Focusing a `background-image` on a Precise Location with Percentages

Let's say you have an element with a background-image, where only part of the image is visible, because the image is bigger than the element itself. The rest is cropped away, outside the element.

Now you want to move that background-image such that you're focusing the center of the element on a specific point in it. You also want to do that with percentage values rather than pixels. We're going to have to get clever.