Averageifs

The result is right.
the values shall not be the same.

The values would be the same basically only (excep of some other very special cases) if number of each records for each year would be the same.
See this:
if you take
2001 100
2001 100
2001 100
2014 1000
then avg for 2001 is 100 and for 2014 is 1000 avg of this two is 550 while avg for all deta is 325 - right?

of course for data
2001 100
2001 100
2014 1000
2014 1000

anyway you calculate avg - it is always 550


so avg of all data
and
avg of avgs of subsets of different quantities
shall be in almost all cases different