We can calculate the "average year length" of a Gregorian calendar year. The calendar cycles every 400 years, so this is just the average length of a year over a single cycle.

How many leap years do we get in one cycle? 100, except for 4, except for 1, or 97 leap years. And the length of an ordinary year is 365 days, while a leap year is 366 days. Averaging out, we get

97 * 366  +  (400-97) * 365
---------------------------  =  365.2425
The correct (official; there are several ways of measuring this value, depending exactly what you'd like to get) value for the tropical year is currently around 365.24219, so the calendar is 0.00031 days too fast (each year). In other words, it gains almost a third of a day every 1000 years.

But of course, the value of the tropical year also changes...