Harzel
Adventurer
I know that in D&D 5e, a lot of problems can be resolved by simply homebrewing rules based on the DM's rulling. However, i want to know, following the rules set out by the Core Rulebooks, what the full limitations of the mage hand spell can do.
I don't mean to be unkind or snippy, but for this you have very truly come to the wrong game. One of the intentional pieces of 5e design is to value simplicity and straightforwardness rules strongly over covering all possible variations and corner cases, leaving uncovered cases up to the DM. If you want the whole story, you'll have to ask your DM, or, if you are the DM, make it up.
I know that in the PHB, a normal Mage hand spell can summon a Spectral floating hand, that can move within 30 feet of you, can manipulate objects, open an unlocked door or container, stow or retrieve an item, pour contents out of a vial, can carry upto 10lb. in weight, and can not attack or activate spells.
Also in th PHB, an Arcane trickster can on top of all this, use the hand to stow and retreive items from containers and also use theieves tools to open locks or disarm traps.
So the question i want to ask, does the spectral floating mage hand have its own stats, or does it use the stats of the player?
I ask this as an acrance trickster uses there Dexterity (Sleight of Hand) check contested by the creature’s Wisdom (Perception) check, when perform one of the arcane trickster tasks. Would that same logic apply to a normal mage hand?
Would it also apply to making strength checks to throwing objects that are 10lb or less? etc...
Asking these questions here, you will get a variety of (usually) informed opinion that will give you an idea about how the (possibly not very representative of all DMs) population of EnWorld would rule. In a few cases, we may be able to point out some additional features of RAW that you have overlooked, or RAI wisdom that the designers have dispensed. Be careful about RAW or RAI claims though; sometimes folks think their interpretation is the only one possible when it is not. I know this, if for no other reason than I have done it myself, though I try to make sure I retract if someone points out a reasonable alternative.
Anyway, enough metababble. To your questions.
For stats, since the mage hand is not an independent creature, and apparently can act only at the behest of its caster to do physical tasks, I would think that it would be subject at most to DEX and STR checks. For DEX, I would extrapolate from the Arcane Trickster description and use the caster's DEX. However, I would be liberal with situational penalties, even more so (including saying no can do) in cases that would step on the AT's toes.
For STR, someone else proposed a modifier of -4 or -5; I would probably go with -5. For throwing in particular, if the intent is just to throw something away or in a general direction, then STR check with penalties for weight > 1lb and range > 5ft. Max range even for small objects (e.g. ball bearing, coin) is ~30 ft. If you're aiming at something, there will be a DEX check also. It should be pretty hard to throw something with Mage Hand, but not impossible.