In this work, we explore the possibility of finding a simple mathematical function that describes XPS background intensities as a function of energy and depth of emission. We describe the shape of the global structure of the background in XPS survey spectra for organic overlayer films with thicknesses greater than~10 nm. In this situation, the shape of XPS backgrounds becomes statistical, and the detailed structure of, for example, energy-loss functions and elastic-scattering cross sections can be disregarded. Using Irganox 1010 as a model organic overlayer on silicon dioxide, gold, and silver substrates, a consistent description of the XPS background can be found, and overlayer thicknesses greater than 50 nm can be measured in the case of gold substrates.Furthermore, by using a suitable subset of these spectra, it is possible to separate the influence of overlayer thickness, electron kinetic energy, and intensity on the global shape of the spectrum. We show that it is possible to fully describe the shape of calibrated XPS survey spectra with reasonable accuracy for samples that have organic overlayers using only binding energy and sensitivity factor data. The same functions are shown to provide a reasonable description of the XPS spectra of silicon with an oxide overlayer.