How do we size the Business Analyst (BA) team in our organisation? Is there a standard, or best practice that helps to determine the ideal BA pool size according to a) number of projects run paralel, or b) size of the organisation, or c) size of project portfolio budget, or d) anything else that can be the basis of our planning?

If you want a quality analysis, then I'd consider the number of and diversity or content areas first as a floor. A high grade BA may be able to transition between content areas but since the function is often understaffed / under qualified one content area per BA could give you good coverage. Allocation may be driven by number of, or complexity of, projects but all projects should be assessed and analyzed for people / process / technology impacts and resulting changes needed to meet project outcomes.

I would say sizing a team is a combo art & science. Here's some questions to use as a guide: How many projects does your org run? What's the variance in complexity? How good are your stakeholders at conveying requirements? Does it typically require more than 2 sessions with back and forth during? How tight are your scrum processes? I would say general rule, the harder it is to get really good requirements + projects tend to have a large amount of complexity, the number of BAs doesn't matter if your frameworks for req collection and scoping aren't tight.