsv and wilks-women.tsv) and fits the following reciprocal polynomial on them:
coeff = g / (a + b ⋅ x + c ⋅ x2 + d ⋅ x3 + e ⋅ x4 + f ⋅ x5)
Where x is the athlete's body weight in kilogram and the independent parameters a, b, c, … g are to optimized to fit the curve to the given coefficients.
It turns out that the following values make the formula almost perfectly fit the coefficients:
| Men | Women | |
|---|---|---|
| a | 3.63670138e+04 | -9.31498570e+04 |
| b | 6.55937783e+03 | 1.01904268e+04 |
| c | 5.65741690e+01 | -2.43239016e+01 |
| d | -1.07472551e+00 | -7.84945613e-01 |
| e | 5.45052301e-03 | 7.00489691e-03 |
| f | -9.30455617e-06 | -1.74074520e-05 |
| g | 4.63384381e+05 | 4.46372497e+05 |
- Python 3.x
- Pipenv
Clone the repository, then enter the created directory:
git clone https://github.com/ola-ct/wilks.git
cd wilks
Install required modules:
pipenv install
Open Jupyter notebook:
pipenv run jupyter notebook
A browser window containing the notebook should open.
You can now run the code by pressing the "Run" button.
Copyright © 2020 Oliver Lau
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.