Wadsley-Roth phases have emerged as highly promising anode materials for Li-ion batteries and are an important class of phases that can form as part of the oxide scales of refractory multiprinciple element alloys. An algorithmic approach is described to systematically enumerate two classes of Wadsley-Roth crystallographic shear structures. An analysis of algorithmically generated Wadsley-Roth phases reveals that a diverse set of oxide crystal structures belongs to the Wadsley-Roth family of phases. First-principles calculations enable the identification of crystallographic and chemical factors that affect Wadsley-Roth phase stability, pointing in particular to the importance of the number and nature of the edges shared by neighboring metal-oxygen octahedra. A systematic study of Wadsley-Roth phases in the Ti-Nb-O ternary system shows that the cations with the highest oxidation states segregate to octahedral sites that minimize the number of shared edges, while cations with the lowest oxidation state accumulate to edge-sharing octahedra at shear boundaries.