We all know about Leap Years. That is when February has an extra day. The Leap Year corrects a slight inaccuracy in the Gregorian Calendar. (There is NO need for the concept of a Leap Year in the Mayan Calendrical System so do not ask if the Mayan Calendar takes into account Leap Years - the question is not valid but YES is pretty close to being right.)
I am going to summarize information from
here to explain how the Mayan Calendar is slightly more accurate than our Gregorian Calendar.
I'll get more specifics on the calculations soon but here is the breakdown:
The accepted definition of a solar tropical year is approximately 365.2422 days.
The Gregorian Calendar year has an average length of approximately 365.2425 days. The Gregorian calculation for a year is ((400 * 365) + 100 - 3 = 146,097) / 400 = 365.2425
The Mayan Calendar year comparison has an average length of approximately 365.2420 days. The Mayan calculation for a solar year is divided by 5,124 year periods which give the calendar the increased accuracy.
The variation for the Gregorian calendar is .0003. The variation for the Mayan Calendar is .0002. Small numbers until you start working with periods of time greater than 100,000 years or so, which is what the Long Count is doing.