There are three layers of skin, the Epidermis, Dermis, and Hypodermis. The needles penetrate the dermis, which is fairly permanent. Since the epidermis is constantly replenishing itself with new skin cells, they have to go deeper.
At most 1/16". They are trying to implant the ink in the dermis, so the stroke needs to be long enough to penetrate the epidermis. But at the same time, they don't want to go through the dermis because that will cause more trauma than necessary.