TLDR

Adams used some assumptions about how strength works to create his formula, instead of looking at actual lift data.

Formula

https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8163fd40b9c6e943b2c73dff642c223f62cc27

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Background

The Adams 1RM calculator formula was derived by Dr. Michael Adams in a slightly different empirical manner compared to Brzycki's approach.

Instead of using regression analysis on a large dataset, Dr. Adams developed his formula from first principles based on certain assumptions about the strength curve and fatigue characteristics during maximal lifts.

The basic assumptions were:

1. The maximum number of repetitions possible at any % of 1RM follows a linear relationship.
2. At higher reps (e.g. >10), the average percentage of the 1RM lifted decreases in a linear manner as reps increase.

From these assumptions, Dr. Adams derived the following formula algebraically:

1RM = Weight / (1 - (Reps x 0.025)) Where: Weight = The load lifted for the given rep max set Reps = Number of reps completed

The 0.025 coefficient represents the assumed average percentage decrement in load per additional rep above 10 reps.

So unlike Brzycki who empirically fit the formula to data, Adams worked backwards from theoretical assumptions to derive an equation that aligned with observed strength curves. While more theoretically derived, the Adams formula tends to be less accurate than Brzycki's at lower rep ranges (< 5 reps), but can provide reasonable 1RM estimates especially for higher rep sets in some cases.

Both the Brzycki and Adams formulas demonstrate different approaches - empirical regression analysis vs theoretical first principles derivation - in developing these useful 1RM prediction equations.