We can distinguish two general approaches to modeling probabilistic, variable linguistic behavior. The first, which we can call the gradient grammar approach, incorporates gradient, real-valued parameters directly into the grammar as objects whose values must be fitted or learned. In contrast, a second approach, grammar sampling, posits random sampling from a set of parameter values for some categorical grammar, with membership in the set determined by learned categorical restrictions. The primary thrust of this paper is to demonstrate that in a grammar sampling model of the English dative alternation, the categorical facts contain the seed of the variable facts. That is, the grammatical implications of what doesn't vary restrict the set of possible grammars to one that, when sampled from randomly, corresponds closely to the frequency structure of what does vary.