An accurate EMTP model of a HV overhead line under the influence of a direct lightning stroke is used in a novel stochastic approach towards the assessment of the lightning performance of OHLs. This approach combines systematic simulations on our EMTP model with probability distribution functions which were obtained from a statistical analysis of the lightning performance of existing HV transmission networks and from experimental data by other authors. Using this approach we find the probability distributions for the number of flashovers across insulator strings, or fault types, as a result of lightning striking a line. We call these distributions 'stochastic lightning performance characteristics' and use them as a convenient and meaningful measure to describe, and to compare, the lightning performance of overhead lines with different configurations. Practical recommendations based on this approach are made for the lightning performance enhancement of an actual unshielded 110 kV transmission line with wooden supports and non-earthed metal cross-arms.