*2.5. Acromion Angles*

From these two acromion landmarks, we defined four specific acromion angles (Figure 1): the acromion posterior angle (APA), the acromion tilt angle (ATA), the acromion length angle (ALA), and the acromion axial tilt angle (AXA). The APA is the angle between the inferosuperior axis (Y) and the axis formed by the AA landmark and AI, projected in the plane perpendicular to the medio-lateral axis (i.e., ~"sagittal" plane). The ATA is the angle between the AA-AC segmen<sup>t</sup> and the *x*-axis, in the *xy* plane (i.e., ~"sagittal"). The ALA corresponds to the distance between AA and AC landmarks (in the *xy* —i.e., ~"sagittal"plane), measured as an angle from AI. Finally, the AXA is the angle between the AA–AC segmen<sup>t</sup> and the *x* axis in the *zx* plane (i.e., ~"axial").

#### *2.6. Glenoid Retroversion Angle*

The glenoid retroversion angle (GRA) was measured in 3D from the CT scans using the same software (Amira) and method as above [19]: the angle between the medio-lateral axis (*z*) and the glenoid centerline projected in the axial plane (perpendicular to the inferosuperior axis). The glenoid centerline was defined by the vector joining the center of the glenoid cavity and the center of a sphere fitting the glenoid cavity (Figure 1, right). This method has previously shown good to excellent inter- and intra-observer reliability [19]. For simplicity, we defined here retroversion as positive, and anteversion as negative. The glenoid centerline and all other 3D quantities and computations defined above were performed with Matlab (MathWorks). This script takes as input the three coordinates of all the scapular landmarks and all the points on the surface of the glenoid cavity to provide all reported measurements in the scapular coordinate system, for each case individually.
