Interestingly, and most importantly, we find that the num-ber of molecules necessary to saturate the collective effects for linear transmission spectroscopy to be N ∼ 100 or less, irrespective of the disorder type and magnitude.We emphasize that this convergence is only with respect to the linear spectroscopic features and not with respect to any dynamical properties such as the non-radiative relaxation between polaritonic states, which depends on the number of molecules (i.e.. the number of intermediate polariton states) in the system. Therefore, our results should be considered as the first step in understanding collective effects on linear spectroscopy as a whole.