When treatment cannot be manipulated, propensity score analysis provides a useful way to making causal claims under the assumption of no unobserved confounders. However, it is still rarely utilised in leadership and applied psychology research. The purpose of this paper is threefold. First, it explains and discusses the application and key assumptions of the method with a particular focus on propensity score weighting. This approach is readily implementable since a weighted regression is available in most statistical software. Moreover, the approach can offer a “double robust” protection against misspecification of either the propensity score or the outcome model by including confounding variables in both models. A second aim is to discuss how propensity score analysis (and propensity score weighting, specifically) has been conducted in recent management studies and examine future challenges. Finally, we present an advanced application of the approach to illustrate how it can be employed to estimate the causal impact of leadership succession on performance using data from Italian football. The case also exemplifies how to extend the standard single treatment analysis to estimate the separate impact of different managerial characteristic changes between the old and the new manager.