This paper addresses the sizing problem of an energy storage system (ESS) while considering statistical tolerance for a two-body wave energy converter (WEC), which is designed to support ocean sensing applications with sustained power for long-term functioning. The power is extracted by assuming ideal power take-off (PTO) based upon historical ocean data record (significant wave height and period of wave swell) from Martha’s Vineyard Coastal Observatory. A gamma distribution is applied to generate the extracted power distribution of each sample in the time-series using Bayesian methodology. The means and standard deviation of the extracted power distributions compose the statistical annual power time-series. Finally, the required capacities for the ESS sizing are estimated and discussed while considering both ground truth values and statistical values.