Modelling the relationship between load and repetitions to failure in resistance training: A Bayesian analysis

To identify the relationship between load and the number of repetitions performed to momentary failure in the pin press exercise, the present study compared different statistical model types and structures using a Bayesian approach. Thirty resistance-trained men and women were tested on two separate occasions. During the first visit, participants underwent assessment of their one-repetition maximum (1-RM) in the pin press exercise. On the second visit, they performed sets to momentary failure at 90%, 80% and 70% of their 1-RM in a fixed order during a single session. The relationship between relative load and repetitions performed to failure was fitted using linear regression, exponential regression and the critical load model. Each model was fitted according to the Bayesian framework in two ways: using an across-subjects pooled data structure and using a multilevel structure. Models were compared based on the variance explained (R²) and leave-one-out cross-validation information criterion (LOOIC). Multilevel models, which incorporate higher-level commonalities into individual relationships, demonstrated a substantially better fit (R²: 0.97-0.98) and better predictive accuracy compared to generalised pooled-data models (R²: 0.89-0.93). The multilevel 2-parameter exponential regression emerged as the best representation of data in terms of model fit, predictive accuracy and model simplicity. The relationship between load and repetitions performed to failure follows an individually expressed exponential trend in the pin press exercise. To accurately predict the load that is associated with a certain repetition maximum, the relationship should therefore be modelled on a subject-specific level.