Counting the days
Scaliger defined something he called the Julian Period of 7980 years, which was a product of three different dating cycles: The 19-year Meton cycle used in lunar-solar calendars, such as the Jewish one, the 28-year solar cycle, which is the number of years it takes for days of the week to repeat in the Julian calendar and the 15-year indiction cycle used for dating medieval manuscripts. Working backwards 4731 BCE is the last time that all three cycles were in their respective first years. Scaliger chose this date because it preceded his own calculated date for creation, 3949 BCE.
It’s sometimes falsely claimed that Scaliger named his epoch after his father, however this is not true. He stated quite clearly that it is named after the Julian calendar, as his years are Julian years and not Gregorian ones.