The Skill Point Formula Has Been Reverse Engineered

Skylaar · Jun 28, 2021

you are all madmen

ocu · Jun 28, 2021

Salted said: ↑

^i mean it all in good fun, of course. i couldn't resist doing that while reading this thread. anyway yea, the community often finds insane formulas that even I don't understand at all for my own game. the vast majority of the time, all I did was some very basic spreadsheet design. it's generally more useful when designing stuff as you can quickly visualise every part of the progression at a glance.
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“Doesn’t even name the columns in his sheet”

liar.

touhoku · Jun 28, 2021

oculism said: ↑

“Doesn’t even name the columns in his sheet”

liar.
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pretty sure the contents of the sheet are also a lie... don't think the base being 0.9925 for sp effectiveness checks out either...

iTechnically · Jun 28, 2021

touhoku said: ↑

pretty sure the contents of the sheet are also a lie... don't think the base being 0.9925 for sp effectiveness checks out either...
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it is in fact a lie, it doesn't check out (150 sp = 90 effectiveness), but funnily enough it actually is just a geometric sum so that's pretty much complete confirmation, maybe even for the base (old sp?)

NcMugget · Jun 28, 2021

Salted said: ↑

^i mean it all in good fun, of course. i couldn't resist doing that while reading this thread. anyway yea, the community often finds insane formulas that even I don't understand at all for my own game. the vast majority of the time, all I did was some very basic spreadsheet design. it's generally more useful when designing stuff as you can quickly visualise every part of the progression at a glance.
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in the 1.20.2 hotfix #6 post, you jokingly said that you could put 200 skill points manually into a single skill(with 99.13% effectiveness).
https://forums.wynncraft.com/threads/1-20-2-hotfix-6.291381/
I used the skill point formula that was found, and i got...

90.7% effectiveness
so, salted, you weren't lying when you said that you made up that number. also, you weren't even close!

DaCorruption · Jun 28, 2021

2015 lore that never got changed is less confusing than this

MineMasterRC · Jun 29, 2021

I do not understand this

StormKing3 · Jun 29, 2021

Basedlord Ayobe said: ↑

Well folks, it's been done. Though I'd been working on this some weeks ago, I never truly nailed the answer until today: the formula for extrapolating the effectiveness of a skill point based on the points invested in it.

Today we discovered the formula was something no one (presumably) had previously considered; a geometric series.
View attachment 173913

While there were incredibly accurate attempts prior, such as that of ferricles,
we had never been quite there until today. With hours of time poured into doing the math for this, we were finally able to determine the exact formula, which is the following:
View attachment 173907

Here's what you need to know about this formula:
- x is the number of skill points in a certain category, and E(x) is the effectiveness out of 100. This means that at x = 150, E(x) = 80.8.
- The round(x,y) function rounds the value of X to the yth digit. For example, round(1.6368, 2) = 1.64, whereas round(1.6368, 3) = 1.637.

While my original formula followed the format
View attachment 173908 ,

I had decided after seeing the results of ferricles much more accurate equation that an exponential was the way to go. However, the idea of using a geometric sum actually just occurred to me while I had walked fresh out of my math class. With the thought fresh on my mind, I sat down and attempted to use the new form:

View attachment 173910 .
Using the built in logarithmic regression feature in Desmos, I was able to calculate that a = -1.00289 and b = .990801; while not the cleanest numbers, they net me an R^2 value of 1, or at least so close to it that Desmos rounded to that. After this, I decided that was good enough for me, and let it go for a while. This was around in May.

Fast forward to today, June 27, 2021, and I'm talking to epic moderator SayaDuck about something or other in the Wynncraft #questions channel. During this conversation I mention my old formula, thinking it's a neat function but nothing more. When Saya asked if mine was closer than ferricles, I went to his friend hppeng, the creator of Wynnbuilder. He suggested to me that it might be more accurate if a = -1. From here, I removed the .000001 on the end of b to get a = -1, b = .9908. When this new formula is rounded to the nearest 10th, you get an equation of perfect accuracy except for one edge case; x < 0, which would return -1% effectiveness instead of 0. However, all values above x = 0 were accurate. With a suggestion from iTechnically, I switched it from
View attachment 173911

to this

View attachment 173912 .

To verify it's accuracy, I used a program which would return false if the value output by my formula E(x) was not equal to the real value of the effectiveness at a given point. After writing this algorithm, the equation checked out; we had found it.

This wouldn't have been possible without the help of some lovely folks who I'd like to credit below with their discord names :)

- @ferricles#6344 for his equation, which opened my mind to considering exponentials as an option
- @hppeng#8609 for simplifying some numbers to increase the overall accuracy of the equation
- @iTechnically#4671 for simplifying it to account for x-values less than 0
- @Saya#8503 who pushed me to continue my work after I had given up
- @touhoku#8699 who helped me write this thread

:)
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Very interesting. I have no idea what any of this means but if you got the formulas correct well done indeed!

Stormarend · Jun 29, 2021

It kinda pisses me off that someone went through the effort of reverse-engineering the formula and making a thread which clearly explains what the formula is and how it came to be, only for people to say "I don't know what this means" because they're afraid of the summation sign or something.

touhoku · Jun 30, 2021

Stormarend said: ↑

It kinda pisses me off that someone went through the effort of reverse-engineering the formula and making a thread which clearly explains what the formula is and how it came to be, only for people to say "I don't know what this means" because they're afraid of the summation sign or something.
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eh, we do it for fun for the most part. (we as in the people that do the math)

also its entertaining seeing how people with a range of math experience respond ngl

yy8erig · Jul 5, 2021

NamesAreHard said: ↑

Sometimes I wonder what kind of person would design a game this way, why they would subject us to all this arbitrary strangeness. Could it really be a mere mortal who created such an elaborate maze of contradictions and nonsense?
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cow man

Fwap a Durp · Jul 7, 2021

can't wait to get 285 skill points in defence and get 100% damage reduction

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The Skill Point Formula Has Been Reverse Engineered

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