Once in a blue moon I get the urge to run some analysis or another on sports stats, but I almost inevitably end up having second thoughts when I realize obtaining good data is going to be an ongoing chore.
I'll also echo the suggestion from @scottrblock on the potential usefulness of various metadata. If all you have are game statistics, while people can obviously do lots of novel analysis on the data, it's fairly obvious what the "use" is. With a wide spectrum of metadata, you might end up simultaneously creating something of value to someone analyzing the effect of weather on different sports/teams/players and for hotel chains trying to set prices based on the historical attendance for all sporting events within 50 miles.
If you could create a revenue model that supports delivering the service both to continual high-volume business users and to users just using the API occasionally to support an analysis project, perhaps it's possible to pass revenue downstream to other data sources. Granted, this adds a number of administrative problems (people submitting data collected/generated/sold by other parties as their own to collect revenue on it; getting low-quality/falsified data; etc.)
* I wasn't aware of stattleship or sportsradar before this thread; no idea how well they cover these.