The statistical patterns of language are systematic linguistic data which must be accounted for in linguistic theory. The phonotactics of  the Arabic verbal roots are presented as a case study. In Arabic, the  acceptability of a verbal root is gradiently dependent on the  similarity of homorganic consonant pairs within the root. We propose  the stochastic constraint model of phonological patterning, in which  the relative frequency of a phonological form provides a measure of its  acceptability. The stochastic constraint model can be parameterized to  account for gradient or categorical constraints. We also propose a novel similarity metric for phonological segments based on the representational framework of structured specification. Structured specification provides a basis for a similarity metric for phonemes  that is sensitive to featural redundancy and contrastiveness. This  metric is superior to previous proposals using underspecification. The  account of Arabic consonant cooccurrence using similarity and the  stochastic constraint provides a more accurate account of the data than the non-quantitative autosegmental account, demonstrating that a quantitative description is necessary to capture the true pattern of  the data.