[Mr. K]

I was surprised that each team controls a set of balls

I would have expected that the referees would control a basket of 50 balls (or whatever) that are weighed and measured to be regulation, that they have ready for each game.

Then only referees put a ball into play, or grab a new one when a player decides to keep one or toss it into the stands.

[billyboy15]

The refs used to have full control over all game balls. Tom Brady was instrumental in getting this changed and allowing each team to take responsibility for its own balls (game :-))

[Alberta's Child]

NFL officials used to control the balls during the game, but some NFL quarterbacks pressed to have the rule changed because they wanted the ability to vary the pressure to fit their own grips.