That depends on the make, model, and year of car. If it is a Ford from 1980 - 1990 then it is most likely a bad earth connection to the body of the car. Other cars have other problems that can also cause this.
A partial earth
Had the same problem. Bought a re-conditioned alternator, turned out it was bad. Usually if battery draining, it's alternator or battery or both.
the battery
Something is on draining your battery overnight. Any light or any relay. It can also be your battery has a dead cell draining it overnight.
Defective alternator, loose alternator drive belt, dead cell in battery, or something is on pulling power from the battery.
did you unhook the battery before replacing the alternator
my battery is still on after changing battery and altnator
many things can do it suck as junk battery, junk alternator , or leaving anything on in the car
You might have a bad battery, a poor connection between the battery and alternator, or a bad ground from the battery.
Something is on draining the battery or it has a dead cell and needs replacing.
Your alternator is shot.
your alternator ain't charging your battery or a bad connection draining the battery