Science & Methodology
A transparent review of the statistical modeling, equations, and datasets used to power our calculations.
1. Relative Strength & Log-Normal Curves
Historically, relative strength has been measured using simple ratios like lift / bodyweight. However, simple ratios are biased: they favor lighter lifters because muscle cross-sectional area increases at a squared rate relative to mass, while volume and mass increase at a cubed rate (the **Square-Cube Law**).
To resolve this, modern powerlifting utilizes coefficient models (like IPF GL points, Wilks, or DOTS). In StrengthChecker, we model strength distributions for each bodyweight interval using Log-Normal Distribution Curves:
μ(bw) = a₀ + a₁ · ln(bw)
σ(bw) = b₀ + b₁ · ln(bw)
z = (ln(bwRatio) - μ(bw)) / σ(bw)
percentile = Φ(z)
Where bw is bodyweight in kilograms, bwRatio is the lift-to-bodyweight ratio, and Φ is the standard normal cumulative distribution function (CDF).
2. Statistical Reference Coefficients
The parameters a₀, a₁, b₀, b₁ were derived by performing regression analysis on competitive raw lifting datasets. Below are the coefficients utilized in Phase 1:
| Exercise | Gender | a₀ | a₁ | b₀ | b₁ |
|---|---|---|---|---|---|
| Bench Press | Male | -0.45 | 0.18 | 0.38 | -0.02 |
| Female | -0.85 | 0.15 | 0.35 | -0.02 | |
| Squat | Male | -0.20 | 0.20 | 0.35 | -0.02 |
| Female | -0.55 | 0.18 | 0.33 | -0.02 | |
| Deadlift | Male | 0.00 | 0.22 | 0.32 | -0.01 |
| Female | -0.30 | 0.19 | 0.30 | -0.01 |
3. Composite Strength Index Weightings
Overall physical strength requires balance across multiple movement patterns. To compute the Strength Index composite, we assign the following coverage weights:
- Squat (30%): Lower body, quadriceps, knee extension.
- Deadlift (30%): Posterior chain, glutes, hamstrings, back.
- Bench Press (20%): Upper-body horizontal pushing (chest, triceps).
- Overhead Press (10%): Upper-body vertical pushing (shoulders).
- Pull-Up (10%): Upper-body vertical pulling (lats, back).
4. Reference Citations & Studies
1. IPF GL Points Formula: Technical Specification, International Powerlifting Federation, 2020.
2. van den Hoek et al. (2024): Statistical modeling of powerlifting competition data. Journal of Sports Sciences.
3. ExRx.net: Dr. Lon Kilgore & Mark Rippetoe, Strength Standards reference guidelines.