Through the report feature, at the end of the game.
It hit, you were in its range. Skills don't always appear to hit their mark, Because the animation isn't the same as the actual skill shots width.
I think you are mistaking what a scripter does really. Scripting has nothing to do with the size of the object. There have been more scripters thab usual it seems though.
if the arrow is point blank range its easy to lane long shots like bot to top are harder but even scripts can't predict where you are in fog of war, if you'll keep walking(etc) you just dealt with a good ashe
also as others have mentioned the hit box is bigger than it appears. Its roughly right, but again its a box not an arrow, so a little correction is fine