Quantitatively-oriented linguists have made great strides in applying off-the-shelf inferential tools to questions of language change, but less progress has been made in developing mechanistic models of change that start from what we know about individual language users and make quantitative predictions about population-level developments. This talk presents a simple model of the shift from morphological case marking to adpositions, building on Nanosyntax, the Variational Learner, and the Final-over-Final Condition, and shows how the model can be applied to historical corpus data from the history of Balkan Slavic.