LOL, No one has figured out the math yet. I'll revise a post made on the MYM forumns by AKI (http://www.mymym.com/en/item/1496.html).

I believe this is the answer:

PART 1: The Basics

(For the first three sections, we will ignore magic damage).

H = health

A = armor

EH = effective health points

Dr = damage reduction

To clarify EH, it’s a normalized measurement of how much physical abuse you can sustain, which makes it a function of health and armor. Low health and high armor can give the same EH as high health and low armor (ignoring magic damage).

Part 1: Understanding Armor Damage Reduction.

DR = A/(100+A)

If you have 100 armor, then,

100/(100+100) = 50% damage reduction

To figure out your effective hit points:

EH = H / (1 - DR)

If you have 50 armor and 1000 life, then you 2000 effective hit points

2000 = 1000/ (1-.5)

//It is important to understand that armor does not have diminishing returns; as you gain more H, you should be investing more into armor! If you have 100 armor, you have 2X as many EH and 50% reduction, if you have 200 armor you have 3X as many EH and 66% reduction, if you have 300 armor you have 4X as many EH and 75% Damage reduction. What is important is that although the percentage of reduction increases as a deacreasing rate, the advantage gained from armor is an increasing linear function.

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PART 2: Cost of Armor and Gold

The only way to compare armor to health is by normalizing them to in-game. The problem is that the amount of armor you receive per gold is not constant in game, lets make a few rough estimates:

Cost of Armor:

Cloth Armor = 20a/300g = 2a/30g = 14a/210g

Leather Armor = 50a/700g = 5a/70g = 15a/210g

The cost of the amount of armor per 1 gold in basic items is .642857a/1g.

Cost of Gold:

Ruby Crystal = 475h/1150g

Giant's Belt = 200h/475g

The average cost of health per one gold point is basic items is 417048h/1g.

So one gold equals either .42 health or .064 armor. This is only a generalization from basic items.

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PART 3: Finding the equations for if it is better to invest one gold point into armor or hitpoints

Now we need to combing the equations from above. Remember that:

EH = H / (1 - DR) and A/(100+A),

Hence,

EH = (H)/(1-(A/(100+A)))

EH = H(100 + A)/100

EH = AH/100 + H

If you spend that 1 gold on health (.42), your EH goes to:

EH = AH/100 + H

EH = A(H+.42)/100 + (H + .42)

If you spend that 1 gold on armor(.064), your EHP goes to:

EH = AH/100 + H

EH = (A+.064) H/100 + H

Setting them equal to each other,

EH = A(H+.42)/100 + (H + .42) = (A+.064) H/100 + H

AH+.A42 + 100H + 42 = AH+.064H + 100H

.42A + 42 =.064H

H = 6.5625a + 656.25

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- THIS IS THE KEY EQUATION: H = 6.5625a + 656.25 -

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If you plug in how much health you have, it tells you how much armor would be most effecient. Notice that that armor is not worth it until you have 657 life.

1000 52.38095238

1500 128.5714286

2000 204.7619048

2500 280.952381

3000 357.1428571

3500 433.3333333

4000 509.5238095

//again this ignores magic damage

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PART 4: Factoring In Magic:

So far we have ignored magical damage, but at this point adding in magic damage is easy. Simply, how much magic damage to you expect to absorb in a typical battle? Whatever that is, add it to the health above (basically assume you instantly lose X amount of health prior to absorbing physical attack damage). Essentially the equations changes from:

H = 6.5625a + 657

to,

H = 6.5625a + 657 + Expected magic damage.

If you expect to receive 500 health worth of nukes/magic, don’t worry about armor until you rush your health to 500 + 657 = 1157.

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PART 5: Extra Credit:

Easy Question: If you were to expect 750 magic damage, How much armor should have if you have 3500 life.

Hard Question: Null magic Mantle Costs 400 for 25% reduction and Negatron Cloaks costs 740 for 50% resistance. If someone was to expect equal amounts of magic and physical damage, at what point should they start buying armor and magic resistance.

Author's Note:

If you find mistakes please let me know! Additionally, I can make this into a PDF if people would find is useful. Graphs seemed pointless, so I did not include them (sorry for you visual learners!

The important point is that Armor is not that helpful when you have low life and the other team is doing magic damage. However, armor becomes much more effective when you have a lot of life and there is less magical damage. Don't forget that your character also has a natural increase in armor and magic resistance as he or she levels.