05 February 2018

Guild Wars 2: Damage Increase Part 3: Ascended Gear

We've reached the third step of our adventure through the mathematical comparing of different qualities. This is most likely the most interesting one as the question of how much better the ascended gear is than the exotic gear.

The Plan

So first we'll compare the exotic gear, stats and damage to the ascended stats and damage. Simple so far. Next, we're going to place jewels into the exotic gear and compare it to the ascended gear again. The reason we do this is that you can't place jewels in ascended gear. It is commonly known that the damage increase from exotic with jewels to ascended is 5%. So we'll check this number and bust it if it's not.

How To?

Just like in the first and second post we do the same procedure. To recap it we're calculating the increase by comparing the updated, new or the value after the change with the older, previous or value before the change via division. The result from this is a percentage that tells us the new damage we do. So basically the old damage summed up with the damage increase. If we want the damage increase we have to subtract the old damage. Since this percentage relates to the old damage in a way that the old damage is 100% we just have to subtract this 100%.

For example, if we do 2000 damage and after the change, we do 3000 damage. By how much did it increase? Of course, we can see it's 1000, but what's the percentage?
Calculating 3000 / 2000 = 1.5 or 150%. If we do 2000 multiplied by 1.5 we get our 3000 again.
So if the old damage of 2000 is 100%, the new damage of 3000 is 150% and we get the damage increase by subtracting the old value from the new value (to get the difference or the delta) we get 3000 - 2000 = 1000 which is then 150% - 100% = 50%.

That's a lot of steps so let's shorten it. We calculate 150% minus 100%. The 150% has been calculated by dividing the new value through the old value. So we get (3000 / 2000) - 100%.
That's the formula I use to calculate it.

Exotic Stats Recap

We don't want to jump between both posts so I'm gonna recap the exotic gear data from the last post here.

Our exotic gear with backpack gave us 1139 power, 809 precision, and 809 ferocity. The average weapon damage was 952.5. The formula to calculate the damage we used in the last posts was the following.

avgdmg = weaponStrengthAvg * power * (1 + ((prec / 21 / 100) + 0.05) * ((fero / 15 / 100) + 0.5))
dmg stands for damage; weaponStrengthAvg stands for the average weapon strength; prec stands for precision; fero stands for ferocity;

With all this set up and clarified let's jump into gathering our ascended data.

Ascended Stats

Of course, we'll use a table to simplify the summing of the items for us.

Item Power Precision Ferocity
Zojja's Masque 63 45 45
Zojja's Epaulets 47 34 34
Zojja's Doublet 141 101 101
Zojja's Wristguards 47 34 34
Zojja's Breeches 94 67 67
Zojja's Footwear 47 34 34
Zojja's Reaver 125 90 90
Zojja's Reaver 125 90 90
Fractal Capacitor (Infused) 63 40 40
Althea's Ashes 110 74 74
Magister's Field 110 74 74
Mark of the Tethyos Houses 157 108 108
Attuned Ring of Red Death (Infused) 126 85 85
Attuned Crystalline Band (Infused) 126 85 85
Total 1381 961 961

Great! The last thing is the weapon damage which is between 900 and 1100 for axes. This means our average damage is (1100 - 900) / 2 + 900 = 1000.
So we have everything set up to start our comparison.

The Moment of Truth: Ascended vs Exotic

The moment has come let's get it done. 
Our exotic damage is:

952.5 * 2139 * (1 + ((809 / 21 / 100) + 0.05) * ((809 / 15 / 100) + 0.5)) = 2959029.46

Next our ascended damage is:

1000 * 2381 * (1 + ((961 / 21 / 100) + 0.05) * ((961 / 15 / 100) + 0.5)) = 3759656.45

Calculating the damage increase we get:

(3759656.45 / 2959029.46) - 1 = 0.2706

So there you have it. The last jump from exotic gear to ascended gear is actually 27.06%. But wait! We're not done it. Oh, no, no, no. There's a difference between ascended and exotic rings, accessories, amulets, and backpack we haven't taken into account. Our weapons and armor will most likely have runes and sigils in it. Our ascended trinkets can only be filled with infusions. Our exotic trinkets can be filled with jewels though. Even better there is Berserker jewelry. So what's the damage increase if we have the best of the best?

The best available Berserker jewels are the Exquisite Ruby Jewel which gives us a boost of 25 power, 15 precision, and 15 ferocity. We have six slots that can be equipped with this. So we get 6 * 25 = 125 power, 6 * 15 = 90 precision and 6 * 15 = 90 ferocity. This means our new numbers for exotic gear are 1139 + 125 = 1264 power, 809 + 90 = 899 precision and 809 + 90 = 899 ferocity.

Now our exotic damage changes to this value:

952.5 * 2264 * (1 + ((899 / 21 / 100) + 0.05) * ((899 / 15 / 100) + 0.5)) = 3289865.25

If we recalculate the damage increase we get:

(3759656.45 / 3289865.25) - 1 = 0.1428

Even with the best, we have available, ascended allows us to deal with 14.28% more damage on average.

Conclusion

So where did the 5% come from? What we did here was comparing the gear itself. Unfortunately, the damage increase changes respective to the amount of power you have. If you get buffs or use food or your power changes in any other way the 14.28% may change respectively. The question here is the order in which the damage increase is calculated. Do we expect the person to have the gear on it and then decide to use buff food and buffs and their build? Or do we expect the person to play a certain build in a predetermined raid group and then change their equipment respectively? This plays a huge role. In the case of these blog posts, I expect the person to get the equip and then change their build accordingly. Another reason I like to do it this way is that it makes more sense to me. First I have the stats from me just being level 80, the base stats. Then I equip myself with gear. Next, I'm gonna take a build and then I'm gonna get temporal buffs on me even if they have a 100% guaranteed uptime. Another reason I do it this way is to make it easier to change your build, buffs, foo,d and traits than changing your gear (- at least without full legendary). So what happens here is.. my build, traits, buffs and buff food have now a lower damage increase since I considered my gear prior. This is because of the natural diminishing returns.

Natural Diminishing Returns

So how does natural diminishing returns work? Easy. You start in Guild Wars 2 with 1000 power. If we take all other variables out of the way we can say we deal 1000 damage. If we double our power we deal twice the damage. 2000 power = 2000 damage. Now if we add the same amount of power to us we get 3000 power and 3000 damage. We added the same amount but the damage wasn't doubled. We got only a 50% damage increase. If we repeat the procedure the same amount of power is worth even less damage increase, only 25% now. So what does that mean? If we want to keep on double our damage we also need more power. However games, especially those which don't have a power creep (gear progression for example) only allow a limited amount of power. So doubling our damage gets harder and harder as we reach the maximum available damage. This means our need to double the damage increases and the supply decreases. This phenomenon can be called natural diminishing returns with diminishing returns meaning if you put something in you get less and the natural comes from this being mathematically given

Fun Part: Damage Against Armored Foes

To end this post on a good note though let's check out those damage numbers against foes with 2597 armor.

Our exotic damage was 2959029.46 / 2597 = 1139.41.

 Using the jewelry we get 3289865.25 / 2597 = 1266.79.

 Last but not least our ascended gear allows 3759656.45 / 2597 = 1447.69.

The next part will be on the infusions.
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