I think the offset into the elected (or otherwise) ruler, by name. Confer the inscription atop the Pantheon "M Agrippa L F Cos Tertivm Fecit" where the gist is M Agrippa <whenever L F Cos the third> made (it).

From Wikipedia's page on the Pantheon: "M[arcus] Agrippa L[ucii] f[ilius] co[n]s[ul] tertium fecit," meaning "Marcus Agrippa, son of Lucius, made [this building] when consul for the third time.

> During the Roman Republic [509 BC–27 BC], years were named after the consuls, who were elected annually (see List of Republican Roman Consuls). Thus, the name of the year identified a consular term of office, not a calendar year. For example, 205 BC was "The year of the consulship of Publius Cornelius Scipio Africanus and Publius Licinius Crassus", who took office on 15 March of that year, and their consular year ran until 14 March 204 BC. Lists of consuls were maintained in the fasti.

> In the later Republic, historians and scholars began to count years from the founding of the city of Rome. Different scholars used different dates for this event. The date most widely used today is that calculated by Varro, 753 BC, but other systems varied by up to several decades.

I'd have to assume that one of those systems would apply here.