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The paper argues for, and discusses, the practice of “Strong Empirical Modelling”. This involves a shift in effort from the internals of a model towards how the model relates to observational data. This kind of modelling is contrasted to theory-based modelling which, it is argued, will not be sufficient for making substantive progress understanding social phenomena in a scientific manner, due to the inherent weakness of social theory. However, there are different ways of relating data to modelling, so these are reviewed and criteria for their strength and the difficulties discussed. A sketch of how to define the empirical strength of a model is discussed, and the piece ends with a suggested system of “Modelling Ready Levels” to eliminate confusion about the state of modelling projects.