Sirius Black's math mistake?

[Jamie Lipton]

No: HPFGUIDX 37847

Facts:  If Harry was born in July, 1980, then Voldemort was defeated in
October, 1981.  Sirius Black went to Azkaban in November, 1981.  Sirius
escapes in July, 1993, and the scene in the Shrieking Shack takes place in
June, 1994.

This means that Sirius was in Azkaban for 12 years, and he verifies this
himself: "'I've waited twelve years, I'm not going to wait much longer.'"
(PoA, hardcover American, p. 352)

Question:  When Sirius speaks to Peter (p. 370) he says, "Voldemort's been
in hiding for fifteen years, they say he's half dead."  As far as I can
tell, Voldemort can only have been in hiding for twelve to thirteen years,
if the infant Harry defeated him on Halloween, 1981.  It may be just a rough
estimation on Sirius's part, but why would he be so unspecific when he
clearly knows exactly how many years he spent in prison?
That being said, is Sirius just really bad at math?  Or does he know
something that we don't?

- Jamie