Dry adhesives using surface microstructures inspired by climbing animals have been recognized for their potentially novel capabilities, with relevance to a range of applications including pick-and-place handling. Past work has suggested that performance may be strongly dependent on variability in the critical defect size among fibrillar sub-contacts. However, it has not been directly verified that the resulting adhesive strength distribution is well described by the statistical theory of fracture used. Using in situ contact visualization, we characterize adhesive strength on a fibril-by-fibril basis for a synthetic fibrillar adhesive. Two distinct detachment mechanisms are observed. The fundamental, design-dependent mechanism involves defect propagation from within the contact. The secondary mechanism involves defect propagation from fabrication imperfections at the perimeter. The existence of two defect populations complicates characterization of the statistical properties. This is addressed by using the mean order ranking method to isolate the fundamental mechanism. The statistical properties obtained are subsequently used within a bimodal framework, allowing description of the secondary mechanism. Implications for performance are discussed, including the improvement of strength associated with elimination of fabrication imperfections. This statistical analysis of defect-dependent detachment represents a more complete approach to the characterization of fibrillar adhesives, offering new insight for design and fabrication.