Seeing as damage reduction got quite a nice buff this patch, I figured it might be worth doing the math and looking at the numbers.
EDIT: Updating this to correct my mathematical mistakes!
As always, TL;DR at the bottom!
First off, just how much extra damage does the 8.4% let you absorb?
8.4%, simple as that?
Actually no! You do get a slightly stronger boost from it.
To properly calculate the extra effective health you gain, the math is as following:
1 / (1- TotalDamageReduction).
For 8.4% (or 0.084), this gives 1/0.916 = ~1.092. So it is actually more than a 9% increase in effective health!
But how does it work if we have several sources of Damage Reduction?
Damage reduction stacks multiplicative
This simply means that every effect of damage reduction takes place one after the other, rather than mashing all of them together to one big value.
Here is an example:
Assume we have two Boldurs. One with 10% damage reduction gear and one without.
Both have 2000 health, all this just to make the math easier.
If the 0% Boldur gets hit with 100 damage, he loses 100 health, very simple. He has 2000 effective health.
If the 10% Boldur gets hit for 100 damage, he only loses 90 health.
This gives him an effective health of 2000/0.9 = 2222 (or approximately 11% more)
Now, let us assume Boldur is in rage and has the level 5 mutation. If I recall correctly this is exactly +40% Damage Reduction.
So, now that 40% gets modified with the numbers above, like this.
The 0% Boldur has only 40% damage reduction, this means he takes 60% damage.
His effective health is 2000/0.6 = 3333.
The 10% Boldur has both one modifier for 40% and one for 10%.
This means the Boldur will take 0.9*0.6 times total damage. (Since it is multiplicative, you can put them in any order, it does not matter.)
This means he takes 54% damage, giving him 2000/0.54 = 3704 effective health.
If the Boldur gets another gear that gives him an additional 4% damage reduction, the total becomes 0.90.960.6 = 0.5184, which makes it a total of 3858 effective health.
Damage Reduction indirectly improves healing and health regen
Yes, it does!
Since you take less damage, every point of health you regain is tougher to take down.
A simple example, you have 50% damage reduction.
If you get healed 200, it would take 400 damage to get your health back to the same as it was before, since you only took half of it.
If you regain 20 health per second (not hard with Boldur), it would now take 40 damage per second just to prevent your health from rising.
This of course also applies to shield regen and life steal.
And knowing this is teaching you when to use Damage Reduction.
If you have health regen, shield regen, life steal or get healed a lot it, damage reduction will add up over time to help those stats become stronger.
It also helps against burst, but not as well as Max Health gear.
But a basic number to remember is that you need 3054 health before a max health gear is less effective than damage reduction, assuming two primary gear stats.
The way to calculate this is (BonusHealth/DamageReduction) - BonusHealth.
For example, +280 and -8.4% gives (280/0.084) - 280 -> 3333.33 - 280 = 3053.33
You can test that by comparing 3053+280 (= 3333) to 3053/0.916 = 3332.97, rounded up to 3333.
As for Damage Reduction versus Healing Received, it is quite harder to count on, especially since you can never tell for sure when you have a support and how much they will heal you.
Basically, you need to figure out when the extra health gained is equal to the amount of damage reduced.
The simple formula is (HealingHealingReceived) vs (DamageTakenDamageReduction).
The one that is higher is more effective.
Here is a small example:
Assume you get healed for +50 per second, and you are taking 100 Damage per second.
You have either a +14% healing received or -8.4% damage taken, which helps you more?
Without any gear, you will drop by 50 health per second.
Healing Received will improve that to 57, making you lose 43 health per second.
Damage Reduction will reduce damage taken to 91.6, meaning you lose 41.6 health per second.
In this case, Damage Reduction was slightly more effective.
However, we can also figure out how much healing versus damage you need for either stat to be better or worse than the other.
Your total damage reduction divided by your total bonus to healing received gives you a decimal. That number is how much percentage of damage taken you need to have as healing for them to be exactly equal. Higher than that and healing received is better. Lower than that and damage reduction is better.
Example:
8.4% damage reduction vs 14% healing received.
8.4/14 = 0.6. This means we need to heal for 60% damage taken for them to be equally effective.
How about a test?
60 healing per second, 100 damage taken. Default loss is 40 per second.
With healing received we heal 68.4 per second, 100 damage taken. We lose 31.6 health per second.
With damage reduction, we heal 60 per second and take 91.6 damage. We lose 31.6 health per second.
In our previous example, damage reduction was a bit ahead, because we only healed 50% of damage taken.
Alright, enough math! Tell me when to use damage reduction already!
Well, generally speaking I would say Damage Reduction is stuck in between sustain (life-steal, shield regen, health regen…) and anti-burst (Max Health, Max Shield).
It compliments all of those stats pretty well, but it is not stronger than any of them by itself.
If your character in some way gets a lot of sustain, it might be worth looking into.
Tanks are therefore naturally a nice option, but it also gets a bit iffy with math to when it is just better to have healing received.
Stacking damage reduction is still valid. It might seem like diminishing returns (in a sense it both is and is not). Since it is multiplicative, the added damage reduction will always reduce damage by the correct percentage of the damage you would have taken. But since it is already reduced, it feels like less compared to if you would start at 0%. I know this sounds very iffy, so feel free to ask if you would like an explanation.
A good thing to note is that Damage Reduction is the only gear stat you can have that improves your overshield.
I have not tested if damage reduction affects the shields that Boldur, Galilea and ISIC have. If it does, this is another aspect that only Damage Reduction improves with gear.
Here is a bit of a rundown of the character types:
Supports: Since you have ways to either heal yourself or your shield, Damage Reduction does benefit you. However, you are also prone to pick up heal power, which works against it. Max Health might also be stronger overall if you are afraid of getting burst down.
Life Stealers/Regenerators: AKA sustain. If you are stuck in combat, but constantly gaining health, damage reduction and health regen is the only stat that helps you along during that time.
High health/shield: Like I wrote above, if you have high enough health, damage reduction will outweigh max health gear, but the only one who can probably reach that high without max health gear is probably Kelvin or Attikus.
I would also suggest going for the Rogue shoulders if you plan on using rares. Extra bonus for 10 seconds after using a skill is way better than Eldrid (While health is full, ironically works best if you use a strong shield character), LLC (While shield is full, just utterly useless). UPR has the bonus for 5 seconds after reload, but I think the only character that reloads a lot and is self-sustainable is Whiskey or possibly Ghalt if you picked the bigger shield and want to get some boost out of it. However, on Ghalt, the shield recharge delay might generally be a better pick for him.
The Eldrid one could easily be changed to either “while under 50% health” or “for 3 seconds after taking health damage”. Both of those are more fitting into the entire “Eldrid” Theme of not having shield. I would suggest “while under 50% health” since that is the same as the uncommon effect trigger and the other effect is almost a permanent effect.
The LLC one should be changed to trigger on “For 3 seconds after taking shield damage”, so it would be a slightly weaker version than Shayne’s default, but it fits the LLC theme.
TL;DR So what can we make of this?
Basically, get Damage Reduction for a character that can sustain itself, but you can not rely on constantly having a support. However, it is common for it to clash with other stats in one way or another.
If you can get overshields one way or another damage reduction is the only stat that helps improving it.
Well, that was it for this time. Feel free to point out any inaccuracies or other mistakes.
Would you guys want me to do some math on the recently buffed Health regeneration as well?
