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How does protection on one set of armor compare to unenchanted armor of a higher rank? Such as leather armor with protection III v. Iron armor. Also how much damage does the protection enchantment protect against? Or how many hearts does it block from damage?

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A full set of Leather Armor gives 7 'armor points', while a full set of Iron Armor gives 15. (Each armor point gives a 4% damage reduction, so Leather Armor reduces all damage by 28% and Iron Armor by 60%).

The Protection enchantments are actually fairly complicated (at least, more complicated than the standard armor formula). Each enchantment has a certain value which the Minecraft Wiki calls the EPF (Enchantment Protection Factor). Whenever you take damage, the EPF of all of your enchantments are added together to a max of 25, which is then multiplied by a random number between 0.5 and 1, and lowered down to 20 if it was above it. The remaining number is then added to your armor points (so, 4% damage reduction per point)

Every enchantment has a different EPF number, which you can find here. Protection III has an EPF of 3.

With a full set of Protection III Leather Armor, you will have a base EPF of 12 (3 EPF x 4 pieces of armor). This means the minimum amount of damage reduction you will get is 52% (28% for the armour, 12 x 0.5 x 4% = 24% for the enchantments). The maximum, though, is 76% (12 x 1 x 4% = 48%). So, on average a full set of Leather Armor with Protection III will give you 64% damage reduction, while a full set of unenchanted Iron Armor will give you 60%.

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    This is not entirely correct. Protection Armor Points are not added to Regular Armor Points, but act as a sort of second layer of armor. Leather Armor will block 28% of the damage, the Protection III Enchantments will collectively block another 24-48% of the remaining 72% damage, which means it will average out at around 49% of overall damage getting through. The full approximate* formula for average damage taken is Damage dealt * (1-totalArmor*0.04) * (1-0.75*totalEPF*0.04). *This formula does not take the EPF caps of 25 and 20 into account.
    – MrLemon
    Commented Jul 17, 2014 at 15:40

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