We study the statistics of the optical spectra of individual ring-shaped molecular aggregates in which the site energies and transfer interactions are perturbed by both weak random disorder and a regular modulation due to a deformation of the ring. Under these conditions, the spectrum is dominated by two lines. We present an analytical expression for the joined probability distribution of the splitting between these lines and their average position. We compare our results to recent experiments performed on the bacterial antenna system LH2. Our analysis indicates the importance of intercomplex disorder.