There's a bit of a chicken and egg problem here. You don't know how many ticks you can fit if you don't know what the tick labels contain. And you don't know what the tick labels contain until you know how many ticks there are.

Therefore this is just based on a heuristic that the text will have an aspect ratio of around 4:1. Probably not always true, and there are perhaps better ways to estimate based on what the tick formatter actually is, or by rendering just one of them and using that.