Bayesian predictive power, the expectation of the power function with respect to an assumed distribution on the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the distribution on the true underlying effect. The density of power values induced by a given prior is derived analytically and its shape characterized as a function of the input parameters. We find that the shape of this density might have a u-shape for a typical clinical trial scenario. The implication of this shape on a portfolio of trials is discussed. Finally, alternative priors are proposed and practical recommendations to assess the sensitivity of Bayesian predictive power are provided.