The morphological analysis of paradigms (morpheme tables) generally proposes a distinction between accidental homophony (to and two represent different concepts, but sound the same) and systematic homophony (you (vs German singular du and plural ihr ) corresponds to the concept `2nd Person'). No specific assumptions are usually made about the distribution of accidental homophony, though. Therefore current assumptions cannot proof satisfactorily what should be regarded as systematic in morphology. We propose that accidental homophony should be assumed to be a random event in the statistical sense with a constant probability across languages and across paradigms. This approach allows us to assign a likelihood to any actual typological distribution of syncretism given a morphological analysis. And by computing such likelihoods for a range of analyses, we can then apply maximum likelihood analysis to determine the best analyses. Hence, the statistical foundation allow us to empirically test morphological analyses that include accidental syncretism. In this paper, we primarily introduce the conceptual and mathematical foundations of a statistical modeling technique, Syncretism Distribution Modeling, and show how it overcomes the problem of accidental homophony. In addition, we apply the technique to show that person paradigms must involve both accidental homophony and systematic syncretism.