Hello, I figured this was a good day to write about something math related, so here we go!
As I’m sure many players have noticed, as you get more paragon points (and/or augments) on your items and start stacking that Dexterity, your DH gets stronger!
However, what isn’t as obvious, is that your DH gets stronger in a way that isn’t quite balanced. What I mean by that is your toughness grows faster than your damage when comparing GR levels!
To illustrate this, consider an example of a beefy P2000 or so UE Mulitshot DH with the following relevant stats:
Paragon 2000 DH
- 4,000,000 DPS (sheet damage)
- 500,000,000 Toughness (sheet toughness)
- 20,000 Dexterity (total from all sources)
- 4,000 Armor (only from equipment)
With +25% armor from paragon, this beefy DH will have 30,000 total armor (1.25 x 24000 = 30000). This corresponds to a toughness multiplier from armor = 1 + 30000/3500 = 9.571. As an aside, on the character details tab, this armor multiplier would be shown as a damage reduction of 1 - 1/9.571 = 89.55%.
So far so good?
Now, let’s assume the DH grinds to 3000 paragon and is unlucky along the way (no new upgrades or augments). This same DH with P3000 will have the following stats now:
Paragon 3000 DH
- 4,995,025 DPS (sheet damage)
- 593,283,582 Toughness (sheet toughness)
- 25,000 Dexterity (total from all sources)
- 4,000 Armor (only from equipment)
How did I calculate the increase in sheet DPS? Well the Dexterity multiplier for damage is (1 + Dexterity/100), so that 20,000 Dexterity gives 201x damage multiplier and 25,000 Dexterity gives a 251x damage multiplier. Thus taking the 4M sheet DPS and multiplying it by 251/201 (1.2488) gives the new DPS.
Next, how was the new toughness calculated? This one is slightly more complicated but not too difficult if using toughness multipliers. The old toughness multiplier was (1 + 24000 x 1.25/3500) = 9.571, and thus the new toughness multiplier is (1 + 29000 x 1.25/3500) = 11.357. The ratio of these multipliers (1.1866) leads to the relative increase in toughness.
So far so good?
If you’re lost, just look at the damage and toughness numbers in the bulleted lists above for the paragon 2000 and 3000 DH examples and trust me on the numbers!
Now looking at those those two sets of numbers, we see that 2000->3000 paragon gave a damage increase of 24.88% and a toughness increase of 18.66%. So it seems that Dexterity increases damage more than toughness!
However, note that GRs do NOT scale monster damage and health at the same rate! After GR70, monster life increases at 17% per GR level (multiplicatively) and 2.3% per GR level (multiplicatively). For example, in a GR100, monsters do about 1.255x damage and have 4.807x as much life as compared to a GR90!
Now returning to the paragon 2000->3000 example, by how many GRs did the DH improve? To answer this, we use our algebra friend the logarithm!
Damage_GRs = log(1.2488) / log(1.17) = 1.415
Toughness_GRs = log(1.1866) / log(1.023) = 7.524
What this means is the paragon 3000 DH can kill monsters in 1-2 GRs higher than the paragon 2000 DH at the same speed. However, the paragon 3000 DH can take hits from monsters 7-8 GRs higher than the paragon 2000 DH with the same damage taken!
Since monster kill speed is often the limiting factor in GR clearing, by increasing the paragon from 2000->3000, the example DH can clear content 1-2 GRs higher but will be more tanky. Of course, in real progression, the player will often change to gear and skills with more damage to offset this imbalance but the example illustrates the point that paragon scales player toughness considerably faster than damage when considering GRs.
This concept is the reason why some builds are only played with very high paragon, since very high toughness is needed to be able to utilize them properly (e.g. some Rapid Fire builds)!
If you made it this far by reading the whole post, congratulations! You made it through one of my math posts in one piece!
