How is it work? - zsnmwy/ONI-geyser-calculator GitHub Wiki

Except Leaky Oil Fissure, the Average Yield of a geyser roughly equals Daily Eruption x Active Percent (kg/600s).

These two parameters can't be reviewed directly in game, but can be calculated.

These two parameters are independent and uniform distribution.

Therefore, we can draw a rectangle in the coordinate system to represent the probability distribution of the Average Yield.

a, ka means min, max Daily Eruption;

b, mb means min, max Active Percent.

$\begin{cases} & \text{ } a=Daily Eruption\sim min \\ & \text{ } ka=Daily Eruption\sim max \\ & \text{ } b=Active Percent\sim min \\ & \text{ } mb=Active Percent\sim max \end{cases}$

For a certain Average Yield n

we can draw a line $xy=n$

The upper right area of the line has larger yield.

The lower left area has lower yield.

The area of the rectangle

s=(k-1)(m-1)ab

$s=(k-1)(m-1)ab$

z means the proportion of the lower left area to the total area of the rectangle

z=

When abk<n1, [n*ln(abkm/n)+n-abkm]/s+1

When abm<n2<abk, [n*ln(m)+(1-m)ab]/s

When n3<abm, [n*ln(n/ab)-n+ab]/s

$\begin{cases} abk< n1 & \text{ } z=\frac{[n*ln(\frac{abkm}{n}) + n - abkm ]}{s} + 1 \\ abn< n2< abk & \text{ } z=\frac{[n*ln(m)+(1-m)ab]}{s} \\ n3< abm & \text{ } z=\frac{[n*ln(\frac{n}{ab})-n+ab]}{s} \end{cases}$

Currently, for every kind of geyser

$mb = 0.8 \: \: \: \: \: b=0.4$

So $m = 2$

Assume $x=\frac{n}{ab}$

Now lets bring

$m = 2\, \, \, \, \, \, x=\frac{n}{ab}$

into the original formula and get a simplified formula

z=

When x<2,=[x*ln(x)-x+1]/(k-1)

When 2<x<k,=[x*ln(2)-1]/(k-1)

When k<x,=[x*ln(2k/x)+x-2k]/(k-1)+1

$\begin{cases} x<2 & \text{ } z=\frac{[x*ln(x)-x+1]}{k-1}\\ 2<x<k & \text{ } z=\frac{[x*ln(2)-1]}{k-1} \\ k<x & \text{ } z=\frac{[x*ln(\frac{2k}{x})+x-2k]}{k-1}+1 \end{cases}$

In this formula, z means how many percents of same type of geyser are exceeded by this geyser.

$x=\frac{Average \, \, Yield \, \, of\, \, this \, \, geyser}{Min \, \, Yield \, \, of\, \, same\, \, type\, \, of\, \, geyser}$

$k=\frac{Max\, \, Daily \, \, Eruption\, \, of \, \, same \, \, type\, \, of \, \, geyser}{Min\, \, Daily\, \, Eruption \, \, of\, \, same\, \, type\, \, of\, \, geyser }$