Short abstract: The same categorical phenomena which are attributed to hard grammatical constraints in some languages continue to show up as statistical preferences in other languages. This is the "stochastic generalization", already observed in syntax by Givon (1979: 26-31), In this talk I will give an overview of recent evidence for the stochastic generalization in syntax and its unifying analysis within the framework of Stochastic Optimality Theory. The example domains include - A. Cross-linguistic variation (passives in English and Lummi) B. Diachronic change (differential object marking in Spanish) C. Style shift (case ellipsis in Japanese and Korean) D. Language internal variation ("'s" and "of" genitives in English)