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. This characterization is used to show that summarizing the power value density in one number, the mean, might not fully capture the features of that distribution. Conditions under which this summary statistic is more sensible for a Normal prior are derived. Alternative priors are proposed and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided.