The polyphonic music of William Byrd (c. 1543–1623) poses significant challenges to analysts of early music. The category of ‘imitative’ polyphony, which suggests a mode of analysis that seeks to identify successive identical (or at least, very similar) entries of a clearly-defined subject, is ill-fitting. Byrd’s polyphony is varied and discursive. On occasion, no two entries in his polyphonic passages (or ‘points’) are identical, either rhythmically or melodically. Recent studies of Byrd and continental contemporaries have offered the term fuga to describe this flexible formal procedure. John Milsom has provided a lexicon for the analysis of fuga, which accounts for the variation processes which the fuga subject undergoes. These processes are referred to here as subject deformations. A brief summary of the analytical history of Byrd’s counterpoint in general, and of his consort music is provided. The most useful analytical terminologies and taxonomies are adopted for use in a quantitative model of fuga which tracks the amount subject deformation as it appears in successively deformed entries in Byrd’s points. A simple ‘subject deformation metric’ between pairs of entries is formally defined, and is used to describe both the amount and rate of deformation in Byrd’s points. Some improvements and graphical applications of the metric are described, and three model analyses of three- and four- part instrumental consort music are provided, to demonstrate the application of this new metric in the analysis of the music of Byrd.