Personally, I'd tend more toward defining distances as in 'jumpable', 'not jumpable', and 'maybe jumpable', and make the die roll only for the 'maybe' category.
Also, I'm not sure how switching from a d20 vs. a stat is more random than a fixed d5 or d3 for total footage that creates much the same situation; "Sorry, you missed that jump by 1 foot".
Thanks for the input.
Yes. I like the "maybe jumpable" and only roll for that.
I think if a character missed a jump over something like a pit but was within arms length 2' for the larger classes and 1' for halflings I would be inclined to give them a Agility test to see if they can grab hold of the edge. Starting at DC10 and then modified for various condition. If there was something to grab onto the DC would be lower. If there was snow and/or ice or broken glass the DC would be higher.
P.S. Maybe thieves would get some kind of bonus for the Agility test to gab onto the edge.