I am able to get the "Salivate-tion" angel upgrade on the Moon in adventure-capitalist which grants x9 to all profits. Right now I would have to spend half of my angels to get this upgrade (500 quindecillion angels), but whether or not it is worth it seems like it should be true regardless of what the relative percentage of angels would be. Correct? My Bonus Per Angel is 11% so it should only take 81 angels (9/.11) to achieve a x9 upgrade. So isn't it always a waste to buy these instead of letting the angels do their bonus?
Edit: I went ahead and did it! I ended up with a net 4.9x increase after giving up 45% of my active angels.
Best Answer
It's worth it (assuming you keep it running long enough to get your angels back, anyway) because the extra Angels aren't separate multipliers, they are addition to an existing multiplier.
What happens is your profits are:
Doubling your angels will change it to:
Doubling your Angels is effectively doubling your bonus, regardless of how many Angels you had (or have). In your case, you would need another 1000 quindecillion of them just to see x2 profits.
On the other hand, if you trade in half your Angels for an extra x9 modifer, you get the following:
This is a 4.5x rise in your profits. Sacrificing half your Angels cuts your bonus in half; the new total is multiplied by another 9.
There is an enourmous difference between an additive multiplier (going from x20 to x21) and multiplicative multipliers (is that a word?) (going from x20 to x20x2)
Adding more Angels is always additive; everything else is multiplicative.
So once you hit the point where you spend less than 1 - 1/(multiplier) of your Angels, you'll earn. In this case, 1 - 1/9 is about 89%, you'll be fine with spending 50% of them.
Just keep in mind you should not reset until you've earned them back, which might take a while.