I also do some scraping in my spare time and i can tell you that large companies will have... precautions in place to prevent you from scraping their by-the-minute sports stats they pay millions for. Id also say right now scraping is a gray market, airlines in particular have proven that they are willing to fight for their (public) data, so tread carefully.
Scraping is a problematic way to do this too, because how can you verify what is up to date? You have to rely on one single authoritative source, otherwise youll be relying on some stat calc which “guesses” what the right stat is. Additionally, if you take live data that multiple large businesses feel they own, now they can split the lawyering fees on you and even if they lose, it will be cheaper for them together.
The historical content probably would be trivial to get, and its hosts most likely dont care if you have it. its the recent/live data which may be particularly difficult to take. In my professional opinion this is two separate projects- a paid up to date version with live stats and a free historical wiki.