Why do we skip leap year every 100 years instead of every 25?

[The_oMeGa]

i know this question has probably been answered long ago, but the solar year is 365.24(22?) days long. every 4 years, we have .96 (and some change) left over, therefore we have leap year. but .96 is not 1.00, so shouldn't we "skip" leap year every 25 years? or perhaps, over 100 years, have leap year every 4 years, 5, 5, 5, 4...

the most accurate pattern would be

one leap day every 4 years; one leap day every 5 years; 5; 5; 4; 5; 5; 5; 4; 5; 5; 5; 4; 5; 5; 5; 4; 5; 5; 5; 5|... 21 days/100 years instead of 25/100yrs.

 

[Janus]

The solar year is 365.2425 days. The modern Gregorian calendar adjusts
By the following Rule:
Every century year (1800, 1900 etc.) that is not divisible by 400 (2000 e.g.) are not leap years. So while 1900, which by the four year rule, would have normally been a leap year, wasn't a leap year, 2000 was, because 2000 is divisible by 400.

The problem with your plan is that the extra .03 day accumlates over 4 years (Every leap year cycle), not one. In a century there are 100/4 = 25 four year cycles.

25* .03 = .75 extra days per century.

If we drop one leap year per century(giving us only 24 leap days/century), that leaves us short .25 days per century. After 4 centuries, we are short one day, so we put back one leap year (Every 4th century has 25 leap days). This gives us the pattern I mentioned above.