We report measurements of the attachment rates of water molecules onto massselected cationic pyrene clusters for size from n=4 to 13 pyrene units and for different collision energies. Comparison of the attachment rates with the collision rates measured in collision induced dissociation experiments provides access to the values of the sticking coefficient. The strong dependence of the attachment rates on size and collision energy is rationalized through a model in which we use a Langevin-type collision rate and adjust on experimental data the statistical dissociation rate of the water molecule from the cluster after attachment. This allows us to extrapolate our results to the conditions of isolation and long time scales encountered in astrophysical environments.