How is elemental and physical damage reduction/protection calculated?

Question

How is physical and elemental damage reduction calculated? If I equip two items with 10% reduction each, will this give me 20% damage reduction?

Answer 1

Damage reduction is not calculated flat. The damage you receive after reduction is instead a compound ratio of the reduction. E.g. If you take 100 damage without any reduction and you equip one 10% damage reduction item, you will now receive 90% damage. But if you equip two 10% protection items then you will now receive 81 damage instead of 100.
Please keep in mind that physical protection is applied after armor.

The damage you take can be calculated in two ways, the first method gives you the exact reduction (not included rounding from a decimal number to an integer, i.e. you cant take 100.1 damage). The second method is quick and easy to use and remember but is not very exact, in fact the estimate will be worse and worse the more protection you have.

• Method 1: Take (1 - protection ratio), where protection ratio is e.g. 0.1 if you have 10% protection, for all items and take the product of them.
  E.g. you have two 10% protection items, (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
  
  So if you were to receive 100 damage without protection you will now receive 100 * 0.81 = 81 damage.
   
• Method 2: Not very good method. Take 0.99 to the power of the total sum of protection.
  E.g. you have two 10% protection items, 0.99^(10+10) = 0.99⁽²⁰⁾ = 0.8179.
  In reality it is 0.81, which means that it is 1% to high. With a lot of protection this will increase dramatically. In fact it will increase to more than 100% as can be seen below.
  
  E.g. you equip a item which gives you 80% protection (stone skin amulet), this should make you take only 20 damage out of an original 100, but according to this calculation it would be
  (100 * 0.99⁸⁰ = 100 * 0.4475 = 44.75 damage.
  So instead of 20 damage it tells you that you take 44.75 which is almost 125% more than in reality.

I would recommend the first method and please keep in mind that physical protection is applied after armor.

For more information about protection damage and what damage physical protection will reduce you should read tibia-stats articles about shielding and armor.

• resistances
• armor
• shielding

Comments

Great answer! Allow me to add something: if I recall correctly, in game it's actually calculated step by step, and not using Method 1. On every step, the value is rounded. What this means is that for a higher number of equipment, even Method 1 may result in slightly wrong values. Nothing nearly as bad as method 2, but it's something to keep in mind if you ever come across a different theoretical and practical number. I'm afraid I don't know the exact order used by the game, however.