Marcos Pereira

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Logarithmic progression in games

Apr 27, 2024

Logarithmic progression is a simple but powerful idea. It became clear to me when thinking about incremental/idle games such as cookie clicker, but I think the concept applies to almost any other genre.

The idea is simple - any progress made by the player only makes it possible to make more progress, but never takes away from the user’s necessity to make progress through their own effort.

In incremental/idle games, success follows a logarithmic scale - your numbers are always increasing, but they never increase fast enough that you can just sit back and watch the game move on without you - you always need to do something to move up to the next level of the logarithmic scale.

You may make 1000 of something per second, but it would still take over 16 minutes to accumulate a million of it. If you need 10 million to advance, you’ll still have to do something to improve the rate at which you make things - even though you already got to 1000 per second!

It’s a logarithmic treadmill of dopamine.

This doesn’t just apply to raw numbers. Think about the farming mechanic in a game like Minecraft, for example. It takes little effort to farm some wheat and curb your hunger indefinitely. There is no logarithmic progression here, it’s just linear! But what if you could colonize a village, and have to feed 1000 mouths? What if you could herd 1000 sheep? What if you could feed tons of wheat into a carbon processing machine that creates biofuel to power a rocket so you can fly to the moon?