There is near-unanimous agreement in the ancient sources that the Coroibos Olympics took place in the year corresponding to 776 bce. There is, however, one ancient author who offers a slightly different date. Moreover, some modern scholars have attempted to prove the existence of variant dates for the Coroibos Olympics. Finally, a different system of numbering the Olympiads, which put Olympiad 1 in the year corresponding to 1581/80 bce, was used at least briefly at Olympia. All these facets of Olympiad dating are considered here.

Velleius Paterculus (1.8) places the first Olympiad 823 years before the consulship of Marcus Vinicius, which is typically dated to 30 ce. This gives a date for the first Olympiad of 793. The text has been variously emended so that it agrees with received chronologies. It is also possible that Velleius had some problems synchronizing Greek and Roman systems of time reckoning.

Dimitri Panchenko has recently argued that Hippias dated the first Olympiad to 744/3 and that this was later adjusted to 776/5 by either Timaeus or Eratosthenes. Panchenko's conclusion is based on the assumption that Hippias calculated his date for the first Olympiad using Democritus' statement that he published his Diakosmos 730 years after the Fall of Troy. There is no evidence of any kind for this assumption, and Panchenko is surely wrong when he writes that “there was no obvious reason to relate the list of Olympic victors with that of the Spartan kings.”