Dexterity scaling vs GR progression

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!

19 Likes

:rofl::rofl::rofl::rofl:

Now to actually read what you posted and learn something new!

Nice informative post. There are a few DH builds out there that get to switch in items like CoE, made possible only by extreme paragon:

  • N6 Rapid Fire w/ Aughild and CoE
  • LoN RF w/ Cubed CoE
  • S6 Impale w/ Aughild and CoE
  • M6 Cluster Bombs w/ F&R and CoE
  • N6 FoK w/ Shi Mizu
  • UE6 Multishot w/ F&R, Squirts and CoE

Some of these require 3k+ paragon to feel comfy, others still don’t feel quite right at 4k. Most will stick with Elusive ring / Unity until they accrue the paragon.

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).

To my knowledge it was 4% monster life increase per level.
But I may be out of the loop here. And it wouldn’t change the direction.

Edit: meant damage taken with 4%. Remembered 17% and 4%.

It’s 17% per level after GR70. As a reference, T15 to T16 is a 5 GR difference and the monster life for T15 is 6,334,823% normal and T16 is 13,888,770% normal. The ratio is thus 2.192447800 which is only 0.000000003 off from 1.17^5 (this is due to rounding).

As for the monster damage, I was slightly mistaken, I said it was 2.3% but it’s actually closer to 2.337% (it doesn’t appear to be a nice truncated number).

https://us.diablo3.com/en/game/guide/gameplay/game-difficulty

Edit: blah, I’m still not TL3 so I can’t embed links in my posts yet… FFS this is Blizzard’s OWN website.

Edit 2: I just got TL3 overnight so I can link Blizzard posts now lol.

2 Likes

Very good post.
I just want to add that as a consequence with low paragon you usually forced to put paragon points in vita. In this case 1k VIT is better than 7 AS on gloves and even may be better than 6 CHC on a helm.

A very engaging read, thank you!

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Thanks Iria. This is a really illustrative post to explain why certain gearing choices work better at higher paragon levels and why there seems to be a ceiling no matter how skilled one might be.

Now someone just level me to 10k paragon so I can take over the leaderboard… j/k

EDIT: Wow …love replying to necroed threads…

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It’s fine, this was an informative thread which is still relevant and I see when people post to it!

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This thread should be pinned.

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agree 100%

One sticky for DH is not enough.

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Now the question is, how do we go about getting this stickied?

I mean, it took us a month of posting here and on GD to get the one we have.

I mentioned this very thing on stream when PezRadar stopped by. I asked about Class forums getting more popular, informative topics pinned to the top so that they don’t get lost. His response:

I agree with that feedback. Will work on that - I think bandwidth is an issue at the moment. But I’ve got a CM I hired that will be starting soon and another in the pipeline so bandwidth will be less of an issue here soonish.

We may see some improvements in this area in the future :slight_smile:

5 Likes