Vainglory’s Math Class

Introduction

As most well know red items (Weapon Power, or WP) increase the damage of your Basic Attacks, and blue items (Crystal Power, or CP) increase the damage of your abilities.
Armor increases your defense against Weapon Power, and Shield increases your defense against Crystal Power.
How much more damage will I do if I buy Sorrowblade? By how much Metal Jacket will reduce the damage taken?
Learn the math behind Vainglory!

Notes:
I will round all decimal numbers. When the game displays damage, it also rounds numbers, however, it does so only to display damage, server-side it will calculate the numbers without rounding (Example, you take 195.6 damage, the game will display 196, but, if your max HP were 200, you would have 4.4 HP left)

A huge thank you to BlueBadger, that years ago discovered the formulas behind Vainglory. You can see his work here:
https://www.vaingloryfire.com/vainglory/guide/complete-guide-to-vainglorys-hidden-stats-and-calculations-by-an-engineer-4311
The pierce formula was wrong though. You’ll find the right one below!

Check out the math channel in our discord server for some examples: https://discord.gg/QJWkqfP

The basics

Basic Attacks

Formula:
Basic Attack/(1+(Target armor/100))
Let’s say you are playing Vox, whose ATK at level 1 is 54, and you buy 2 Weapon Blade (+10 ATK each), then, you attack a level 1 Ringo (Armor: 25) that bought Light Armor (+25 Armor)
74 (Vox ATK+10 for Weapon Blade+10 for second Weapon Blade)/1+(50[25 Ringo Armor+25 Light Armor]/100)
For simplicity, I’ll rewrite the formula without any added explanation:
74/(1+(50/100))=49

Abilities

Abilities formula:
Base Ability Damage + Multiplers/(1 + Target Shield/100)
Let’s do an example:
Krul’s B, Spectral Smite at level 5, at max stacks with 1 Shatterglass, against a target with 75 Shield + 1 Aegis (+45 shield)

Spectral Smite Damage: 360 (+90% CP Ratio)
Damage / Stack: 100 (+30% CP Ratio) x8 (since we said, max stacks, which is 8)=800 (+240% CP Ratio)
Total: 1160

Now, we also bought a shatterglass (+130 Crystal Power):
Damage= 0.9*130=117. So, Shatterglass will add 117 CP damage
Damage / Stack= 0.3*130=39. So Shatterglass will add 39 CP damage per stack, since we have 8 stacks, that’s 312 damage!
Let’s sum all together now:
Damage=360 (base damage)+117 (CP ratio)=477
Damage / Stack= 800 (base damage at 8 stacks)*312 (CP Ratio at 8 stacks)=
1589!
We went from 1160 to 1589 with just 1 Shatterglass thanks to the enormous CP Ratio of Spectral Smite (330% total at max stacks)
However, just like Weapon Power can be reduced with Armor, Crystal Power can be reduced with Shield.
So, initially we said we were going to use Spectral Smite on a target with 75 Shield and 1 Aegis (+45 Shield), in total 120 Shield

1589/(1+(120/100)=1589/(1+1.2)=1589/2.2=722
And that’s the damage you’ll really do to a target with 120 Defense! Defense reduced the damage by more than half uh!

True damage

True damage does exactly as much as it says. 100 true damage, removes exactly 100 HP. True damage can not be reduced by shield nor armor.

Pierce and Shred, the defense counter

As we have seen, Armor and Shield can reduce by quite a lot the amount of damage done.
What can be done to counter high amount of armor and shield?

Pierce

Pierce makes you ignore a portion of the enemy’s defense.
120-45%=120-54=66
So, with 45% pierce we’ll ignore 54 of the enemy’s defense.

Using the previous example, Krul gets a second shatterglass now (so, 260 crystal power), Spectral Smite goes up to 2018 damage. Against a target with 120 defense, this will do only 917 damage.

What if instead of a second shatterglass, we buy broken myth for that 45% damage pierce?
BrokenMyth provides 50 Crystal Power compared to shatterglass 130, will that 45% pierce make up for it? Let’s calculate!
I won’t show the full calculation again as there is no need, Spectral Smite with 1 Shatterglass and 1 Broken Myth (180 Crystal Power) goes up to 1754 (in the same situation declared previously, 8 stacks).

To a target with 120 Shield, this would only result in 797 damage. However, Broken myth also provides shield pierce alongside 50 Crystal Power.
120-45%=120-54=66
Thanks to broken myth, we have to only deal with 66 shield (from 120!)

1754/1.66=1057

We missed out on 70 Crystal Power by replacing Shatterglass with Broken Myth(130-50=70), but in the end we did more damage due to the pierce!

For basic attacks, it works the same way.

Example
We are a level 12 Vox (109) with 2 Sorrowblade (+120 Weapon Power each) against a target with 180 Armor.
What would add more damage, 3 Weapon Blade (+10 Weapon Power each, 30 in total) or a Piercing Spear (+15 Weapon Power, +10% armor pierce)?
Let’s calculate Vox total weapon power with 2 sorrowblade.
109+120+120=349

With 3 weapon blade=379 Weapon Power
379/(1+(180/100))=379/2.8=135

With Piercing Spear=359 Weapon Power and 10% Armor Pierce
Let’s calculate the armor pierce:
180-10%=180-18=162 armor

Now that we know the amount of armor, let’s calculate the damage:
359/2.62=137

The 10% Armor Pierce provided more damage than 15 more Weapon Power.

