Pirates waves - how they scale, how they are triggered, do they work at all?

I've been trying to figure out how pirate waves work for a while now. I always seem to get mixed results. I'd like to call upon the community and Schine staff to disclose the math behind the game choosing which wave to spawn upon a trigger event (like the attack on a shop or a pirate station.)
I ask this because my results have been erratic, and I'm not alone with it.
What exactly are the factors that determine the wave? Does the game care at all about the mass of ships in a wave, or does...

Pirates waves - how they scale, how they are triggered, do they work at all?