A stochastic model of downward lightning propagation and attachment was developed based on existing models of the propagation of a negative leader as a gas diffusion problem. Attachment was modelled using the rolling sphere concept. The resulting simulation enables Monte Carlo methods of assessing the efficacy of geometric lightning protection schemes. Protection afforded to a 100 m by 50 m building was investigated to elucidate the relative impact of selected protection configuration parameters. The results were found to be insensitive to variations in building height for configurations of less than 30 m. Variation in footprint area found protection for large buildings generally exhibits worse performance relative to smaller structures. This trend was examined in detail for a regular, square arrangement of lightning rods. Variation in building aspect ratio was found to have a pronounced impact on protection performance and is attributed to non-preferential striking to the available geometries. A method for arriving at the expected rate of a given building being stuck is outlined which expects the aforementioned structure to be struck at a rate of about four times per 10 000 years.