In discussing corrections to the Julian calendar, I think it is more understandable if one treats each successive correction in the average year-length explicitly and in the SAME UNITS (e.g. fractions of a day per 365-day year rather than leap days per 4 years, or 100 years, or 400 years, or 4000 years). Further, if one waits until the end to add up all these corrections, then their relative magnitudes, standing side by side, are also clearer.
The true length of a year on Earth is 365.2422 days, or about 365.25 days. We keep our calendar in sync with the seasons by having most years 365 days long but making just under 1/4 of all years 366-day "leap" years. Exercise: Design a reasonable calendar for an imaginary planet. Your calendar will consist of a pattern of 366-day "leap" years and 365-day regular years that approximates your planet's average number of days per year.
