Although the Ancient Olympic Games were established during Archaic Greece, it was not until the Hellenistic period, beginning with Ephorus, that the Olympiad was used as a calendar epoch. Converting to the modern BC/AD dating system, the first Olympiad began in the summer of 776 BC and lasted until the summer of 772 BC, when the second Olympiad would begin with the commencement of the next games.
Thus, for N less than 195, Olympiad N started in the year BC and ended four years later. For N greater than or equal to 195, Olympiad N started in AD and ended four years later. By extrapolation, the 1st year of the 700th Olympiad began roughly around 2 August, 2021.
A modern Olympiad refers to a four-year period beginning January 1 of the year the Olympic Summer Games are normally held. Thus, the first modern Olympiad began January 1, 1896, the second January 1, 1900, and so on (the 32nd began January 1, 2020: see the Olympic Charter).
Allowing for the absence of a year zero between the Olympiad of 4 BC and the one of 4 AD – since the Julian calendar goes directly from 1 BC to 1 AD – this means the ancient Olympic cycle is behind the modern Olympic cycle by one year.