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.
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.