Creation success tool and Wurm's normal RNG math.

[Ogare 74]

I'm trying to make a tool calculate creation success. I dislike "it depends" answers. It is possible to inform of skill level and tool qualities need to get the 6% creation chance.

 

I'd like help understanding code rollGaussian().

I want to use Python's optimized methods to roll random values from a normal distribution. I can include a mean and standard deviation for the roll. But I don't understand how Wurm is arriving at mean and sigma.

 

Here is the code snip from Skill.rollGaussian()

final float slide = (skill * skill * skill - difficulty * difficulty * difficulty) / 50000.0f + (skill - difficulty);
final float w = 30.0f - Math.abs(skill - difficulty) / 4.0f;
...
result = (float)Skill.random.nextGaussian() * (w + Math.abs(slide) / 6.0f) + slide;

Here I think "slide" is mean. Is this sigma "(w + math.abs(slide) / 6.0f)?

 

I'll include in the simulation that Wurm rolls again values which fall outside the cutoff. Don't worry about this part.

[Lethyria 161]

This is just a basic liner transformation of a normal variable. To in its general form let X be our random variable where X~N(µ, σ^2), and Y is another random variable where Y = kX + c. Y can be represented as Y~N(kµ+c, k^2*σ^2).

So in this case rollgausian is a standard normal i.e. N(0,1). k is (w+|slide|/6) and c is slide.

 

So our result is Result~N(0*(w+|slide|/6)+slide, (w+|slide|/6)^2*1)

 

Simplified Result~N(slide, (w+|slide|/6)^2)

So your mean is slide and variance is (w+|slide|/6)^2 

And standard deviation (σ) is  (w+|slide|/6)

 

 

I don't know what sigma refers to exactly in the python library you are using but usually it'd be standard deviation.

 

A source for more reading on normal transformations: https://web.stanford.edu/class/archive/cs/cs109/cs109.1178/lectureHandouts/110-normal-distribution.pdf

Edited March 4, 2021 by Lethyria
Sauced