How does armor compare to health? Should I buy Scale Mail (+600 Armor) or should I wait to buy Banded Armor (+400 Health, +5 Health per Second) instead? Faced with these questions, I though to myself, "this is a chance to brush up on my grade 9 algebra!" Huzzah! (... yes, slow work day.)
Starting with my (... flawed?) assumptions:
1) I am assuming that armor works as advertised: namely, it reduces all incoming damage by the stated percentage.
2) To kill a Demigod, you have to deal damage equal to his health, plus additional damage equal to the amount soaked up by his armor.
3) The damage soaked up by armor equals 100*[1 - 2500/(2500 + Armor)] (as posted here)
If all of that is true, then the following formula will tell you the equivalent +Health bonus ('ΔH') for a given +Armor bonus ('ΔA'), depending on your Demigod's current health ('H') and current armor ('A'). If you want to mess around with it yourself, I tried to make it cut-and-pasteable into an Excel spreadsheet cell (but you'll have to plug in the variables yourself):
ΔH = H*(1-100*(1-2500/(2500+A)))/(1-100*(1-2500/(2500+A+ΔA)))-H
Now an example, answering the question above, for a Level 1 Erebus: How effective is Scale Mail (+600 Armor) compared to Banded Armor (+400 Health)?
Answer: After plugging in Erebus' Level 1 Health (H=1650), Armor (A=220) and the Scale Mail bonus (ΔA=600), the formula spits out ΔH = 364. So, all other things being equal, buying Scale Mail at Level 1 will protect you just as much as buying a +364 Health item would. This seems to correspond with what we'd expect, as Banded Armor provides +400 health and some regeneration for around 40% more gold. Should Erebus have 3000 Health and 500 Armor instead, then that bonus rises to an even +600 Health. So Armor has better staying power, improving over time, whereas increases to Health are static.
Of course, this doesn't take into account health regeneration, or potions, or any other subtleties that distinguish health from armor. But I think it's a good starting point, as it lets us compare armor to health directly. That is, as long as my math is right... anyone else care to verify?