We present a statistic evaluation of the azimuth orientations of flat-adsorbed oligopyridine molecules in disordered adlayers on Au(111) and (111) oriented Ag-adlayers on Ru(0001). On both surfaces, we find a strong preference for a set of twelve angles, which belong to one specific, unsymmetrical alignment and its symmetry equivalents. These angles are also those that exclusively occur in more densely packed, ordered structures on the same surfaces. We describe a geometric fitting algorithm, which correctly predicts these angles, and which only requires the substrate lattice and the positions of the nitrogen atoms within the flat-adsorbed molecule as input parameters. Such predictions are particularly valuable to reduce the parameter space in structure simulations [C. Rohr, M. Balbás Gambra, K. Gruber, E. C. Constable, E. Frey, T. Franosch, B. A. Hermann, Nano Lett. 2009, 10, 833].