Background and Objective: While there is a reported correlation between shoulder condition and scapular morphology, the precise impact of typical anatomical variables remains a subject of ongoing debate. This study aimed to evaluate this causal association, by emphasizing the importance of scientific modeling before statistical analysis. Methods: We examined the effect of scapular anatomy on shoulder condition, and conditioning on sex, age, height, and weight. We considered the two most common pathologies: primary osteoarthritis (OA) and cuff tear arthropathy (CTA). We combined the other pathologies into a single category (OTH) and included a control category (CTRL) of adult subjects without pathology. We represented acromion and glenoid morphology by acromion angle (AA), acromion posterior angle (APA), acromion tilt angle (ATA), glenoid inclination angle (GIA), and glenoid version angle (GVA). GVA was negative for posterior orientation. These variables were automatically calculated from CT scans of 396 subjects in the 4 shoulder condition groups by a deep learning model. We applied do-calculus to assess the identifiability of the causal associations and used a multinomial logistic regression Bayesian model to estimate them. To isolate the effect of each anatomical variable on each shoulder condition, we increased it from -2 to 2 z-score while constraining all other variables to their average value, and reported the effect on shoulder condition probability as percentage points (pp) for females and males. Results: Increasing AA reduced the probability of OA by 44 pp for females and 17 pp for males while increasing the probability of CTA by 36 pp for females and 33 pp for males. Increasing APA raised the probability of OA by 15 pp for females and 4 pp for males and increased the probability of CTA by 12 pp for females and 4 pp for males. Increasing ATA increased the probability of OA by 15 pp for females but decreased it by 25 pp for males, while also raising the probability of CTA by 11 pp for females and 21 pp for males. Increasing GIA decreased the probability of OA by 55 pp for females and 23 pp for males while increasing the probability of CTA by 45 pp for females and 31 pp for males. GVA (more anterior), decreased the probability of OA by 33 pp for females and 63 pp for males. The effects of APA and ATA were less important compared to the other variables. Overall, morphological effects were more pronounced for females than for males, except for GVA's impact on OA. Conclusions: We developed a Bayesian causal model to answer interventional questions about the scapular anatomy's effect on shoulder condition. Our results, consistent with clinical knowledge, hold promise for aiding in early pathology detection and optimizing surgical planning within clinical settings.