The explanation is easy.
An analytic prompt contains the facts necessary for the response. This means the LLM acts as a translator.
A synthetic prompt does not contain the facts necessary for the response. This means the LLM acts as a synthesizer.
A complete baseball box score being converted into an entertaining paragraph description of the game is an analytic prompt and it will reliably produce a factual outcome.
https://www.williamcotton.com/articles/chatgpt-and-the-analy...
There’s a bunch of active research in this area: