The math behind ESO has changed many times, and likely will change many more times. You’ll hear theory crafters talking about additive or multiplicative sets, buffs, debuffs, champion points, and skills. Here’s what that means with some math examples:
For the purpose of this example, the attacker is going to hit the defender with a skill. The base damage of the skill is 10,000 damage. If both parties are not using any gear, have no champion points, no buffs, zero armour and zero magic resist, then the defender will take the full 10,000 damage.
Consider the attacker then adds some champion points that adjust their damage output by 25%. That’s great, as their attack will now do (10,000 * 1.25 = 12,500) damage. In that first calculation, it doesn’t matter if we multiply the base damage by 1.25, or if we take 25% of that damage and add it to the total. With only one calculation (there’s NEVER only one calculation) the result is the same. Here are the two possible equations:
- Multiplicative: 10,000 * 1.25 = 12,500
- Additive: 10,000 + (10,000 * 0.25) = 12,500
Next, consider what happens if the attacker uses a buff that increases their damage output by 25% more. There are a few ways that this can play out depending on if the math is additive or multiplicative:
- Multiplicative: 10,000 * 1.25 * 1.25 = 15,625
- Additive: 10,000 + (10,000 * 0.25) + (10,000 * 0.25) = 15,000
In this case, there’s only a difference of 625 damage, but consider that there may be 10+ different parts of the equation in normal fighting, and different sets, buffs, debuffs, champion points, and skills may each be treated differently (multiplicative or additive) in the equations. This is rendered even more challenging as the ZOS team may change how a particular item is treated in each patch, so a theory crafter will need to test and keep track of numbers / math for every set, buff, debuff, champion point, etc. every patch!
With ten instances of a 25% increase in damage (remember that this isn’t possible, it’s just being used to demonstrate how the math works):
- Multiplicative: 10,000 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 * 1.25 = 93,132
- Additive: 10,000 + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25) + (10,000 * 0.25)= 35,000
The difference in this case is enormous!
One more example to put this into perspective is damage mitigation. For this example, we’re going to consider an AoE damage skill hitting someone with the following mitigation. Note that the likelihood of this actually happening is low, but it makes for a good example to understand.
- Major Protection (30% Mitigation)
- Minor Protection (8% Mitigation)
- Heartland 4-Set Bonus (5% Mitigation)
- Heartland 5-set Bonus (20% Mitigation)
- Major Evasion (25% Mitigation)
- Minor Evasion (10% Mitigation)
- Swift Set (10% Mitigation)
- Elemental Defender CP (15% Mitigation)
- Thick Skinned CP (25% Mitigation)
If we add up all that mitigation together: 30+8+5+20+25+10+10+15+25 = 148.
148% mitigation doesn’t make sense, and would reduce any AoE from players down to zero damage.
If all mitigation is multiplicative (it’s not like that, but for this example we’re pretending that it is), it will make more sense. Note that 20% mitigation means I will multiply the damage by 0.80. The calculation for how to turn a percentage into a multiplier is: (damage * (1 – 0.mitigation%))
With all nine sources of mitigation multiplicative, 0.70 * 0.92 * 0.95 * 0.80 * 0.75 * 0.90 * 0.90 * 0.85 * 0.75 = 0.19
In this case, the defender will have 81% mitigation and take 19% damage. From our original example of 10,000 damage (before buffs, CP, and sets that increase damage, the defender would take 1,895 damage. Note again that this is NOT a comprehensive example and does not include armour, magic resist, and other multipliers. It’s just an example to help you understand the math.
Note that per the notes for patch 5.1.5 (August 12, 2019):
- Sources of Stamina, Health, and Magicka cost reduction that are obtained from passives, abilities, or item sets are now all multiplicative, rather than being a mixture of additive and multiplicative.
- Block mitigation now has a cap of 90%. This was done to prevent situations where you could reach 100% damage mitigation.
In Conclusion: Not everything is multiplicative, so it’s up to you to figure out which sources of damage and mitigation work out best for your build and/or group composition, and ensure that you have (at least) those available if you’re going to min/max.