The project management field has the imperative to increase the success probability of projects. Experts have developed several Project Management Maturity (PMM) models to assess project management practices and improve the project outcome. However, the current literature lacks models that allow experts to correlate the measured maturity with the expected probability of success. The present paper develops a general framework and a method to estimate the impact of PMM on project performance. It uses Bayesian networks to formalize project management experts’ knowledge and to extract knowledge from a database of past projects. An industrial case concerning large projects in the oil and gas industry is used to illustrate the application of the method to reduce the risk of project cost (or budget) overruns.