Shred

Shred reduces the target’s defense.
It’s different from pierce: pierce makes a portion of your damage ignore enemy defense, shred lowers that defense. The difference is that with shred your teammates will also be able to do more damage!

Bonesaw gives 30% Weapon Power, +30% Attack Speed, 20% Armor pierce and:
every basic attack shred the target’s armor for 3s. Max 5 stacks
So, what does that mean?
Let’s say we perform 5 basic attacks in 3 seconds. Now we shred the 50% of the target armor
If the target has 150 armor, his armor will drop to 75. It’s just like, but now you also increased the weapon power damage your teammates will do to your target!

Critical Hit

Critical Hits increase damage by a certain percentage. By default, 50%.
Let’s say you have 150 Weapon Power and buy a Lucky Strike which provides +20% Critical Chance and +5% Critical Damage.
In this case, you have a 20% chance to do a critical hit, which will increase your damage by 55%, or, in other words, from 150 to 232 (150*1.55).
As I said, this will only happen 20% of the times, so, 1 time every 5 attacks on average.
What increases more my damage, an Heavy Steel or a Lucky Strike?
Let’s average this out.
Formula:
(Weapon Power * % Critical Damage*Critical Chance) +
(Weapon Power * (1-Critical Chance))

150*1.55*0.2=46
150*(1-0.2)=150*0.8=120
46+120=166, which is inferior to buy an Heavy Steel (150+45=195).
In the end, Lucky Strike only added 16 damage (166-150=16) on average, while Heavy Steel increases that by 45. A huge difference!

What if we compare 2 Sorrowblade (+120 damage each) and 2 Tyrant’s Monocle (+60 Weapon Power, +35% Critical Chance, +15% Critical Damage)?
Let’s see if something changes

150+120+120=390, that’s what 2x Sorrowblade will do.
Now on the Monocle:

150+60+60=270, with a 70% Critical Chance and 80% Critical Damage.
270*1.8*0.7) = 340
270*0.3=81
Total=421
421>390, on average, 2 Monocle will do more damage than 2 sorrowblade when you already have 150 Weapon Damage.
Monocle will also save you a some gold, since it has lower price! Nice.

Mortal Wound

Mortal Wound reduces the target’s heals by 33%. Heals include: healing (which includes lifesteal), barriers, fortified health.
Let’s say your target heals 500 HP, with mortal wound this would be reduced by 165, so 335. Mortal Wound just negated 165 HP to the enemy!

Think about it as a form of “indirect” damage since you negate a certain amount of healing rather than output bigger numbers with your attacks. Whether this is worth or not depends on how much damage you can do and how much your enemies are healing.
While mortal wound may or may not provide more damage (in an indirect form) than other items, do not forget that with this item burst down someone and removing him from the fight could be a lot easier. Transform the fight instantly in 4v5 could be much more advantageous than simply averaging an higher damage output.
At the same time, mortal wound “indirect damage” won’t help you scale that Breaking Point, nor will scale with critical damage items.

ATK Speed and Stutter-Step

Read this detailed article by brokenmyth.net:

In that article, you’ll hear about a stutter-step penalty. If you have never heard of stutter-step, watch this tutorial:
Practice and do it every time!

If you are done reading that article, let’s start doing some sample calculations!

Hero “A”
Weapon Power: 300
Base Attack Speed: 100%
Attack Cooldown: 0.8
Attack Delay: 0.3
No Stutter-Step Penalty: 0.2
Attack Speed Modifier: 100%
Bought 55% Attack Speed through items
Against a target with 150 Armor

BAT=0.8+0.3+0.2=1.3
So, our hero will perform 1 attack every 1.3 seconds at 100% attack speed. However, our hero as 155% attack speed (100+55 he bought), so he will attack faster!
1.3/(1+0.55*1)=0.83870

300/(0.83870/1)=358 damage per second
Finally, since the enemy as 150 armor:
358/(1+150/100)=358/2.5=143
And that’s our damage per second.

Cooldown and Spellweaving

Cooldown

Cooldown reduction increases the frequency you can activate skills.
Let’s say your skill has a base cooldown of 60 seconds. If you buy 35% cooldown reduction, it’ll be 39 seconds.
Note: cooldown reduction limit is 35%. Have more than this will do nothing.

Skill cooldown*cooldown reduction/100
Examples:
15 skill cooldown*20 cooldown reduction/100=3, so 20% cooldown reduction on a skill with 15 seconds cooldown will reduce the cooldown of 3 seconds, making the skill usable every 12 seconds.
120*15/100=18. In this case, a 120 seconds skill will be active every 102 seconds.

Spellweaving

Similarly to stutter-step, spellweaving consists in doing something (usually walk or using basic attacks) in the time between your skills. This does not increases your dps, differently from stutter-step.
Example of this are Kestrel autoattacking after every A (AA-A-AA-A-AA-A-AA-A), or Celeste using her A to kite backward while running from the enemies.
It should be noted that, by hitting the enemies with an ability exactly the moment Clockwork passive’s cooldown is off, you can maximize the effect and gain much more cooldown reduction from it.
Thanks to Vyzeox for his explanation