When should a Midas be purchased?

You're right in this regard, but if you want to be picky, this isn't entirely true either, the instant effect of Midas means that you save the time taken to kill the creep (esp big jungle creeps), which can be used to kill other stuff and hence get more gold. The maths of this are complex as it depends what your damage/AS/skills are that would determine how long you take to kill it, and what other farm is available in the area.

Gold income is based on Gold Earned, Time taken to Earn it, and Time taken to travel to the area to farm it.

The XP thing also comes into the mix - XP is still a game resource, even though it's harder to measure/evaluate than gold. I'd also argue sometimes Hand of Midas has some utility against creep converters like Chen and Enchantress, Helm of the Dominator to a lesser extent. Some minions can also be converted, although not that many are worthwhile.

I like Xyrus's example though - it shows the thinking that should be behind your decisions. Sometimes, Midas is the right answer, sometimes farming items are, sometimes you should be getting items to help teamfight, push, survive, etc.

Hopefully this helps inform the OP - all of these choices are situational, there is no straight right or wrong answer without taking into account all the factors at play.

Midas gives attackspeed which increases farm as well. So if you want to be very accurate you need to take that into account.

dont forget that midas should be mostly about the extra XP. its especially good on heroes that need level 16 and slower farmers.

wraith king, void, invoker, sven are some really good midas heroes.

I feel like a lot of you guys are saying that for the majority of situations Hand of Midas isn't worth it. From my experience, I would tend to agree with this. I feel like if you focus farm, the game won't last long enough for it to matter. Discuss.

If you KNOW the game is gonna go late, and you HAVE enough early game balance, AND you can get it under 6 min only then. Even then its situational.

^ pretty much this

If you find yourself sitting on a ton on gold 6 minutes into the game, you're playing a hero who only truly starts shining in the late game, and you think the game will go late, you can get a midas.

But honestly it's a pretty low impact item in pubs, Midas is an item that only really thrives in long passive games with very few kills/minute, the complete opposite of pubs where there is a lot of snowballing (and sadly, feeding).

^ and this

I'm rolling in cash with midas and still lose, ( good and kind teammates but too many mistakes and too much ganks ).

And also you can see people get 20min+ midas in pub.

Been in too many pub games where 3 of your team mates decide to go Hand of Midas against a strong middle-game team. It's really not pretty and wrecks almost any chance of winning the game.

Midas is probably the most situational item in Dota 2.

Heroes who can use it better than most:
Nature's Prophet
Invoker
Alchemist

They don't call him Nature's Profit for nothing. But it goes beyond just making money for him. It completely removes one of the creeps from a wave and speeds up pushing, plus the attack speed is good on him for felling towers. Invoker needs as many levels as fast as possible, and he can usually get a Midas pretty quick in the mid lane. It's good on a full farm mode Alchemist because it just pairs well with Greevil's Gold. Definitely not core on him, but it works if you can get it quick. With Midas and Maelstrom you can get some ridiculous farm going on.

Situations when I buy it:
I random a carry in a pub and have a good start with that extra gold.
I somehow get a kill or two in lane before I've even had a chance to get boots.
I know that I'm going to get absolute free farm until I'm ready to fight.

Other than that I don't really touch it. The only non-carry heroes I get it on are listed up there, and most carries already have a better farming mechanism so it isn't needed.

I usually buy it when I play a slow-farming carry and things go smoothly with me getting free-farm. I also get it on some supports who need levels. But my favourite hero to get it is on Puck when the game is even or when I'm leading. He doesn't really need any major item after Blink Dagger, but can really benefit from extra levels and it also speeds up my item progression beyond that as I really don't farm that much after my blink as I'm trying to create space for the carry.