IANAL, but I asked one about this while ago; let's see if I can remember: It's complicated. The NFL broadcasts are copyrighted, and come with a statement that (among other things) distributing descriptions of the game is not allowed. That could be considered a derivative work.
On the other hand, a live performance is generally not protected from copyright, so if you attend a live game to collect the data, you may be in the clear.
The data isn't owned by the NFL, but all recordings of the games are, and so any data obtained by watching recordings of the games could potentially be controlled by the NFL.