As you can see, after 6 minutes, your 100f investment nets a STAGGERING 4.5 food profit (in real terms).
HOWEVER, if you research Selective Breeding for 300 resources, you get that 4.5 food back a WHOLE 54 SECONDS MORE QUICKLY. So after a mere 67 sheep trained, this upgrade pays for itself in no time!
However, let's be real. No one builds the pen to train livestock. The more interesting question is, how many animals do I need to bring back to my base before it's worth making a pen? I'm not sure what the answer is but I have done some maths to help find out!
Here's how 'profitable' a livestock pen will be with varying numbers of animals found:
These numbers take into account the fact that livestock slowly fatten without a pen. (This is another 'opportunity cost')
So if a livestock pen costs 200w (400vs), to break even, you need to find:
But breaking even isn't good enough because this is a 200w investment over approx 6 minutes. The question is then, how much profit makes this worthwhile? 200w could be a trading post which generates aprox 1.2xp/s http://www.rts-sanctuary.com/Age-Of-Empires-3/showtopic=109488. So you can sort of compare it too 432 xp. More if you get stagecoach I suppose. 200w (400vs) + 432 xp. Does that mean you need about ~850f to profit from the livestock? It's hard to know because food & xp aren't all that comparable.
But it does seem like you'd need:
That doesn't sound right though? People have been building pens on fewer animals than that?
I suppose there is also the fact to consider that making a pen is a way to generate a food source in a game where the first player to run out of natural resources usually loses. So perhaps there is some intangible benefit there to consider. Eitherway, I think some more opinions on this would be good.