The polaron describes the interaction of a charged particle with a bosonic field. For a class of polaron-type models with regular particle-field interaction, I present a framework that allows us to compare ground state properties of the polaron to those of an explicitly diagonalizable Hamiltonian. For this, we will compare point processes associated with the two Hamiltonians in the sense of stochastic order. This can be applied in order to derive the strong-coupling asymptotics of the vacuum overlap and the expected boson number of the ground state at total momentum zero, as well as to show linear divergence of the effective mass in the coupling parameter.