The goal of tr ansitioning towar d 100% renewable ener gy sources (RES) poses ser ious challenges to the black star t ser vice in electr ical power systems. In the instance of a blackout, black star t units must restore the power. Conventional black star t sources are often taken out of oper ation to accommodate a larger share of RES and this jeopar dises the resiliency of the gr id. To replace conventional black star t units, offshore wind far ms (OWFs) can become future black star t provider s. However, a black star t unit must meet str ingent technical requirements, and due to the var iable power output of OWFs, it may be challenging to meet these requirements without external suppor t. Therefore, batter y ener gy stor age systems (BESSs) are a promising solution to suppor t OWFs to satisfy black star t requirements.In this paper, a probabilistic method is applied to deter mine the optimal BESS power output to suppor t the OWF dur ing black star t oper ation. The considered black star t technical requirements are taken from the Br itish Tr ansmission System Oper ator (TSO). The wind gener ation behavior is approximated with a Weibull distr ibution, and BESS power output is estimated consider ing a wor st-case scenar io logic. Finally, results are validated with a ser ies of load-flow simulations to ver ify the time ser ies gener ation of an OWF. The analysis conducted shows that the required power output from a BESS is dependent mainly on the size of the OWF and the availability requirement dictated by the TSO.