Damage Formula

In *Curse of the Dead Gods*, the calculation used to determine the damage output of each attack uses several factors and values. This **Damage Formula** directly determines the Player's damage output and ties together a large number of game concepts and important mechanics : as such, it is a central part of the game.

However, it is not necessary to know it perfectly to enjoy the game : a few hours of playtime will probably be enough to get a "feel" of how the damage mechanic works. This article is dedicated to discussing the details of the formula and its implications, and probably goes far beyond what most players will ever need to know.

Players who just want the main takeaways can simply consider the following points :

* You can (and should) stack as many damage bonuses as possible. The higher the numbers, the better. Just make sure that, if you have contextual bonuses, you actually benefit from them.
* You can greatly increase your damage by dealing Critical Hits and inflicting Weakness. They are very powerful tools.
* Upgrading your Weapon (or buying higher-level Weapons) is a reliable way of increasing your damage. However, don't overdo it : the higher your Weapon's level, the more expensive upgrading is, and it can be less effective than buying a good damage-enhancing Relic.
* Different Attack Moves can have different damage multipliers. You generally can't just "spam" your weapon's most powerful moves, but taking the time to study your moveset cannot hurt.
* Stat Rooms aren't very good at improving your damage. They're still good (for other reasons) but if your only concern is to increase your damage output you'll probably be better off visiting a Relic or Upgrade Room.

## The Damage Formula

The damage calculation formula of *Curse of the Dead Gods* is as follows :

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{\displaystyle Final Damage = Z \times L \times (B+C) \times D \times (E+F)}

 where :

* **Z:** the **base damage** of the Weapon at level 1
* **L:** the **Weapon Level factor** (+20% per level above 1).
* **B:** the **permanent damage increase factor** (produces the yellow number in the Weapon's description sheet ; notably includes the Dexterity bonus)
* **C:** the **contextual damage increase factor** (e.g. additional damage to Fire attacks, "in-the-back" damage bonus affixes...)
* **D:** the **Attack Move factor** (e.g. a charged Sword attack inflicts 200% damage)
* **E:** the **Critical Hit factor**, when applicable (+50% by default, increased by effects increasing Critical Damage)
* **F:** the **Weakened factor** when hitting a Weakened enemy (+50% by default, increased by the effects increasing damage on Weakened enemies)

### Notes

* Aside from Z, all those values are expressed in percentages.

* Stacking effects that increase the same factor are combined additively. For example, using two Very Rare Jaguar Claws Relics (+45% Fire damage each) means your Fire attacks will deal +90% damage. They will both increase C.

* Similarly, multipliers granted by Critical Damage-enhancing Relics or Relics that increase damage dealt to Weakened enemies are added to the default (+50%) damage multipliers granted by Critical Hits and Weakness respectively. For example, using a Very Rare Onyx Shards Relic (+45% Critical damage) means your Critical Hits will deal +95% damage.

* Figuring out if a given modifier falls under B or C can be tricky : the difference between a "true" permanent modifier and a very generous contextual modifier that seems to be active all the time isn't always clear. However, it does not really matter : since B and C are added up, any increase to B will have the same effect than a similar increase to C. See the Analysis below for more detail.

## Analysis

### Main Takeaways

By studying the formula and the game mechanics that are tied to each of its values, it is possible to come up with a number of simple observations regarding its concrete impact on the gameplay and how the Player should build in order to maximize their damage output.

* The type of Weapon used is the formula's most crucial element : it defines your base damage (the Z factor) and moveset (which determines the D factor). However, since each weapon plays differently and comes with its own advantages and drawbacks (range, speed, stamina costs...), players should probably focus on finding a weapon they like and feel at ease with, *and only then* work on optimizing its damage output.
* Besides, while there is a lot of variability in damage output between Attack Moves, it is generally not possible to "spam" the best attacks, as they are often more stamina-intensive and/or locked behind lengthy combos.
* E and F (the Critical Damage and Weakness values) can be *extremely* impactful. The base +50% bonuses granted whenever you deal a Critical Hit or attack a Weak enemy are extremely impressive, and they can be combined. In short : Weaken your enemies and deal Critical Hits as often as you can !
* L (the Weapon Level factor) is decently powerful : getting a 20% damage increase for each level above 1 is nothing to scoff at. However, weapon upgrades can get *really* expensive at higher levels, and there are plenty of Relics that offer higher damage increases for a comparable or lower price. Upgrading is therefore particularly good when your weapon is low-level and wouldn't benefit all that much from damage-enhancing Relics (if it does not deal elemental/status damage nor Critical Hits, for example), but it is not always the best way to spend your resources.
* Stat Rooms aren't very good at increasing your damage output. At best, you'll get 5 Dexterity points, which translate to a 10% increase to B : that's weaker than getting a weapon upgrade or even a half-decent Relic. Of course, Stat Rooms remain valuable as a source of Constitution and Perception points, and some Affixes and weapons benefit more from Stat points which can make them much more attractive in certain cases.

### Damage Formula Dilemmas

As we can see, most decisions relative to increasing one's damage output are relatively trivial. Once you've picked a weapon, you just have to get your hands on the most powerful damage bonuses you can find and spam Critical Hits and Weakness whenever possible. This is obviously complicated by the game's economic layer (you can't always *afford* to buy/upgrade items), but this is beyond the scope of this article.

However, the Player can sometimes find themselves in a situation where they have to choose between two damage modifiers (be they Relics, Affixes, etc) that look equivalent but affect different factors of the Damage Formula. Which one must they pick ? These are very niche situations, and frankly the gains realized by making the optimal choice (if it exists) are usually marginal, but still : it is impossible to answer with certainty to these dilemmas without a deeper understanding of the Formula.

