If the program is a composed from trivial data conversion steps that are implementable using standard transforms (C++:s stl algorithms, ML:s folds, etc) then it is very likely that it works when it compiles. If there are various branches in the logic and I can encode those branches using types as invariants then that eliminates a particular category of bugs altogether which reduces logical errors. If I use immutable variables it helps even more. I'd say the 'compiles and works' means that if one can leverage existing operations on containers and use types as helpfull invariants then those two stylistic choices reduce the possible number of bugs in various categories.

I would not claim all errors are removed... e.g. numeric code that depends on the precision of arithmetic on floating points is as error prone with or without static types.