E - Increases the amount of HP gained when leveling up. P - Slows the arrows down during Crits. From the in-game help guide, we are told what P, E, A, and L do for exploring and combat. While this thread is quite old and the game itself has been ported to other platform, (PC which I recently started playing on), I've been trying to compile a complete and accurate list as to what the stats actually do. (There is speculation that the radiation immunity may not have been intended and could be nerfed in a future patch) For example, having 11 or more Endurance makes the explorer practically immune to radiation. Also note that while dwellers can be trained up to a 10 in each SPECIAL stat, the bonuses from outfits stack and provide benefits beyond a 10. Luck helps them find better loot and more caps.Īs far as which to prioritize, Endurance, Luck, and Perception are most likely to get you better gear and more caps, but eventually having an explorer with straight 10s is good. Agility lowers the damage they take in combat. 
Intelligence makes them run away from combat faster, losing less HP. Charisma makes it more likely they will resolve situations with strangers in a more positive light (gain more XP or caps, lose fewer HP). Endurance and level provide more HP, allowing them to survive longer on the same number of stims.
Perception helps them find opportunities for caps, XP, and loot. It depends on what you want the explorer to do.
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