A new method for the prediction of coordination numbers in random packings of rigid spherical particles is presented, consisting of improvements of basic relationships of percolation theory for the determination of numbers of contacts, percolation thresholds and probability of connection in binary mixtures and their extension to multicomponent and polydisperse mixtures. The proposed model is critically compared with previous percolation theories, showing a satisfactory agreement with experimental data and computer simulations of random packings over a wide range of particle sizes and compositions for both binary and multicomponent/polydisperse mixtures. (C) 2011 Elsevier B.V. All rights reserved.