Well, this is a year later, but I was in the same search for almost 3 years. I have not found an open free API yet. ESPN provides several pieces of data for free, but usually in bulk and difficult to use if you are looking for specific data (I create fan sites for one team). They do not provide any registry, schedule or rating information for any sport to the public.
http://developer.espn.com/
The only glimmer of hope I found is a British company that offers free use of “some” historical data. You must apply to gain access, and I am still waiting for them to return to me.
http://www.optasports.com/playground-section.aspx
Here's a post about some other options, although some of the api data are historical and no longer work. http://riccomini.name/posts/game-time-baby/2012-09-29-streaming-live-sports-schedule-scores-stats-api/
Also, the cheapest api I found (also listed in the above post below): http://www.xmlteam.com/fod/
They take a loan of $ 0.25, and then have a multi-level structure by the number of loans, each of which will cost the API. The more credits you buy, the cheaper it is, but it is still equal to $ 30 for the season of game statistics for the football team. The price varies depending on the sport, so it may be more or less for the sport you are looking for.
If I find anything else, I'll let you know. At some point, this api should become available from somewhere.