Weird y scaling issue

Suppose I have an image placed at the center, with a Y scale of 1.6. This ensures that the image is high enough to cover the entire height of a screen with 960 Y resolution.

Now, suppose I want to display the image on a 800 y screen. I divide 800 by 960, I get 0.83. Multiply that by the original scale (1.6), and you end up with a new y scale of 1.33

I put that in my y scaling input box, and change the resolution so it is 800 in height. But guess what, the sprite's size is way too small, compared to what is should be(cover the height of the screen correctly).

I do not care about width at all right now, I just want to know why this simple operation fails?