Something interesting is the fact about dividing a key, has anyone managed to divide 1 through 15 by different divisor to see the left most characters of resulting scalar? Yeah do that and you will realize the starting hex chars of your result depends on the ending chars of your target.
These are natural behaviors when you're working on a curve over a finite field. You need to study them more (properties of curves over prime fields, pairings, embedding degree, etc) in order to avoid attributing a magical aura to every result that pops out.