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Dazzle(Shadow Priest) and Razor(Lightning Revenant) ultimate are one of the few skills I knew that can render an enemy heroes' armor into a negative value.

Supposedly a enemy heroes armor is -10 and you have an attack of let say 60. Does that mean that the total damage dealt will be 70 or a negative value is simply just equal to 0 armor?

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The Medallion of Courage item effect can reduce armor too. And, Slark stealing agility can reduce armor as well. –  Luck Dec 29 '12 at 23:00

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Yes, but armor doesn't work the way you think it does.

Armor acts like a damage multiplier, not addition or subtraction.

So a unit with -10 armor actually takes 46.1% more damage!

However, negative armor caps out at -20, which is equivalent to 71% more damage.

You also have to take into account of the type of armor. Remember that heroes have an innate resistance to most types of damage except from other heroes. Also, armor only works against physical damage.

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"Armor acts like a damage multiplier, not addition or subtraction" is actually confusing and contradiction statement. "Armour is damage reducer" would be more clear –  GeoStrike Dec 31 '12 at 10:26
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@GeoStrike I disagree, halving damage or multiplying damage by 0.5 are equivalent, at least to me –  z ' Dec 31 '12 at 21:38
    
Here's a very useful chart that gives the effectiveness of armor reduction against various armor values: i.imgur.com/nZXsG.png ... A good rule of thumb is to try to get your opponents slightly into the negatives for armor. Any more reduction than that is usually overkill. –  Decency Jan 1 '13 at 21:36
    
The 'real' formula for the real damage out put is this: assuming that the armor damage reduction is 71% then the damage reduction should be equals to: real_damage = (1-0.71)*dmg while the if the armor is negative and the damage reduction let's say 71% then the formula:real_damage = (1+0.71)*dmg. –  Ulfric Stormcloak Jul 19 '13 at 9:04

Armour actually reduces intake damage which means, a hero with more armor takes lesser damage, a hero with less armor takes more intake damage (but still lesser than actual damage dealt to him)

Since in dota, armor can go negative (below zero) armor means much painful intake damage. In other words, it amplifies the intake damage.

Zero armor is straight forward, no damage is reduced so exactly same amount of damage is taken.

to give you and idea without going into much math,

Say drow and sniper are in clash

Say sniper has 10 damage and he hits drow 5 times. Now mathematically drow took 10x5 = 50 damage but its not.

Now how much drow takes damage?

It depends on how much drow's armor is

If drow has +10 armor, she takes less than 50 damage (less than 10 damage per hit)

If drow has 0 armor, she takes exactly 50 damage (10 damage per hit)

If drow has -10 armour, she take more than 50 damage, (more than 10 damage per hit)

Check Armor and Damage to know in full details and math

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