I thought this way as well, but professional sports leagues argue that their efforts generate the data, so they own it (i.e. without their venues, players, coaches and additional resources, those numbers wouldn't exist). They will allow you to consume that data in approved ways, such as going to see a game or watching it on TV, but they do not allow you to record and use that data for profit without permission. The companies who provide sports data feeds have jumped through a lot of hoops and pay significant fees to license that data. The companies that use those feeds do, too (e.g. fantasy sports league manager services, sports reporting services, sports betting services, etc.)

Unfortunately, some people think facts can be copyrighted: see http://www.premierleague.com/en-gb/news/news/football-dataco...

I'm honestly not sure about what is free to use and what is not. If you guys are looking for a free stats solution for MLB, head over to http://erikberg.com/mlb/ .

Perhaps an expert can say whether it is legal to make money via advertisements if you use this data.