Mathematics of PVP: Guide for Damage Calculations for Reworks

I can left click and that's all that matters

 

I had a copy of the source code handy so I figured I might as well take a look

I'll provide some pseudocode snippets that show what's going on, but the real code is probably illegal to distribute, and my body isn't ready for the Mojang(tm) lawyers

Code:

if (player is invulnerable) or (player is in creative) or (health < 0):
    cancel damage

Simple checks to make sure the player is able to take damage

Code:

if (player is sleeping):
    wake up player

That's just rude.

Code:

if (damage amount is 0):
    cancel damage

We don't care if the amount of damage to deal is zero, so we just kill the event to save cpu cycles.

Code:

if (damage is of fire type) and (player has fire resist potion effect):
    cancel damage

Prevents fire damage if the player has fire resist.

Code:

if (damage is from a falling block) and (player is wearing a helmet):
    damage the helmet for `2d (2 + rand(0, 1))`
    multiply damage amount by 0.75

If the player has a helmet and you drop an anvil on them, the helmet takes damage equal to that formula, where d is the amount of damage dealt and the rand(x, y) function generates a random number from x, inclusively, to y, exclusively. Then, the total damage is reduced by 25%. Essentially, the helmet is taking some of the damage for the player.

Code:

if (player was hit recently):
    if (damage amount <= previous damage amount):
        cancel damage
    deal damage
else:
    deal damage
    grant invincibility frames

This part is kind of strange. We all know about the invincibility frames you receive after taking a hit, but apparently the invincibility only applies if the amount of damage taken in the second hit is greater than the amount in the first hit. What's even weirder is that this applies after the anvil thing, so getting an anvil dropped on you while you have invincibility frames might negate the damage to you but still damage your helmet. Furthermore, you don't get additional invincibility frames if you take damage from this second hit, which is just weird.

Now let's take a look at that "deal damage" bit. If we expand it into pseudocode, it look something like this:

Code:

if (damage source is affected by armour):
    damage armour for `d(25 - a)`
    set damage to `d(25 - a) / 25`

First, we check to make sure the damage can be blocked by armour; potion damage, for example, bypasses armour. Then we damage the armour and reduce the total damage by those formulae above. The d stands for the damage amount, and the a stands for the player's armour. Since the maximum armor value is 20, damage can be reduced by 80% at most. Essentially, each point of armour reduces the damage by 4%.

Code:

if (player has resistance) and (damage is affected by potions):
    set damage to `d(25 - 5(r + 1)) / 25`
    if (damage < 0):
        set damage to 0

Nullifies some damage based on resistance. r here represents the potion effect level, starting at 0 for Resistance I, 1 for Resistance II, and so on. It would appear to cap at 4, or Resistance V, since the multiplier becomes 0 at that point. Essentially, damage is reduced by 20% for each level of resistance.

Code:

for each armour item:
    if (item has protection):
        add `0.75(6 + p^2) / 3` to the total protection
    else if (item has fire protection) and (damage source is of fire type):
        add `1.25(6 + p^2) / 3` to the total protection
    else if (item has feather falling) and (damage source is of falling type):
        add `2.5(6 + p^2) / 3` to the total protection
    else if (item has blast protection) and (damage source is of explosive type):
        add `1.5(6 + p^2) / 3` to the total protection
    else if (item has projectile protection) and (damage source is of projectile type):
        add `1.5(6 + p^2) / 3` to the total protection
clamp the total protection between 0 and 25
set total protection to `((p + 1) / 2) + (rand(0, 1 + p / 2))`
set damage to `d(25 - p) / 25`

Wow, what a mess. We'll just ignore all protection types except general protection, which is at the top of this massive if-else chain. For each protection item, we add an amount to the total protection based on the formula above, where p represents the level of the enchantment, starting at 0 for Protection I. Since p is squared, higher levels of the enchantment offer more additional protection than lower levels. After summing up all the protection, we do some weird math on it and reduce the damage respectively. I think I can reduce it to this formula here:

Code:

M = 0.98 - ((4.5n + 0.75(p1^2 + p2^2 + ...)) / 150)

Where M is the multiplier for damage, n is the total number of armour pieces with protection, and p1, p2, etc. are the various levels of protection on armour. Not a very nice looking formula.

Code:

subtract damage from health

Finally, the important bit! There's also some logic involving absorption before this, but we don't really care about that.

If we take all the damage modifiers and combine them into a massive formula, here's what it looks like (assuming the damage source is someone hitting you):

Code:

Df = Di * (1 - a / 25) * (1 - (r + 1) / 5) * (0.98 - ((4.5n + 0.75(p1^2 + p2^2 + ... + pn^2)) / 150))

ew.

also i did this all at 11:30 so there might be some wrong stuff

 

Nice Job Tiki.

 

D=X(P+1)
This implies Dwarf's diamond sword with Sharpness XI deals 88 health points of damage, or 44 hearts.
Psssst... It doesn't.

 

You are a ****ing legend