Moving on from the previous charisma topic, (http://www.gamesas.com/topic/1526122-the-ability-to-charisma-everything-is-an-absolute-must/page-5) we have the all important stat: Luck.
You know those comedies where a character is an incompetent moron and somehow everything goes his way? This should be a trait of luck.
Seriously though. For starters you could put missions on the outcome of luck. Murphy's law and it's relatives should all be genuine gameplay mechanics. A simple example would be the following: You're fighting off wave after wave of radscorpions and waiting on a wagon crossing a bridge. at 10 luck the bridge explodes in such a way that the wagon flies forward into the most convenient possition possible and nothing non-scorpion is harmed. at 8 luck the wagon speeds up, taking risks to get there faster, and nothing bad happens. at 5-7 the wagon comes at a normal speed. at 4-3 the wagon breaks down a few times on the way. at 2 the wagon and possibly the bridge break completely and you need to do the rest manualy. At luck 1 something hillariously bad happens, like a giant mutated eagle picks the wagon up and throws it into a distant mountain, or it turns out the wagon wasn't holding what you needed and they're going to need to go back and bring supplies again (leaving you alone with a lot of scorpions) or maybe it turns out that the wagon was just haulling more scorpions.
But this could apply to everything. A company of soldiers could all have easily treated wounds (or miraculous stories as to why the death-rays didn't kill them with high luck) Or they could all die from sickness, wounds that were worse than they thought, random radscorpion attacks that have nothing to do at all with the conflict, or comical 'final destination' style rediculousness.
From things like guessing the password, to fixing a machine by kicking it. from having a raider's gun's jam and explode in his face, to having a fully clad brotherhood of steel paladin fall over in his power armour and struggle to get up like the turtle he is. Even simple stuff like rad x being more common if you're struggling from radiation poison, to finding that all water sources the unlucky player has access to are host to giant irradiated parasites.
Sometimes It could be a little bit of combination. You could use luck and charisma to do that whole 'I talk to your dead relatives' thing on tv (did someone die? Was it a he? She? Yes. They liked oranges? They didn't like oranges? Yes. I'm talking to cathy, I meant katy. yep) or even a science/luck thing (ICE CREAM)
Anyhow, Fallout is notable for it's particular humour (black, black humour) . Quite simply if you play with luck 1 or 10 you deserve some bizarre and wildly different results.