Olympiad

Every Greek city had a different calendar, often naming the year after a magistrate, making it very difficult to date events in the past. For example, Herodotus was unable to date the events he was describing. When his successor Thucydides had to date the outbreak of the Archidamian War, he used five ways to describe the year and added the season: according to the number of years that had passed since a peace treaty had been concluded, according to the years of the priestess of Hera in Argos, according to a magistrate in Sparta and a magistrate in Athens, according to the number of months since an important battle, and according to the seasons.

For fourteen years the Thirty Years' Peace ... remained unbroken. But in the fifteenth year, when Chrysis the high-priestess of Argos was in the forty-eighth year of her priesthood, Aenesias being ephor at Sparta, and at Athens Pythodorus having two months of his archonship to run, in the sixth month after the engagement at Potidaea and at the beginning of spring.^note[Thucydides, History of the Peloponnesian War 2.1; tr. Benjamin Jowett.]

If this was a solution, it was not a very practical one. (We would call it the spring of 431 BCE.) In the third century BCE, a more practical solution was found: using the list of Olympic victors, which had been made by Hippias the Sophist in the fifth century and was well-known, the historian Timaeus of Tauromenium created a common era for the Greek world. Events could be dated to the first, second, third, or fourth year of an "Olympiad", i.e. the four-year period between two Olympic Games. For example:

This was quite an improvement and it seems that the Alexandrine scientist Eratosthenes of Cyrene expanded it by counting backwards to the ages before the first Olympic Games, offering, for example, a date for the Trojan War (1184/1183 BCE). This practice was widely accepted; in his Preparation to the Gospel, the Christian author Eusebius dates Moses to 808 years before the first Olympiad (i.e., 1584/1583 BCE).^note[Eusebius, Preparation ot the Gospel 10.9.]

Still, it could be quite complex. Writing during the reign of the emperor Augustus, Dionysius of Halicarnassus tried to establish the year in which Rome had been built. He found that earlier scholars had reached different conclusions.

Timaeus … places it at the same time as the founding of Carthage, that is, in the thirty-eighth year before the first Olympiad; Lucius Cincius ... places it about the fourth year of the twelfth Olympiad, and Quintus Fabius [Pictor] in the first year of the eighth Olympiad. Porcius Cato does not give the time according to Greek reckoning, but … places its founding four hundred and thirty-two years after the Trojan war; and this time, being compared with the Chronicles of Eratosthenes, corresponds to the first year of the seventh Olympiad.^note[Dionysius of Halicarnassus, Roman Antiquities 1.74.1-2.]

In other words: 814/813 BCE, 729/728, 748/747, and 752/751 BCE. Later, Varro would expand the chronology of Fabius Pictor by adding four years and place the foundation of Rome in the fourth year of the sixth Olympiad or 753/752 BCE. (This date has become canonical.)

Obviously, the system clearly had its disadvantages and it comes as no surprised that the Seleucid Era, the Varronian Chronology, and the Christian era would become more popular.