I've been looking around for the same. The problem seems to be that there are only a few big outlets (some with exclusive contracts) doing the stats for the big sports. It seems possible to scrape a lot of what you need though, unless you need up to date data daily (which could still be scraped but it would be a much larger undertaking).

My question is, how do you plan on getting data from the daily fantasy sites (e.g. salary caps and salaries of players)? I don't think FanDuel (or any of the other sites) has a public api for anything other than seeing user rankings.