Just to be clear here, distance doesn't affect brightness; velocity does.

Unless I am mistaken, they both do. There are multiple kinds of red shift.

> "Redshifts are attributable to the Doppler effect, familiar in the changes in the apparent pitches of sirens and frequency of the sound waves emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer. Cosmological redshift is seen due to the expansion of the universe, and sufficiently distant light sources (generally more than a few million light years away) show redshift corresponding to the rate of increase of their distance from Earth. Finally, gravitational redshifts are a relativistic effect observed in electromagnetic radiation moving out of gravitational fields. Conversely, a decrease in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field."

The increasing distance between stars due to expansion is not velocity as we traditionally think of it. Things that far away get red-shifted because at distances that large expansion becomes a factor, not because of how they are otherwise moving about. It's basically the general idea behind Hubble's Law.

With Doppler, in space, its the relative changes in position that create the effect, unless I am mistaken. Velocity needs a vector, in other words.

Cosmological redshift isn't Doppler -- the mechanism is different. For cosmological redshift, light's wavelength changes because the space through which the light is moving is expanding, which stretches the waves. Doppler is often brought up in this context, but it has no role to play.

Thanks for the comment. This clarifies the issue.