We present a probabilistic approach to quantify the hazard posed by volcanic ballistic projectiles (VBP) and their potential impact on the built environment. A model named Great Balls of Fire (GBF) is introduced to describe ballistic trajectories of VBPs accounting for a variable drag coefficient and topography. It relies on input parameters easily identifiable in the field and is designed to model large numbers of VBPs stochastically. Associated functions come with the GBF code to post-process model outputs into a comprehensive probabilistic hazard assessment for VBP impacts. Outcomes include probability maps to exceed given thresholds of kinetic energies at impact, hazard curves and probabilistic isoenergy maps. Probabilities are calculated either on equally-sized pixels or zones of interest. The approach is calibrated, validated and applied to La Fossa volcano, Vulcano Island (Italy). We constructed a generic eruption scenario based on stratigraphic studies and numerical inversions of the 1888-1890 long-lasting Vulcanian cycle of La Fossa. Results suggest a similar to 10(-2)% probability of occurrence of VBP impacts with kinetic energies <= 10(4) J at the touristic locality of Porto. In parallel, the vulnerability to roof perforation was estimated by combining field observations and published literature, allowing for a first estimate of the potential impact of VBPs during future Vulcanian eruptions. Results indicate a high physical vulnerability to the VBP hazard, and, consequently, half of the building stock having a >= 2.5 x 10(-3)% probability of roof perforation. (C) 2016 Elsevier B.V. All rights reserved.