We evaluate the effect of mechanical cleavage of graphite on crystallographic orientations, and find that scotch tape exfoliation leads to a wide distribution of flake orientations. STM measurements are compared with statistical surveys of fractures in natural graphite and HOPG samples; in both cases most of the fractures are distributed around the Arm-chair lines. For natural graphite a comparison of fracture statistics before and after exfoliation shows that the cleavage process results in an increase of variance to sigma ~ 5 degrees, and an increase in the Zigzag lines portion. A similar distribution is measured also in exfoliated WSe2, demonstrating that this effect of exfoliation is not material specific. Our results show that fracture statistics of a single crystal are centered at the crystallographic angle and thus can be used as a method for finding the orientation of the original flake. We distinguish between two phenomenological origins of the distribution width - fake facets, and local rotations - and demonstrate the existence of fake facets in AFM measurements. Our results provide bounds on error estimation for identifying orientation by facets, pointing hence at the reason for the technical difficulty of fabricating orientation-sensitive devices.