They adjust the frequency, but nothing else. So if you make them twice as frequent, they will still be as fierce as normal, thus making it twice as difficult. If you make them half as frequent, the same logic holds so the waves are then half as difficult.
Adjusted score is weighted based on selections such as these that are made, by the way. You get a penalty for making things easier, and a boost for making things harder, etc.
Is that actually 100% true? Isn't the number of ships in the wave partly determined by how much time has elapsed since the last wave for that particular AI? So, 1/2 waves have less frequent waves, but the waves are in general larger, and 2x have twice as many but the average size is less?
Only insofar as the AI Progress increases steadily over time but I imagine the effect of that to be minimal.
Well, under normal circumstances, the amount of time between waves does have an internal variance. In other words, let's say that, for the current difficulty, the default median wave time is every 15 minutes. There is an internal multiplier that creates variance between perhaps 0.5 and 2.0, or something like that. That multiplier affects both how frequently the waves come, and the size of the wave. So if you wind up getting several waves every 7.5 minutes apart, half of the median wave time, then you will wind up with each of those waves also being half-sized. If you are only getting waves every 30 minutes, those will be bleeding huge waves even though they are less frequent.
Each wave has its own randomized multiplier, so one might be 7.5 minutes and the next might be 28 minutes and the next might be 14. This is carried out regardless of difficulty level or whatever. The 2x waves and 1/2 waves AI Modifier don't have any effect on this multiplier, but are applied afterward, so that you get waves that are twice as frequent or half as frequent (or off) without affecting their size.
So if you have 2x waves turned on, your median time would simply be 7.5 minutes in the above example, with variance between 3.25 minutes (at half wave size) and 15 minutes (at double wave size). So the AI Modifiers are adjust the base, if that makes sense, which means that the internal multipliers affecting wave size aren't related to this.
Good question, Oewyn!