This paper describes the absorbance properties of pigments in disordered films. The fluorescence quenching of pigment systems at low concentrations are usually attributed to the presence of so-called statistical pairs. We show that, if line broadening mechanisms are taken into account such as homogeneous and inhomogeneous broadening and statistical distribution of distances between the pigments, the number of potential quenchers decreases dramatically, because all of these effects lead to an increase of the dipole strength of the lowest excitonic state of a dimer. We also show, on the basis of Monte Carlo calculations on assemblies of pigments, that spectral effects beyond a general broadening of the spectrum will not be observed, even for concentrated systems, where a larger number of these statistical pairs may assumed to be present.