## 03 February 2018

### Guild Wars 2: Damage Increase Part 2: Next Three Tiers

So in yesterday's post, I set up the basis of everything and explained everything thoroughly. Thanks to this we can jump directly into the calculation. Especially since it makes no sense to go through everything again.

### Recap

For us to continue our adventure we need to recap necessary information though. Just like a developer imports any libraries they need. The next step would be to compare the fine equipment with the masterwork quality. To compare these we have to get the stats from the fine gear which were 499 power, 355 precision, and 355 ferocity. The average weapon damage was 726.5. The formula we use is 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;

### Fine vs Masterwork

Going through masterwork items we finally find Berserker accessories, rings, and amulets but no backpack as of yet. So let's add these to our calculation.

 Item Name Power Precision Ferocity Berserker's Prowler Mask 49 35 35 Berserker's Prowler Shoulders 37 26 26 Berserker's Prowler Coat 110 79 79 Berserker's Prowler Gloves 37 26 26 Berserker's Prowler Pants 73 52 52 Berserker's Prowler Boots 37 26 26 Berserker's Mithril Axe 98 70 70 Berserker's Mithril Axe 98 70 70 Berserker's Ring 73 52 52 Berserker's Ring 73 52 52 Berserker's Amulet 98 70 70 Ruby Mithril Earring 61 44 44 Ruby Mithril Earring 61 44 44 Total (Only armor and weapons) 539 384 384 Total (all) 905 646 646

Our weapon damage is 737 to 831. The average is (831 - 737) / 2 + 737 = 784.
Now that we have our data let's place both into the formula and see our results:

Fine damage:
726.5 * 1499 * (1 + ((355 / 21 / 100) + 0.05) * ((355 / 15 / 100) + 0.5)) = 1264753.86

Masterwork damage:
784 * 1539 * (1 + ((384 / 21 / 100) + 0.05) * ((384 / 15 / 100) + 0.5)) = 1418981.64

784 * 1905 * (1 + ((646 / 21 / 100) + 0.05) * ((646 / 15 / 100) + 0.5)) = 1990599.49

So if we just look at the same gear no new items the damage increase is (1418981.64 / 1264753.86) - 1 = 0.1219 or 12.19%.

If we take everything into account though the damage increase is (1990599.49 / 1264753.86) - 1 = 0.5739 or 57.39%. Understandable since we can now wear 5 new Berserker items.

#### Damage vs Armored Enemies

Since it's quite interesting to see how the numbers change when armor is considered to let's calculate this too using a target with 2597 armor.

1264753.86 / 2597 = 487

1418981.64 / 2597 = 546.39

1990599.49 / 2597 = 766.5

### Masterwork vs Rare

The same procedure as before but different stats now.

 Item Name Power Precision Ferocity Berserker's Masquerade Mantle 53 38 38 Berserker's Banded Pauldrons of Infiltration 40 28 28 Berserker's Panded Coat of Grenth 119 85 85 Berserker's Banded Gauntlets of Infiltration 40 28 28 Berserker's Banded Legs of Lyssa 79 57 57 Berserker's Banded Greaves of the Eagle 40 28 28 Berserker's Iron Axe of Accuracy 106 75 75 Berserker's Iron Axe of Accuracy 106 75 75 Berserker's Ring 79 57 57 Berserker's Ring 79 57 57 Berserker's Amulet 106 75 75 Ruby Mithril Earring 66 47 47 Ruby Mithril Earring 66 47 47 Total 979 697 697

The weapon damage is 759 to 928. On average that's (928 - 759) / 2 + 759 = 843.5. Calculating the damage and comparing it we get:

Masterwork:
784 * 1905 * (1 + ((646 / 21 / 100) + 0.05) * ((646 / 15 / 100) + 0.5)) = 1990599.49

Rare:
843.5 * 1979 * (1 + ((697 / 21 / 100) + 0.05) * ((697 / 15 / 100) + 0.5)) = 2284269.66

So the damage has increased by (2284269.66 / 1990599.49) - 1 = 0.1475 or 14.75%.

Damage vs Armored Enemies

Comparing the damage done on armored enemies we get these results:

1990599.49 / 2597 = 766.5

2284269.66 / 2597 = 879.58

### Rare vs Exotic

And for the last time for today the same procedure.

 Item Name Power Precision Ferocity Berserker's Draconic Helm 60 43 43 Berserker's Draconic Pauldrons 45 32 32 Berserker's Draconic Coat 134 96 96 Berserker's Draconic Gauntlets 45 32 32 Berserker's Draconic Legs 90 64 64 Berserker's Draconic Boots 45 32 32 Mystic Battleaxe 120 85 85 Mystic Battleaxe 120 85 85 Berserker's Ring 90 64 64 Berserker's Ring 90 64 64 Berserker's Amulet 120 85 85 Ruby Orichalcum Earring 75 53 53 Ruby Orichalcum Earring 75 53 53 Prototype Fractal Capacitor 30 21 21 Total (without back) 1109 788 788 Total (with back) 1139 809 809

Exotic weapons have a damage range of 857 to 1048 which means their average is at (1048 - 857) / 2 + 857 = 952.5. Calculating the last comparison we get:

Rare:
843.5 * 1979 * (1 + ((697 / 21 / 100) + 0.05) * ((697 / 15 / 100) + 0.5)) = 2284269.66

Exotic:
952.5 * 2109 * (1 + ((788 / 21 / 100) + 0.05) * ((788 / 15 / 100) + 0.5)) = 2884690.79

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

So the damage increase without backpack is (2884690.79 / 2284269.66) - 1 = 0.2629 or 26.29% and with backpack it's (2959029.46 / 2284269.66) - 1 = 0.2954 or 29.54%

#### Damage vs Armored Enemies

And the last time let's check our damage against those pesky enemies that have 2597 armor.

2284269.66 / 2597 = 879.58

2884690.79 / 2597 = 1110.78

2959029.46 / 2597 = 1139.40

### Conclusion

Got through almost all tiers. The last quality missing is ascended but that's another topic. So now we know that the jump from fine to masterwork quality gave us the most damage increase. Of course, since we got access to additional items. If we ignore that fact the biggest jump was from basic to fine. So overall, we see the highest jumps at the lower quality tiers though the jump from rare to exotic is higher than the jumps in the middle. Another thing we notice is that the jumps between qualities are not equal. They also seem random jumping to higher or lower numbers. We could conclude that there's no formula to calculate these values in the background. Another proof for this would be that if you count all your stats and compare the result with the number in the tooltip there's no rounding error. So compared to WildStar these numbers seem to have no floating-point part.

Last but not least let's get the total damage increase. To calculate this we multiply each damage increase with the factor of one.

1.3852 * 1.5739 * 1.1475 * 1.2629 = 3.1594

This means upgrading from basic to exotic you deal a little more than 3 times as much damage. Your damage increased by 315.94% - 100% = 215.94%.

And next week we'll compare the exotic and ascended gear.

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