The following scenario caused quite of bit of discussion, disagreement and prompted a ruling during our last session.
Here is the scenario: the party was attacked by a Mage, a Knight and a Noble (this is actually in the Hoard of the Dragon Queen, Chapter 5: On the Road – one of the random encounters when the party is shadowing the Cult of the Dragon in the Caravan north of Baldur’s Gate on the way to Waterdeep)
Several rounds into combat, the parties Thief moved and attacked the Mage (on horseback). Round initiative then passed to the Mage who cast greater invisibility, slid off her horse and tiptoed off, using her full move. (Of course everyone just witnessed her wink out of existence after making some strange hand movements and mutter something indistinguishable.)
At that point it was argued the Thief should have been awarded an opportunity attack with disadvantage since the thief assumed she went invisible and could potentially see her tracks or hear her move.
I Ruled: The fight takes place in a dirt track beaten down by countless wagons that traverse the trade way therefore there were no “footprints/tracks made like being made in sand or snow”. Also the melee took place in the middle of a wagon caravan that was currently on the move, and was now in the process of steering horses and wagons to avoid the skirmish and this being a very noisy situation, there was no chance of hearing footsteps or someone sliding off a horse.
We don’t have too many game stoppage for rules discussions and when we do and there is still some disagreement – these forums I think provide an excellent resource to broaden the discussion to folks who have more experience than we do. So thank you in advance for reading this and any feedback you may provide.
Lazurass
Summary of rules I based the decision on (if I'm missing something please let me know) :
Opportunity Attack (PHB pg 195):
… You can make an opportunity attack when a hostile creature that you can see moves out o f your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. The attack interrupts the provoking creature’s movement, occurring right before the creature leaves your reach…
Greater Invisibility (PHB pg 246)
(Casting Time: 1 action
Range: Touch
Components: V, S
Duration: Concentration, up to 1 minute
You or a creature you touch becomes invisible until the spell ends. Anything the target is wearing or carrying is invisible as long as it is on the target’s person.
Condition: Invisible
An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature’s location can be detected by any noise it makes or any tracks it leaves.
Attack rolls against the creature have disadvantage, and the creature’s attack rolls have advantage.
You can't make opportunity attacks against creatures you cannot see, according to the rules. You can't see an invisible creature, even if you can otherwise target them. Thus, no OAs against an invisible creature. If the mage makes no effort to take a Hide action though (or fails to beat the attacker's Perception), the mage can still be targetted with attacks normally.
This is a ruling I would make. Other DMs may rule differently based on the rules, the particulars of the situation, or other considerations.
Strictly according to the RAW you can't make an OA.
The only time I would allow this to happen is if I wanted to add flavor and the PC didnt something fancy. I would mention that on normal occasions that I would not allow this but on this occasion I will.
What did the players actually bring up in rules?
Or did they just bring up fiction - the foot prints, the fictional sounds?
Then they are forgetting that the buck, in this game, stops with the DM. The DM decides it.
But people in general, when it advantages them, will imagine a churned up road and noisey carts going by and a featureless ground and a silent area.
We like to fight for our own personal gain, but we call ourselves even minded as we do it.
iserith wrote:
Thank you all for the feedback.
Iserith, a player can choose to cast a spell or take a hide action but can still move. So, Frodo puts the ring on and makes the move action. I think the absolute pretense is that if you were using this tactic - you would be immeadialy silent as a mouse. Would not be ringing any cow bells 
Unless the rogue was level 14 with blindsense (allowing him to "see" the invisible mage, there is no AoO on invisibile creature. The rule says it very clearly, yyou can take the attack on a creature you can SEE.
If you want in game explaination, you are in the middle of a fight, if you want to take the time to track by sound and footstep it will cost you an free interaction with environment, which you DO NOT HAVE during an AoO.
Lazurass wrote:
There's really a ton of 'GM, you can do X or you can do Y' options with the stealth mechanics. As GM you could just say the invisible character is hidden just by activating the power and by your judgement of the fictional circumstances (churned mud, noise, etc)
People often read a text and treat their own reading as the only one possible (a reader fallacy). So people read the stealth rules and taking their own reading as the only one possible, think their reading IS the rules. When really if the GM is the backstop for decisions, stealth can be run very different ways at different tables.