Motor-evoked potentials (MEPs) are among the few directly observable responses to external brain stimulation and serve a variety of applications, often in the form of input-output (IO) curves. Previous statistical models with two variability sources inherently consider the small MEPs at the low-side plateau as part of the neural recruitment properties. However, recent studies demonstrated that small MEP responses under resting conditions are contaminated and over-shadowed by background noise of mostly technical quality, e.g., caused by the amplifier, and suggested that the neural recruitment curve should continue below this noise level. This work intends to separate physiological variability from background noise and improve the description of recruitment behaviour. We developed a triple-variability-source model around a logarithmic logistic function without a lower plateau and incorporated an additional source for background noise. Compared to models with two or fewer variability sources, our approach better described IO characteristics, evidenced by lower Bayesian Information Criterion scores across all subjects and pulse shapes. The model independently extracted hidden variability information across the stimulated neural system and isolated it from background noise, which led to an accurate estimation of the IO curve parameters. This new model offers a robust tool to analyse brain stimulation IO curves in clinical and experimental neuroscience and reduces the risk of spurious results from inappropriate statistical methods. The presented model together with the corresponding calibration method provides a more accurate representation of MEP responses and variability sources, advances our understanding of cortical excitability, and may improve the assessment of neuromodulation effects.