As an archer, I can tell you that an arrow that misses its target rarely misses short. For someone as skilled as an arcane archer, you're pretty safe changing "rarely" to "never."
The quickest, easiest way to do this, without losing much realism, is to designate the target's square(s) and one square on either side, and randomize amongst them. Trace a straight line from the archer's square through the center of the chosen square and beyond. The arrow impacts either at the end of the current range increment (when it strikes the ground), or on something solid prior to that. (If it passes through a square occupied by a character, use the original attack roll to see if it hits that character. Otherwise it keeps moving.)
For example, if I'm in a cavern 130 feet across, and I'm at one wall and my opponent, an ogre, is 40 feet from the opposite wall, and I missed with my shortbow shot, I roll 1d4 -- an ogre takes up two squares -- and roll a 4. The shot misses wide to the right of the ogre. The ogre was already one RI away, so the shot will continue to the end of the current RI, which for a shortbow is 120 feet, and then hit the ground. It blows up 30 feet behind the ogre and slightly to the right. The ogre gets missed by the fireball.
If the cavern, on the other hand, were 95 feet across, the arrow would impact just behind the ogre and to the right, at the 60 foot RI, blowin' him up real good. And if the cavern were 115 feet across, the arrow would impact on the cavern wall. (The ogre would be out of fireball AoE.)