Boils my brain to try and get a feel for it, but I think there may be a 5D graph possible showing payback period vs panel capacity, orientation, inverter capacity and battery capacity.
For us and I assume many, maxing the panels on one face of the roof was a no brainer as it saved slate (I’m not a fan of surface mount panels).
From that our installer used a sort of rule of thumb/wet finger analysis to give us an inverter/battery pair he’d used loads of times on our sort of size if installation and which was well priced. So the 5D graph and all the AI advanced modelling wasn’t needed.
So no deep thinking needed. Simples.