A reverse shoulder prosthesis includes a humeral adapter tray (300) configured to sit near a resected surface of a humerus, the humeral adapter tray (300) comprising: a cavity (302); a central bore; and a distal face (304) including a boss (310), the boss (310): (i) configured as an extension of the distal face, (ii) posteriorly offset from the central bore by at least 10 mm, and (iii) configured to engage a humeral stem; and a humeral liner (250) comprising: a distal rim (252) configured to sit within the cavity (302) of the humeral adapter tray (300); and a concave articulating surface configured to mate with a convex articulating surface of a glenosphere. Offsetting the reverse shoulder humeral adapter tray shifts the humerus in the posterior direction so as to result in better deltoid wrapping, more anatomic muscle tensioning, and larger muscle moment arms during both abduction and internal/external rotation.