Statistical properties are investigated for the stochastic model of eddy hopping, which is a novel cloud microphysical model that accounts for the effect of the supersaturation fluctuation at unresolved scales on the growth of cloud droplets and on spectral broadening. Two versions of the model, the original version by Grabowski and Abade (2017) and the second version by Abade et al. (2018), are considered and validated against the reference data taken from direct numerical simulations and large-eddy simulations (LESs). It is shown that the original version fails to reproduce a proper scaling for a certain range of parameters, resulting in a deviation of the model prediction from the reference data, while the second version successfully reproduces the proper scaling. In addition, a possible simplification of the model is discussed, which reduces the number of model variables while keeping the statistical properties almost unchanged in the typical parameter range for the model implementation in the LES Lagrangian cloud model.