You all know the two schools of thought on RPG characters.
One says random character generation is more realistic. You never know what you're gonna get--Superman, or Pee Wee Herman. Usually something in between. And those random die rolls can get your creative wheels turning, as you ponder just who such a character is, and why they'd be adventuring.
The other says semi-random (skewed high) or non-random character generation is more realistic. People with mental retardation or cerebral palsy don't get to join the Navy SEALs, so why would any sane group of adventurers take them along? It's unheroic to have low stats because people with low stats wouldn't go dungeon delving where it's near certain death for them.
But what if we turn that thinking around? What if, for whatever reason, Society at Large has rejected these poor slobs, and the ONLY way they've got a chance to be more than just a burden on their families and community is to go seek adventure or death? And the fit, strong, intelligent people know they can easily rise to the top without risking getting turned to stone or dissolved in a pit of green slime, so why would they even consider setting foot into a dungeon?
Probably not what most people would want to play long term, but might make for a fun one-shot. Gamma World is good at producing some random hopeless characters. Go into it with the right attitude (like competing to see who has the most interesting character death, or to see who can actually overcome their limitations and actually thrive), and that could be a real fun game.