I still feel sports stats has a lot of room for disruption. Stats.com is the leader in the space but their feeds are incredibly expensive. I think if a competitor could get the reliability of data as Stats has achieved but with a much, much lower cost they could dominate the space pretty easily.
The problem is the legality of sports stats isn't as clear as you might expect. Yes, the numbers themselves might be facts that are in the public record, but there are issues with how those stats are acquired. This is similar to issues with map data. There is even a practice of occasionally altering the stats to try to catch unauthorized use like catographers would occasionally make up islands.
You would basically need to collect your stats yourself from the game. Considering current technology, that basically means having a human watch the game and record the numbers. However, there are issues with this method because not all stats are 100% objective so your stats might not match the stats. In the end you also need to monetize this enough to cover that large overhead. The end consumer likely isn't going to pay for something they can get for free from the source on the internet. So your customer would only be the people who want this information in bulk.
However, since statistics cannot be copyrighted (at least in the United States), there is significant room for disruption. They only have contract law as a tool to prevent propagation of stats.