The present invention is directed to a modular assembly for an arthroplasty in a long bone and methods for achieving an anatomically accurate reconstruction. A modular arthroplasty assembly includes the components of: a convertible offset coupler bounded on a first side by an implant surface adapted to receive an implant component, and bounded on an opposite second side by a bone anchor engagement surface, prosthesis component and a bone anchor configured to be inserted in bone and adapted for engagement with the convertible offset coupler. Together, the components of the system, including the array of selectable engagement orientations of the components, enables adaptation to the existing anatomy of the patient and the ability to most closely achieve the native anatomy of the healthy shoulder joint so as to provide the patient with the most natural use of the joint. The system also provides a solution for reverse arthroplasty and conversion from anatomically correct to reverse that avoids a boney procedure on revision and minimizes humeral distalization.