Stardance Mult Utility

Tools to visualize and explore the formula that Stardance uses to calculate project multipliers.

Interactive Graph

Drag the point side-to-side to adjust the percentile, and it'll display the multiplier.

Source on Desmos (made by Jonah Crawford)

Calculator

Type a percentile to calculate the exact resulting multiplier, or type a multiplier to calculate the exact required percentile.

% = x mult

Formula

Steps to apply the formula.

\begin{matrix} mult & = & m_{\min} + (m_{\max} - m_{\min}) {(percentile)}^{exp} \\ = & 1 + (20 - 1) {(50%)}^{1.745427173} \\ = & 1 + 19 {(50%)}^{1.745427173} \\ = & 1 + 19 (0.3) \\ = & 1 + 5.67 \\ = & 6.67 \\ percentile & = & \sqrt[\exp]{\frac{(mult - m_{\min})}{(m_{\max} - m_{\min})}} \\ = & \sqrt[1.745427173]{\frac{(6.67 - 1)}{(20 - 1)}} \\ = & \sqrt[1.745427173]{\frac{5.67}{19}} \\ = & \sqrt[1.745427173]{0.3} \\ = & 50.02% \end{matrix}

Code Walkthrough

Excerpts from the actual Stardance source code, annotated with my explanatory comments.

payouts.rb lines 449 to 453

^{# This function implements the actual formula that this whole project is about}
def dollars_per_hour_for_percentile(percentile)
  ^{# See the next code block for an explanation of these}
  low = game_constants.lowest_dollar_per_hour.to_f
  high = game_constants.highest_dollar_per_hour.to_f

  ^{# This is the math part. It normalizes the percentile, applies the exponent}
  ^{# to make it a nonlinear curve, and then converts that normalized value to}
  ^{# between the minimum mult (aka low) and the maximum mult (aka high).}
  ^{# I have no idea where the 1.745427173 exponent comes from.}
  low + (high - low) * ((percentile.to_f / 100.0).clamp(0.0, 1.0) ** 1.745427173)
end

game_constants.yml

^{# These are the variables that control everything}
shared:
  ^{# Internally, stardust is called "tickets". This variable controls the}
  ^{# conversion ratio. At least, hypothetically. It's actually closer to 4}
  ^{# stardust per dollar for most shop items, though it varies.}
  tickets_per_dollar: 5.0

  ^{# This is used for the hour estimates in the shop}
  dollars_per_mean_hour: 2.0

  ^{# All three of these are completely unused}
  min_quality_multiplier: 1.0
  mean_quality_multiplier: 10.0
  max_quality_multiplier: 30.0

  ^{# These two are the ones used in the dollars_per_hour_for_percentile()}
  ^{# function you saw in the previous code block. That's actually the *only*}
  ^{# place where these are used.}
  lowest_dollar_per_hour: 0.2
  highest_dollar_per_hour: 4.0

  ^{# Completely unused}
  sb_min_dollar_per_hour: 1.0