The in-situ ore fragmentation and probability of occurrence of hang-ups at draw points are the most significant factors on the performance of block cave mining. In this study we develop a hybrid methodology to study the uncertainty in the block geometry in the context of blockiness variable and hang-up frequency at a cave mine. This hybrid approach is based on the combination of geostatistical simulation, probabilistic discrete fracture network, geometrical and topological characterization of the fracture networks and supervised Poisson regression models. Our results and hybrid predictive models provide guidance on the systematic characterization of the fractured rock mass at a cave mine for its design, evaluation of production rates, and for risk evaluation purposes. This study can serve as a reference for the rock block geometry analysis in other related fields.