We study the return probability for the Anderson model on the random regular graph and give the evidence of the existence of two distinct phases: a fully ergodic and non-ergodic one. In the ergodic phase the return probability decays polynomially with time with oscillations, being the attribute of the Wigner-Dyson-like behavior, while in the non-ergodic phase the decay follows a stretched exponential decay. We give a phenomenological interpretation of the stretched exponential decay in terms of a classical random walker. Furthermore, comparing typical and mean values of the return probability, we show how to differentiate an ergodic phase from a non-ergodic one. We benchmark this method first in two random matrix models, the power-law random banded matrices and the Rosenzweig-Porter matrices, which host both phases. Second, we apply this method to the Anderson model on the random regular graph to give further evidence of the existence of the two phases.