Babylonian calendar

The Babylonians were pioneers in observational astronomy. They realized the need for intercalary months (adhika maasa) as far back as 1800 B.C. as indicated by a record of the great Babylonian king and lawgiver Hammurabi. It is said that the thirteenth month was proclaimed by royal order throughout the empire on the advice of the priests. Earlier, the Babylonians used 3 adhika maasas in 8 years.

8 tropical years = 8 x 365.2422 = 2921.938 days
Number of lunar months = 8 x 12 + 3 = 99, which corresponds to 99 x 29.530589 = 2923.528 days.

So the discrepancy is small.