Why is a ground-mounted vertical quarter-wave antenna in reasonably open surroundings better for long distance contacts than a half-wave dipole at a quarter wavelength above ground?

Long-distance (DX) communication relies on skywave propagation, which is most effective when the radio wave enters the ionosphere at a very low take-off angle. A ground-mounted vertical quarter-wave antenna naturally concentrates its radiation at a low angle relative to the horizon. Conversely, a horizontal half-wave dipole mounted low (at a quarter wavelength above ground) radiates most of its energy straight up, which is useful for local NVIS communication but poor for DX. While vertical polarization is a characteristic of the vertical antenna, the low vertical radiation angle is specifically what makes it superior for long-distance contacts.