A more in-depth version of this short post is available at The Math of Idle Games, Part I.
At GDC Europe this year I gave a talk that took a deeper look at some of the numbers, formulas, and patterns underlying idle games. The slides for the talk are on Slideshare and the GDC Vault, if you have access there.
In the slides you’ll find information about growth curves, formulas for bulk purchases, purchase optimization models, a variant on growth based on derivatives, a look at prestige cycles, callouts for some great new idle games, and an aside on stupidly large numbers.
However, what I hope becomes the biggest value from the talk is that all of the charts generated for the slides come from spreadsheets that I’ve opened up for general use. If you’re planning on doing a lot with them I recommend downloading the Excel versions, as Google Sheets starts to cry on some of these simulations.
These sheets allow you to play around with values in a variety of situations to see how the curves change. While it’s unlikely you’ll be able to fully model and balance an idle game with these, they will hopefully allow you to better understand the tools that you have available to build an engaging and compelling progression.
As a specific example, Sheet 1e models optimal player choice for buying generators (i.e. the buildings, investments, or whatever generates the main currency), with the ability to set multipliers for the generators that trigger when the player owns a certain number of them (similar to AdVenture Capitalist bonuses). By setting these carefully, you can create a progression that varies over time in terms of the most valuable generator, keeping the gameplay more varied for the player, like this:
I hope these turn out to be useful! If you have questions, find a bug, decide to make an extension to a sheet, or have an awesome new idle game you want to share, please feel free to reach out and email me at email@example.com.