While scaling down resistive random access memory devices can bring many benefits, it also introduces uncertainties during operation. One example is the wide distribution of the resistances in the low‐resistance state (LRS) when the device is connected by a small current compliance () in the microampere range. During the operation under such small , it is believed that the stochastic migration of oxygen vacancies in the oxide layer plays an important role for the variability. To this regard, the model where oxygen vacancies are treated as point defects and the kinetic Monte Carlo method is applied for the stochastic migration of vacancies is extended. The relation between the macroscopic observations in measurements and the microscopic vacancy distribution are discussed. It turns out that three representative configurations are sufficient to describe the vacancy distribution in the LRS. The large spread of the resistance seen in the cycle‐to‐cycle statistics is then due to the change from one of the configuration to the other. The origin for the change between configurations is discussed in terms of the anisotropic zero‐field energy barrier of the diffusion of vacancies.