I have found it useful to send out characters that are not at a high level with a sweet gun and load them up with stimpacks and good armor and allow them to explore until their stimpacks run out, this is particularly useful when you want to lvl and individual quickly and I have found that the cost to revive them ( if you forget to monitor them) is low because they are at a lower level. ago I answered a similar question yesterday on another FO subreddit.

So, assuming you have a maxed out explorer, you don't need endurance or intelligence since those starts are no longer relevant. Overall it is best to have a well rounded special character exploring (as it says in the game) and a higher level character corresponds to more health in general. Higher luck individuals get higher rarity loot. What has been said about endurance, strength, and luck are true in my experience.

I assume that charisma impacts the frequency of encountering non violent scenarios that give you xp ( like when you patch up a run away slaves leg.) Intelligence/perception may also play a role in your ability to defeat harder enemies, like murlocks without taking much damage if any at all. I have a hunch that agility improves your chance of escaping unscathed from a tough battle ( particularly the longer you are out in the wastes).

Fallout shelter luck explore