Binder jet printed components typically have low overall density in the green state and high shrinkage and deformation after heat treatment. It has previously been demonstrated that, by including nanoparticles of the same material in the binder, these properties can be improved as the nanoparticles can fill the interstices and pore throats between the bed particles. The beneficial effects from using these additive binder particles can be improved by maximising the binder particle size, enabling the space within the powder bed to be filled with a higher packing efficiency. The selection of maximum particle size for a binder requires detailed knowledge of the pores and pore throats between the powder bed particles. In this paper, a raindrop model is developed to determine the critical radius at which binder particles can pass between pores and penetrate the bed. The model is validated against helium pycnometry measurements and binder particle drop tests. It is found that the critical radius can be predicted, with acceptable accuracy, using a linear function of the mean and standard deviation of the particle radii. Percolation theory concepts have been employed in order to generalise the results for powder beds that have different mean particle sizes and size distributions. The results of this work can be employed to inform the selection of particle sizes required for binder formulations, to optimise density and reduce shrinkage in printed binder jet components.