This paper describes the absorbance properties of pigments in disordered fi
lms. The fluorescence quenching of pigment systems at low concentrations ar
e usually attributed to the presence of so-called statistical pairs. We sho
w that, if line broadening mechanisms are taken into account such as homoge
neous and inhomogeneous broadening and statistical distribution of distance
s between the pigments, the number of potential quenchers decreases dramati
cally, because all of these effects lead to an increase of the dipole stren
gth 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.