We have recently developed an extended merger-tree model that efficiently follows hierarchical evolution of galaxy clusters and provides a quantitative description of both their dark matter and gas properties. We employed this diagnostic tool to calculate the thermal Sunyaev–Zel’dovich power spectrum and cluster number counts, accounting explicitly for uncertainties in the relevant statistical and intrinsic cluster properties, such as the halo mass function and the gas equation of state. Results of these calculations are compared with those obtained from a direct analytic treatment and from hydrodynamical simulations. We show that under certain assumptions on the gas mass fraction our results are consistent with the latest South Pole Telescope measurement. Our approach can be particularly useful in predicting cluster number counts and their dependence on cluster and cosmological parameters.