By my math, a d4 goes from 2.5 average to 3.15, a d6 to 4.47, a d8 becomes 5.81...

If I were more awake, or if I'd done any simple math in the past few years, I'd be able to do this, but really the question is:

How good is rolling twice and taking the higher? Mathematically.

EDIT: Wow, the math is much simpler than I gave it credit for. To two sig figs:

d4 = 0.63

d6 = 0.97

d8 = 1.31

d10 = 1.65

d12 = 1.99

That is the increase on each die. I think. Not huge, then, but not terrible, either.

The d20, for funsies, is an average increase of 3.325. Yay Avenger.