To determine a trade-off between the battery energy storage system (BESS) size and corresponding benefits in managing the load of distribution systems under high penetration of electric vehicles (EVs), a marginal capacity value-based sizing approach is proposed in this study. First, the yearly load profiles of EVs are estimated considering different factors, such as EV parameters, driver behavior, day types, and customers at each secondary distribution transformer. Then, a utilization index is proposed to quantify the benefits of increasing the BESS size. To this end, an iterative method is proposed to determine the BESS size with a given utilization target. To expedite the convergence speed, a binary and interpolation search-inspired algorithm is proposed, which can determine the BESS size within a limited number of iterations. The performance of the proposed BESS sizing approach is compared with three other approaches, i.e., optimization-based sizing approach, metaheuristic sizing approach, and enumeration-based sizing approach. The obtained results are tested and validated using the data of a real distribution system. Finally, a sensitivity analysis of different user defined factors such as granularity level in BESS size and utilization target levels is carried out. Simulation results have shown that the proposed method can significantly reduce the BESS size while having minute impact on the peak shaving.