This paper introduces a new analytical framework for class identification by applying a mixed method involving simple mathematical modeling and Bayesian statistical modeling. This framework explains the middle concentration tendency of class identification in which the majority of people regard themselves as middle, assuming that the succession of the same Bernoulli m-trials with success probability p determines oneʼs subjective class identification. The modelʼs parameters were estimated from SSM survey data by applying a Bayesian statistical model. The distribution of latent success probability p and number of trials m was estimated by the Markov Chain Monte Carlo method. Differences in distributions of p and m among age cohorts and educational levels were analyzed by hierarchical models. The analysis revealed: (1) assuming approximately five trials of fifty-fifty games with 0.5 success probability describes well the observed class identification distribution in 2015 data; (2) the Japanese postwar period can be divided in two based on peopleʼs subjective evaluations—the period of expanding opportunity (1955 to 1975) and the period of high and constant success probability, but less chance of trials (from 1985); and (3) the different games model on educational levels is always better in terms of goodness of fit to the observed data evaluated by Bayes factors than the common game model in each survey period.