Brown looked at the pattern between reps and max weight, but only for up to 30 reps. Then he made a formula for that range.
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The Brown 1RM formula was developed by Len Brown and Michael Weir. It takes a slightly different approach compared to the other methods discussed. The Brown formula is:
1RM = Weight x (1 + (Reps/30)) Where: Weight = Load lifted (lbs or kg) Reps = Number of reps completed
To derive this formula, Brown and Weir analyzed existing research data on the relationship between the number of repetitions performed and the percentage of 1RM being lifted across a variety of exercises.
Specifically, they looked at studies that measured how many reps could be performed with loads ranging from 60-95% of 1RM for exercises like the bench press, squat, and deadlift.
By plotting this rep-load data, they observed an approximately linear relationship between reps and the percentage of 1RM lifted up to around 30 reps.
Using regression analysis on this data subset of 30 reps or less, they derived the simple 1RM = Weight x (1 + (Reps/30)) equation format.
The key aspect of Brown's approach was limiting the analysis to only lower rep ranges up to 30, as they found the reps-to-percentage relationship became more non-linear beyond that point. This made the Brown formula more accurate for predicting 1RMs from low-moderate rep maxes compared to other generalized equations that tried to model the entire rep range.
So in summary, Brown and Weir empirically derived their formula specifically from analyzing the linear reps-to-percentage relationship in the data for lower rep maxes up to 30 reps.