A major step forward in the statistical analysis of offense specialization was made by Wolfgang et al. through their use of stochastic modeling. However, this paper proposes that the results that were obtained are not as clear as might be hoped because they did not distinguish between offense dynamics that reflected the marginal distributions of the sample as a whole (and thus may be considered random) and dynamics that significantly deviated from this distribution. An analysis of similar longitudinal data for white and nonwhite delinquents shows statistically significant evidence of offense specialization and a random distribution of offenses if no specialization occurs (with one major exception). The implications and problems of the model are discussed.