This study endeavours to introduce a novel model for assessing the agility scope of managers within the banking sector of Iran. The agility scope of branch managers delineates the extent to which agility can be attained within the constraints and authorities inherent to their roles. Specifically, our research centres on devising a comprehensive multi-criteria decision-making (MCDM) framework within a probabilistic and fuzzy environment to effectively gauge managers' agility. To this end, we initially define the boundaries of our investigation by identifying the dimensions of agility. Subsequently, we pinpoint potential areas of change through a combination of established models and expert insights. Experts are tasked with enumerating plausible responses to anticipated environmental shifts. Leveraging the Bayesian best-worst approach (BWM) as an MCDM technique, we rank these criteria, while employing Fuzzy simple additive weighting (FSAW) to prioritize responses. Through this innovative methodology, we delineate the domain of managers' agility. Our findings reveal that managers within the studied bank branches exhibit a 55% level of agility. Moreover, we ascertain that authority levels, utility, and response speed significantly influence managers' agility, with changes in these factors exerting a notable impact. The outcomes of this research offer valuable insights for decision-makers, facilitating the optimization of authority allocations to branch managers and thereby enhancing organizational agility.