He looked at guidelines for how much weight people can lift for different rep ranges. Then he made a formula to match those guidelines.
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The Baechle 1RM formula was derived by Thomas Baechle and takes yet another approach compared to Brzycki and Adams.
Baechle's formula is: 1RM = Weight / (1.0786 - 0.0875 x Reps) Where: Weight = Load lifted (kg or lbs) Reps = Number of reps completed
To derive this formula, Baechle analyzed published strength data and repetition maximum percentages used by the National Strength and Conditioning Association (NSCA). Specifically, he looked at the typical percentages of 1RM that can be lifted for different rep ranges according to the NSCA's loading guidelines. For example: • 1 rep = 100% of 1RM • 2 reps = 95% of 1RM • 6 reps = 85% of 1RM • 10 reps = 75% of 1RM
Baechle then used a curve-fitting approach to find the equation coefficients that best modeled this Representative Percent 1RM vs Reps relationship from the NSCA data. This iterative curve-fitting process resulted in the 1.0786 and 0.0875 coefficients that make up Baechle's published 1RM prediction formula.
So in summary, while Brzycki used regression on actual lifter data and Adams worked from first principles assumptions, Baechle based his formula on curve-fitting to established Rep Max percentage guidelines used by strength coaches.
The different derivation approaches highlight how these 1RM prediction equations, while empirically-based, make different data and assumption inputs when modeling the strength curve relationship.