Guide Wynncraft Math

I've started working on a document a few days ago, which tries to explain the math behind some known concepts in Wynncraft. This thread will have two purposes: firstly, to present said document. Secondly, to provide people with the basic info required to solve the problems in this document themselves, in case you, the reader, want to solve them yourself. We'll tackle 6 problems as of the time of writing this thread:

• Effective Hit/Health Points - how does damage reduction affect your effective hit points?
• Sorcery Damage boost - i.e the average amount of recasts you will get when using the major ID "Sorcery"
• Quake and Sorcery - How much DPS does a Heavy Melee build provides, and Sorcery's effects on it
• Mana steal and Life steal - How do they work and why
• Net / Overall sustain (This isn't really a problem but rather a nice concept to know)
• Horse breeding prices - Purged and generalized from @Yuno F Gasai's thread, Go check it out it's awesome and has been open for 6 (SIX!) years.

Time to get working.

EFFECTIVE HP
​

Effective Hit Points are a way of evaluating survivability. Since mobs in Wynncraft have different damages, the players needed to figure out how to take the concept of damage reduction and reverse it - if, hypothetically, damage reduction wouldn't reduce damage but rather increase HP, how much HP would we actually have with a certain amount of damage reduction?

As it happens the formula that describes the relationship between HP and damage reduction to determine Effective HP looks something like this:
EHP = HP / (1 - Damage reduction %).

To arrive at such a formula all you need to know is that damage reduction functions in the following way:
Given that a mob does 1000 damage, a player with 30% damage reduction will receive 1000-1000*0.3 = 700 damage upon hit. In general, the damage inflicted to a player with a certain amount of damage reduction will simply be decreased by that same amount.

Spoiler: Solution

SORCERY DAMAGE BOOST
​

Sorcery is a major ID that grants the ability for attacks, spells and powder specials to recast, with each recast having a 30% chance to occur. The recasts themselves also have a 30% to recast, as they're still counted as an attack, and this will continue until an attack fails to recast. Knowing that one can compute the average amount of recasts that will occur per attack, thus figuring out a good estimate for the average damage boost Sorcery will add (it won't be exact as powder specials can be charged faster and can also recast).​

Hints:
1) the probability for a certain number of recasts to occur follows a geometric distribution.
2) Using the concept of the mean of a distribution, otherwise known as "Expected Value" may be helpful.
3) The value you should get is 3/7 recasts on average.

Spoiler: Solution

MELEE DAMAGE ACCOUNTING FOR BOTH QUAKE AND SORCERY
​

The goal is to come up with a formula or two that calculates the average DPS of a melee build while taking into account the damage added by Quake (I was using the max damage bonus you get by powdering with tier 6 earth powders, but this can be generalized further), and later on, tackle the problem of how having Sorcery will affect the outcome.​

Helpful information:
1) The end result will contain 3 variables - Single-hit damage, Attack speed, and Hits required to charge up Quake.
2) What Quake does is essentially to take single hit damage and multiply it by 4.15.
3) Quake activates at the expanse of a melee hit (except for Archer).
4) The Quake hit does not count towards charging the special itself (except for Archer).
5) The average amount of recasts that will occur when using sorcery is 3/7 or 0.428571...

Guidelines:
1) Try to figure an expression for out how much damage Quake does in a second.
2) Because sorcery recasts attacks, it shortens the time that it takes to charge up Quake.
3) Don't try to include sorcery straight away, figuring out an expression for the normal scenario and adding sorcery later is easier.

Spoiler: Solution

MANA / LIFE STEAL
​

In Wynncraft, Mana and life steal have a certain probability to activate upon hitting an enemy, and that probability is designed in such a way that the average amount of activations in 3 seconds will be 1. the challenge is to find what those probabilities are given an attack speed of n hits per second.​

Hints:
1) The probability for a certain number of activations to occur out of a certain number of trials follows a Binomial Distribution.
2) Once again, try using the mean of a distribution, only now instead of Geometric, It's the mean of a Binomial distribution.

Spoiler: Solution

NET / OVERALL SUSTAIN
​

There isn't really anything to solve here, the concept is to set a common denominator between Mana steal, Mana regen and Natural mana regen to get a sense of how much Mana sustain you're getting, and then do the same for Life steal and Health regen.​

Spoiler: Yea

HORSE BREEDING PRICES
​

Following in the steps of the immortal thread by Yuno, this is a more generalized explanation of what he presents in his thread.​

Guidelines:
1) Work your way from the bottom up - first the price of a black horse by breeding brown horses, then chestnut by breeding blacks, and White by breeding chestnuts.
2) Try using a variable instead of a specific amount of horses.
3) Each breeding operation takes two horses and returns one.
4) The work process should be:

• Determining the worth of our initial amount of horses.
• Using the known breeding chances for upgrading, downgrading, and getting the same kind of horse out of a breeding operation, in order to calculate how much money we would gain back from getting horses that are the same tier or lower than the tier we started with.
• Subtracting that amount of money from the initial amount of money to find out just how much money our new higher tier horses are worth, and finding the worth of 1 of those horses.

The possible outcomes of breeding horses are:
- Upgrading, with a 20% chance
- Downgrading, with a 30% chance
- Remaining with the same tier, with a 50% chance.

Horses cannot downgrade further than Brown, or upgrade further than White.

Spoiler: Solution

(Here's a simulation by @HeyZeer0 Confirming the prices)

EDIT: I forgot to include the actual document itself so here you go.

 

what a stupid dumb idiot f u itechnically

 

nice thread

 

I cant understand any of this but it sounds cool so i like it

 

Wow...



Well Done!

 

why is nya an option~

 

we do a (little) trolling

 

hey itech why are there so many words

 

Nerd

 

Good thread.

 

Bad thread using both serif and sans serif fonts in a single document, literally terrible formatting. nya~

 

Very cool thread! I like how you not only present the answers but also give readers the opportunity to figure it out by themselves first.

I'd actually started on a Sorcery + Quake document a few days ago as well - while it's not completely finished yet, it's still worth sharing I think since my approach was a bit different, and I ended up with different results.
Essentially, I looked at a regular cycle of melee attacks + a Quake, and then tried to account for how Sorcery affects the cycle duration, or in other words, the effective number of hits required until Quake can be used.

Here's a snippet:

Spoiler: Snippet

Using this, a table of multipliers can be constructed to go from single-hit damages to effective DPS values as follows (assuming the maximum Quake multiplier):

Spoiler: Multipliers

Wasn't sure where to post this, so I'll just post it here to keep the discussion going and hopefully have someone take a critical look at it.

EDIT: You can download the full PDF (in its current state) below.

 

math

 

me when i saw the formulas and stuff: