Quickness means your character does the animation 50% faster.

Imagine you had an animation that normally has 15 steps, and you complete 1 step in 1 second. Total animation is 15 seconds By doing it 50% faster, you do 1.5 steps in 1 second. So in total it takes you only 10 seconds. That is a 33% reduction of cast time.

To generalize, 1s cast becomes 0.66s cast. For it to be a 0.5s cast it would have to be a +100% speedup.

So if we are generous, you would expect a 33% dps increase from quickness. However, doing skills faster doesnt make them come off cd faster, so the extra time is filled with autoattacks. In the end, this puts the dmg increase somewhere between 20 and 30%.