You will find that most sports data is collected by commercial concerns who control licensing rather carefully, especially for current data. (See, for example, this from Sports-Reference.com about why they can't provide their bulk data.)
Most references to sports data that I've found (e.g. DatabaseSports.com) provide web access but not bulk downloads. Other resources frequently seem out of date. (But try googling for "sports data," you'll find lots of leads to follow beyond what I list here.)
Sean Lahman's index of sports data looks pretty carefully maintained and oriented towards bulk data. There's a book, Analyzing Baseball Data with R, which uses Lahman's baseball data as a source.
Tableau Public has a page which collects links to sports data sources for over a dozen sports but a little clicking doesn't show any that have bulk download. (You're advised to check further for the sports which interest you.)
There is a book, Sports Data Mining, which has an entire chapter devoted to data sources. The book is expensive, and was published in 2010 so it's data references may be obsolete… but perhaps you can find it in a library.