Hello everyone!
Some of you may be familiar with the video game Path of Exile, but if you're not its an ARPG where math plays a very important role in how strong your character is. Recently they released their patch notes for their new expansion and in those patch notes there are a bunch of buffs and nerfs to certain skills. I'm trying to figure out the best way to mathematically approach the difference in damage of a skill with two different set ups when considering the nerfs and buffs. So let me show you what I'm working with.
The skill ice trap used to have a max damage of 1347 and the added damage effectiveness of 200% (Added damage effectiveness is a multiplier added to any incoming damage from gear, skills, etc, before its added to the base damage).
It now deals 1912 damage and has the added damage effectiveness of 290%.
Also its important to clarify that when a skills damage is reduced by a multiplicative amount its referred to as "less damage" and when its increased by a multiplicative amount its referred to as "more damage".
On a surface level this looks like a buff, but in Path of Exile your skills are supported by something called support gems, which usually alter the way the skill functions with some sort of side effect, or they just outright increase your overall damage. I mention this because in most ice trap builds they utilize a support gem called cluster traps support which allows you to throw two additional traps at once (for a total of 3) but you will deal a percent less damage (typically it nets you more damage because of the added number of traps). They nerfed this support gem in order to compensate for the increase in damage to the skills base and added effectiveness. The original loss of damage from the support gem was 36% or 0.64 less damage. Its now 55% or 0.45 less damage. So lets say you had 100 added damage from gear or whatever, then the original equation pre nerfs and buffs would look like:
(1347+(100*2.0))*0.64 = 990.08 ([base_damage]+([added_damage]*[added_effectiveness]))*[less_damage]
990.08*3 = 2970.24
And the new one:
(1912+(100*2.9))*0.45 = 990.9
990.9*3 = 2972.7
I multiplied the final number by 3 because you're guaranteed to throw 3 additional traps.
So you can see the damage numbers are very similar. Obviously the second one scales better with more added damage, but not by much. My real question however, lies with another support gem. Players noticed these buffs and nerfs and instead decided to use a different support gem that wouldn't reduce the overall damage by a multiplicative amount (0.45) like cluster traps support does. But this support gem has a funny mechanic and I want to figure out if in the end you are actually dealing more damage because of it, and if so, how much more. The skill gem is called swift assembly support and it gives you 3 different percent chances to throw additional traps. You have an 18% chance to throw 1 additional trap, a 12% chance to throw 2 additional traps, and a 6% chance to throw 3 additional traps. Now on their wiki page it says that the skills supported by this gem throw 0.6 additional traps on average. The equation looks like:
(18%+2*12%+3*6%) = 60% or 0.6
So how would I mathematically check to see how much more damage this is within this equation:
(1912+(100*2.9)) = 2202
Would I just multiply the result by the trap average:
2202*(1+0.6) = 3523.2
Any help with this step would be greatly appreciated. If you have any questions or need more clarification please ask and I'll try my best to answer them.
Some of you may be familiar with the video game Path of Exile, but if you're not its an ARPG where math plays a very important role in how strong your character is. Recently they released their patch notes for their new expansion and in those patch notes there are a bunch of buffs and nerfs to certain skills. I'm trying to figure out the best way to mathematically approach the difference in damage of a skill with two different set ups when considering the nerfs and buffs. So let me show you what I'm working with.
The skill ice trap used to have a max damage of 1347 and the added damage effectiveness of 200% (Added damage effectiveness is a multiplier added to any incoming damage from gear, skills, etc, before its added to the base damage).
It now deals 1912 damage and has the added damage effectiveness of 290%.
Also its important to clarify that when a skills damage is reduced by a multiplicative amount its referred to as "less damage" and when its increased by a multiplicative amount its referred to as "more damage".
On a surface level this looks like a buff, but in Path of Exile your skills are supported by something called support gems, which usually alter the way the skill functions with some sort of side effect, or they just outright increase your overall damage. I mention this because in most ice trap builds they utilize a support gem called cluster traps support which allows you to throw two additional traps at once (for a total of 3) but you will deal a percent less damage (typically it nets you more damage because of the added number of traps). They nerfed this support gem in order to compensate for the increase in damage to the skills base and added effectiveness. The original loss of damage from the support gem was 36% or 0.64 less damage. Its now 55% or 0.45 less damage. So lets say you had 100 added damage from gear or whatever, then the original equation pre nerfs and buffs would look like:
(1347+(100*2.0))*0.64 = 990.08 ([base_damage]+([added_damage]*[added_effectiveness]))*[less_damage]
990.08*3 = 2970.24
And the new one:
(1912+(100*2.9))*0.45 = 990.9
990.9*3 = 2972.7
I multiplied the final number by 3 because you're guaranteed to throw 3 additional traps.
So you can see the damage numbers are very similar. Obviously the second one scales better with more added damage, but not by much. My real question however, lies with another support gem. Players noticed these buffs and nerfs and instead decided to use a different support gem that wouldn't reduce the overall damage by a multiplicative amount (0.45) like cluster traps support does. But this support gem has a funny mechanic and I want to figure out if in the end you are actually dealing more damage because of it, and if so, how much more. The skill gem is called swift assembly support and it gives you 3 different percent chances to throw additional traps. You have an 18% chance to throw 1 additional trap, a 12% chance to throw 2 additional traps, and a 6% chance to throw 3 additional traps. Now on their wiki page it says that the skills supported by this gem throw 0.6 additional traps on average. The equation looks like:
(18%+2*12%+3*6%) = 60% or 0.6
So how would I mathematically check to see how much more damage this is within this equation:
(1912+(100*2.9)) = 2202
Would I just multiply the result by the trap average:
2202*(1+0.6) = 3523.2
Any help with this step would be greatly appreciated. If you have any questions or need more clarification please ask and I'll try my best to answer them.