### Additive modifiers are straightforward

Some values used by the Formula are stacked additively with one another : B and C (the "permanent damage increase" and "contextual damage increase" factors) are added together, not multiplied, and so are E and F (the "Critical Hit" and "Weakness" factors). The resulting sums are then multiplied with the remaining factors of the formula.

This notably means that, for the purpose of calculating damage in a given situation, *you don't actually need to distinguish between B and C.* Increasing one by *x* will be strictly equivalent than increasing the other by the same amount, as long as your contextual modifiers (the C factor) apply in this specific situation.

Same thing with E and F, even though it starts getting a bit silly and overly theoretical : if you somehow *always* inflict Weakness to your targets *and* land Critical Hits all the time, then it does not matter whether you increase your Weakness damage (F factor) or your Critical Damage (E factor). You will end up with the same results in either case.

#### Example

Let's say you have to choose between two Main Weapons of the same type : one has a "+30% damage in darkness" affix (which increases the contextual C factor), while the other has a set of two non-contextual affixes (say, "+10% base damage" and "+20% if you have a pistol") that together increase its damage, through the B factor, by 30%. Assuming there are no other damage modifiers at play, these weapons will be strictly equivalent - *as long as you fight in the dark.*

### Increasing the lowest multipliers is better

The multiplicative modifiers (the Z, L and D factors, as well as the results of B+C and E+F) are more interesting and complicate things a bit. That is because, contrary to additive modifiers, increasing one factor of a calculation by an *x* amount won't necessarily give the same result than increasing another multiplier by the same value. Indeed, all else being equal, **increasing the lowest multiplier is always more interesting than increasing an already higher multiplier by the same amount.**

Of course, make sure you can actually use the modifiers in question. There's no point in increasing your Critical Damage potential if your Weapon does not deal Critical Hits.

#### Example

Let's say you want to defeat the first Serpent Champion, Xucat' the Witch, and have a Sacrificial Macana ("deals Critical Hits when only one enemy is nearby") with the "+1% base damage per point of Dexterity" Affix. What's better, getting 5 extra Dexterity points (which translate to a 15% increase to the B factor) or a common Onyx Shards relic ("+15% critical damage", which will increase the E factor) ? Keep in mind that Xucat' will be alone in her room, so thanks to your Macana's ability you'll do critical hits 100% of the time. Assume that no other damage multipliers are active.

It turns out getting the Dexterity points is (marginally) better. A level 1 Sacrificial Macana deals 15 base damage, getting the 5 Dexterity points means it will inflict 15 x 1.15 x 1.5 = 25.875 damage, while it will only inflict 15 x 1 x 1.65 = 24.75 with the Onyx Shards.

*That is because landing a Critical Hit grants a base 50% damage increase**.*** Since increasing the lowest multipliers is better, increasing B (the "basic damage increase factor", which includes Dexterity bonuses) from 0% to 15% has a higher impact than increasing E (the "Critical Hit factor") from 50% to 65%.

### The "Pocket Formula"

As we've seen before, understanding the additive modifiers (B+C and E+F) and their interactions isn't very complicated. The problems start to appear when the Player must decide which multiplicative modifiers should be increased when they are presented with apparently equivalent choices : in that case, one must choose the option that increases the lowest factor of the Formula.

It is possible to clean up the Formula a bit to "abstract away" the additive modifiers and produce a formula that is uniquely composed of multipliers. The resulting "pocket formula" is less detailed but makes it easier to compare at a glance the level of the different factors, and thus focus on what *actually* matters to one's build instead of getting lost in meaningless questions such as "are Poison damage increases contextual or permanent ?".

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{\displaystyle Final Damage = Z \times L \times D \times G \times H}

 where :

* **Z:** the base damage of the weapon at level 1
* **L:** the Level factor (20% per level above 1)
* **D:** the attack move factor
* **G:** the Critical Damage and Weakness factors (it is the result of E+F)
* **H:** any remaining damage increases, that is, any permanent or contextual damage increases unrelated to L, D or G (it is the result of B+C)

Of course, this formula somewhat obscures contextual bonuses and Weakness/Critical Damage mechanics, but the point of this tool is to arrive at a rough estimation of the relative level of each factor. The Player should use their common sense and estimate whether the contextual bonuses they carry (or consider getting) are going to apply in future fights, whether they actually use Weakness and Critical Hits, etc, then make their building decisions based on these estimations.

## The "Developers' Formula"

The developers described the formula in the November 25, 2020 dev diary, but with slight differences compared to the version described above. While their formula is correct and perfectly usable, it is less detailed : it uses the base damage of the weapon (the white number in its description sheet), called A, even though this number is itself the product of the base weapon's damage at level 1 (the Z factor) and the "Level factor" (the L factor).

The only difference between the two formulas is that the above formula breaks down A and replaces it with

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{\displaystyle Z \times L}

. They otherwise use the same values. For reference, the "Developers' Formula" is reproduced below, with the definitions given by the developers themselves :

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{\displaystyle Final Damage = A \times (B+C) \times D \times (E+F)}

where :

* **A:** The basic power of the weapon (white number in its description sheet)
* **B:** The basic damage increase factor (final result in yellow numbers in its description sheet, including the dexterity bonus)
* **C:** The contextual additional bonus damage factor (e.g. additional damage to fire attacks, in the back damage bonus affixes)
* **D:** The movement factor (e.g. a charged sword attack inflicts 200% damage)
* **E:** The critical hit factor (+50% by default, increased by effects increasing critical hit damage)
* **F:** The weakened factor when hitting a weakened enemy (+50% by default, increased by the effects increasing the damage on weakened enemies)

1. ↑ https://store.steampowered.com/news/app/1123770/view/2914355022546817524?l=english