Theorem:
The relative frequencies of ISO year types are as follows:
52-week ISO year: 82.25%
53-week ISO year: 17.75%
Proof1 (Victor Engel):
One complete cycle of 400 years as defined by the Gregorian calendar is
20871 weeks (this applies to the ISO calendar as well, right?). This exceeds
400 years of 52 weeks each by 71 weeks, so the percentage of 53-week years
is 71/400.
Proof2 (Simon Cassidy):
Gregorian calendar repeats weekdays in an exact 400-year cycle.
ISO week-year is dependent on Gregorian calendar.
Thus for every 400-year (20871 week) interval there must always be
n 52-week ISO years and
m 53-week ISO years where
1) n + m = 400 and
2) n*52 + m*53 = 20871 or 52*(n + m) + m = 20871
thus 52*400 + m = 20871
thus m = 71 which is exactly 17.75% of 400
and n = 329 which is exactly 82.25% of 400