Naclerio used advanced math formulas that model the pattern of how strength drops off as more reps are done.
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The Naclerio et al. 1RM prediction formula is another approach that aims to improve accuracy over some of the more generalized prediction models.
The Naclerio formula is:
1RM = Weight / (1 - (Reps x (1 - e^(-0.05 x Reps))))
Where: Weight = Load lifted (kg or lbs) Reps = Number of reps completed e = Euler's number (approx. 2.718)
To derive this formula, Naclerio and colleagues analyzed strength training data from 93 physically active young adults performing the bench press and parallel squat exercises.
Rather than using linear or polynomial regression like some previous methods, they used non-linear regression modeling techniques to fit an equation to the repetition-load data.
Specifically, they found that an exponential decay model provided the best fit for predicting maximal load (1RM) from the number of repetitions performed at a submaximal load.
The e^(-0.05 x Reps) component represents this exponential decay relationship between reps performed and the percentage of 1RM lifted.
By incorporating this exponential term, Naclerio's formula accounts for the idea that lifting capacity decays non-linearly as more reps are performed, rather than following a simpler linear model.
When validated on their study data, this approach provided higher accuracy for predicting 1RMs across a range of rep maxes compared to other generalized linear formulas.
A potential downside is that Naclerio's equation is more algebraically complex. However, it demonstrates using advanced non-linear modeling to better capture the underlying strength curve characteristics when predicting 1RMs.