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Yes it delays your core items a bit, but I would say it pays back in 5,5min and becomes a free item after 12,5min. And even though you might sell it, it should take more than 12,5min if you get your avarice blades at around 10 min.
EDIT: I just reacted to posts earlier in this thread saying that it "takes 12,5 min just to break even", which makes avarice blades sound alot worse than it is. I think its a valid strategy where you delay your core items a bit for an income insurance.
When you buy it, you are "out" 150 gold (400g buys 8%, so 50% more than 400 is 600, 150 below the Avarice cost).
It takes 300 seconds to earn 150 gold (5 every 10 means 30 iterations, * 10 for time = 300 seconds), or 5 minutes.
At the 5 minute mark, the item is "worth it's cost". So if you buy it at 20:00 and the game ends at 27:00, the item was negative value for 5 minutes, positive for 2 minutes. Based on this, you have to have an Avarice blade for 10 minutes for it to have a net "even" game value (you've benefitted from extra gold in equal weight to the front-loaded cost).
Finally, the item sells for 375 gold, a loss of 375 gold. Which takes 12.5 minutes to earn, so if you sell it in 12.5 minutes or less, it wasn't worth buying, because you didn't end up with NET gain.
So the super question is:
At what point is that front-loaded cost worth the end benefit?
The facts we have to go on:
Initial cost of 150 gold that you gain no stat points for. Would you spend 150 gold at level 5 if it earned you 300 gold (net gain of 150) when you reached level 18? I doubt it. The tempo hit isn't worth it usually.
So what amount does the item need to earn? I believe a 2:1 ratio *minimum*, or a profit of 450 gold, which means you need to earn 300+375 gold for an avarice blade to be "worth" the tempo hit. Which requires 675 gold or 1350 second (22.5 minutes).
Since you can't buy one until at least the 4 minute mark reasonably (90 seconds creep spawns, 30 seconds for them to reach the mid, 1 gank and a few creep waves before a speed recall)... That means your FIRST avarice isn't worth getting unless you know the game will go to 26.5 minutes. Which is a pretty safe bet.
Most games are over by 40:00, or close to being over. Which means that any Avarice purchased after 16:00 isn't really giving any worthwhile return on it's investment, even if it DOES break even - was it worth the tempo hit?
This is why I don't like the 3x or 4x Avarice (or any gold item) builds. They have far too great of a tempo hit, and are banking on a 50 or 60 minute game (or longer).