Indeed, if you just calculate the difference/distance between the opposite side of the paddle and the ball when the collision happens, you get a value that can then be mutated into a velocity. I say mutate it because unless it just happens to be perfect, it won't work right directly. For example, the values you get in the middle will be very small, while the values you get on the edges will be much larger, and I'm understanding you want a smoother scale there.
Another option is to use something I forget the exact name of, where you turn one "scale" into another. For example, the height of your paddle is 50 pixels, and you want values between 10 and -10(to get the velocity on the y axis specifically maybe), you would "convert" from down to -10/10 using a simple division. This is also a form of mutation as I mention above, but it could create a perfectly linear curve, which may or not be what you want.