#### Calculating Damage & Defense 101

Ever wondered about the magic behind the numbers and calculations? How do analysts use existing hero and item statistics to churn out conclusions? This article will cover the basic formulas that govern Vainglory’s damage and defense calculations, as well as some interesting trends. Inspired by BlueBadger’s Complete Guide to Vainglory’s Hidden Stats and Calculations (by an Engineer), this article rephrases and adds on to its content.

**Damage Formulas**

This might seem rather intuitive, but it’s still worth going through. The damage for each basic attacks can be calculated to be as such:

`Base attack damage (raw) = Base WP + Item WP `

**Base WP** is an innate statistic unique to the hero and level, which can be found by looking at the hero stats page in-game.** Item WP **refers to the amount of weapon power that items such as Sorrowblade and Breaking Point provide. For example, an Adagio at Level 1 with a Weapon Blade would have 75 base WP and 15 item WP, meaning he deals 90 raw dmg.

**As for crystal power**, it’s slightly more complicated; while we don’t have base CP on heroes, there is base ability damage, as well as CP ratios.

`Ability Damage (Raw) = Base ability damage + (Item CP x Crystal Ratio) `

The base ability damage and crystal ratio depends on the specific ability, as well as its level. Once again, this can be found by using the hero statistics page in-game. Item CP refers to the amount of crystal power that items such as Shatterglass and Frostburn provide. For example, a Level 1 Heliogenesis from a Celeste with Shatterglass (150 CP) has 100 base dmg and 90% crystal ratio. So a Heliogenesis would deal 100 + 90% x 150 = 235 raw dmg.

The crystal ratio on an ability will determine how much the ability scales with crystal power, and is important when deciding the build. Celeste has high crystal ratios of up to 220% on her abilities, and thus would benefit much more from a crystal build as compared to Lance with crystal ratios of up to 80%.

**Note**: *The formula above ignores the effects of Clockwork and Broken Myth. Clockwork multiplies the Item CP by 130%, while Broken Myth stacks amplify the total ability damage (including the base ability damage).*

**Defense Formulas and Trends**

Damage can be mitigated in two ways:

**Crystal Damage **

^{Actual Crystal Damage (Raw)}⁄_{(1+Shield/100) }

**Weapon Damage **

^{Actual Weapon Damage (Raw)}⁄_{(1+Armor/100) }

There’s no intuitive direct relation between actual damage and defense rating, so let’s take a look at this graph:

Here, we can observe the principle of diminishing returns. It’s a pretty common phenomenon that describes how your results start to plateau the more resources you pump into something. For example, getting from Unranked to Got Swagger on Vainglory might take a week or two, but getting to **L3oN-standard** awesomeness would probably take 10,000 years. The more you allocate resources into something, the worse the output each extra unit of resource gives you. Similarly, having 100 defense from 0 defense reduces the damage by 50%, but adding an extra 100 defense only reduces it by a further 17%.

From here, most people would directly jump to the conclusion that too much gold shouldn’t be invested on defense. **But wait!** There’s more. The best way to measure defense is to calculate how many hits it would take to deal the original amount of raw damage.

From here, we can see that the number of hits actually increases **linearly*** with defense rating. This means that your sustainability is proportional* with your defense rating!

**You get the same amount of tankiness with extra defense item you buy.**

Oh, right. I forgot to mention defense piercing.damn it.

**Here’s the real formula for damage, accounting for defense pierce:**

Damage (Actual) = Damage (Raw) x (Defence pierce + ^{ 1-Defense Pierce}⁄_{1+Defense/100)}

Defense pierce ignores the target’s defense for a percentage of the raw damage. For example, on a hero with 100 defense, a 10% defense pierce would mean the defense reduces damage 90%/2 (unpierced) + 10% (pierced) = 55% instead of 50% with no defense. Once again, the equation here isn’t really that intuitive, so let’s take a look at this graph:

I chose to use 8% pierce as an example, because that’s the amount of pierce in the items Piercing Shard/Spear. Other than the fact that defense pierce increases damage dealt, there’s not much knowledge to be gained from this graph. So let’s look at the next graph:

Here we can see the true power of defense pierce. Instead of having sustainability increasing linearly with defense rating, now we see it starting to plateau as defense increase. **Defense pierce gets more effective as the target builds more defense. **

Conclusion? Piling on defense (shield and armour) is effective only when the enemy doesn’t buy defense pierce. However, a moderate amount of defense is essential to stay alive.

**Effective Health Points**

Having trouble deciding whether to buy health or defense? Here’s where Effective Health Points (EHP) comes into play. EHP is the amount of raw damage your hero can take before dying. For example, a hero that has 1000 health and 0 shield decides to buy some Defense that gives him 100 shield. This 100 shield reduces the amount of crystal damage the hero can take by half, meaning he can take 2000 crystal damage before dying. So his effective health (crystal damage) is 2000. From here we can directly compare Defense and health stats, and conclude that on this hero, an item that provides 100 extra shield is equivalent to one that gives him 1000 extra health.

The formula for calculating EHP is as follows:

`EHP = (Base Health + Item Bonus Health) x (1+Defense/100)`

*Depending on whether the damage source is weapon or crystal, the amount of EHP changes. Thus, EHP can be split into two types: Crystal EHP and Weapon EHP. To see a sample application of EHP, see D&D 101: Carries Can’t Carry Crucible.*

Now that you’ve seen the formulas for calculating damage and defense, feel free to use them as you like, and do some analysis of your own!

**Happy hunting!**