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The incumbent sports organizations will fight you all the way. I wouldn't count on getting the express written consent of Major League Baseball, put it that way.

Probably the best strategy is to give people an incentive -- even if only a social one -- to enter and maintain the data. WikiSports, basically.

Stats aren't copyrightable. You can build one without goodwill.

TXODDS has various pull/push APIs. Betting odds is the focus, but they have more fixture/stats/resulting services under development and can be approached for custom solutions.

https://txodds.com/

SOLID thanks!

http://sportradar.us/ they are not cheap though

OH hai! Maybe this is it. Checking it out

Edit: no gambling data. Maybe that's ok, but I'd want that too. Still looks pretty interesting thanks!

Also, and perhaps less US focused, Opta.

http://www.optasports.com

Check out https://www.stattleship.com/

Cool! Not at all what I want but also a neat thing in and of itself