We assess the benefits of using statistical techniques to ascertain the shareability of protection channels when computing shared-mesh restored lightpaths in optical mesh networks. These optical networks support wavelength conversion everywhere as a byproduct of the electronic nature of the switching in the optical-electronic-optical optical cross connect used. Current deterministic approaches require a detailed level of information proportional to the number of active lightpaths. Although this is not an issue for good sized networks in the foreseeable future, these approaches are not practicable for distributed route computation involving larger networks. On the other hand, distributed approaches that do not make use of shareability information require a significant amount of additional capacity compared to a centralized approach with access to complete shareability information. With the proposed approach we show that even with less information, independent of the amount of traffic demand, it is possible to predict the shareability of protection channels with remarkable accuracy. In addition, we propose a local distributed channel assignment scheme that is used in conjunction with our distributed route computation proposal to assign shared channels when provisioning the backup path. This channel assignment scheme can also be used to further optimize capacity usage in individual links upon certain events or at regular intervals. Experiments are provided that demonstrate that our approach yields faster computation times with no significant penalty in terms of capacity usage than a centralized approach using complete information.