We demonstrate a self-contained methodology for predicting conductance histograms of atomic and molecular junctions. Fast classical molecular-dynamics simulations are combined with accurate density functional theory calculations predicting both quantum transport properties and molecular-dynamics force field parameters. The methodology is confronted with experiments on atomic-sized indium nanojunctions. Beside conductance histograms the distribution of individual channel transmission eigenvalues is also determined by fitting the superconducting subgap features in the I-V curves. The remarkable agreement in the evolution of the channel transmissions demonstrates that the simulated ruptures are able to reproduce a realistic statistical ensemble of contact configurations, whereas simulations on selected ideal geometries show strong deviations from the experimental observations.