Storage devices play an essential role in increasing the flexibility of microgrids. In addition to improving the security and the resiliency of the microgrids, and in turn facilitating the handling of energy generated from intermittent sources, storage devices also allow microgrids to take tactical decisions to improve their efficiency or to increase their revenues. Demand side management, load following, and switching between an island mode and a grid-connected mode are typical examples of applications that are better enabled by the presence of storage devices. In this context, the objective of this paper is to explore how the size of storage devices affect the efficiency of microgrids, and their ability to gain revenues in a competing market. Results obtained in realistic Monte Carlo simulations on the IEEE 39-bus system are provided and discussed for this purpose.