Archive of the Titans Azerite trait stacking

I've done some research and simulations and now have several different results, so I'm not entirely sure how the stacking of the Azerite trait Archive of the Titans really works and what the benefit is in real numbers.

According to the tooltip it's pretty simple:

• 1 stack of Int/Str/Agi per application, up to 20.
• At lvl 385 it's 14 per stack, so the max is 14*20 = 280 of that stat.
• Enables the passive Reorigination Array within Uldir raid.

The stacking effect only applies to the stat buff. The Array will count only once, regardless of the number of traits having it. But how exactly does that buff stack?

I ran the numbers for my character and one piece of this at lvl 385 is worth about 1000 dps, two pieces are worth 1470 dps and three pieces are worth 1900 dps (with the Array at level 5). That makes me think:

1. 1470 - 1000 = 470 dps are the actual gain for the second piece.
2. If the buff stacks 1:1 the net value of it would be 470 for every item.
3. The Reorigination Array is then worth 530 dps.
4. 3 pieces are worth 1900 dps, resulting in a gain of 430 dps this time.
5. 470 vs 430.. the third piece is worth less than the second one.

But that are just plain numbers based on quick calculations and don't explain how they really stack.

We know that one item grants a stackable buff up to 20 stacks. But how do 2 or 3 pieces stack? Based on the numbers above they don't grant an equal value. Does the stat value increase by 14/28/42 per stack up to a total of 20 based on the number of items or is it different? And how does that explain the different value of the second and third piece?

So, how does the stacking of these actually work?

Solution 1:

Each piece of gear with the Archive of the Titans trait will provide a fixed stat buff per stack. For example, you have a 385 head which will give you +14, and a 385 shoulder which also gives +14. That means the buff will give you +28 per stack, up to a maximum of 20 stacks.

I've run an example on my own character, using 3 pieces of gear that can provide Archive of the Titans. I've set Reorigination Array stacks to 0, so it is not counted at all. I've added a gearset with no Archive traits, and with 1, 2 and 3 traits active.

The results are now:

• The baseline* is 12465 DPS
• One trait active is 12831 DPS (+366, or 2.94%)
• Two traits active is 13207 DPS (+376, or 2.93%)
• Three traits active is 13586 DPS (+379, or 2.87%)

*Baseline meaning three items equipped with NO traits active.

See the report here.

The reason each stack does not provide the exact same increase, is because DPS from stats is not a linear increase in the game mechanics. Different abilities or effects might scale in different ways based on the stat, as well. This is then further affected by how this ability is used in a rotation.

In my original answer I did not go into detail too much on this topic, because it is not related to Archive of the Titans - it's related to base game mechanics. The same question could be posed for equipping item A with 50 STR, and equipping an additional item with 50 STR, and not seeing the exact same DPS increase.

Effectively, this might indeed mean that an additional item is not always worth the same amount. It could also mean that an additional item might push you just beyond a cap or treshold, and be worth even more than the other item!