10-player to 3 ref ratio
22 players on the field using the same ratio suggests wait for it 7 refs in an nfl game.
Square feet of an NBA court to cover 4700 square feet. Square feet of football field = 57600. Based on size of field of play, the NFL would 37 referees to have the same coverage.
The idea that three people could cover the field, while on the field, seems crazy.
Here is my crazy idea:
have 66 refs watching on monitors, rather than from on the field, with three people monitoring each player. Similar to Olympic boxing scoring, all three need to signal a penalty on the player they are watching, and there is 1 or 2 people on the field designated to throw the flag. If three people in real time agree a penatly happened, it is almost certain it is a penalty.
66 people may sound like a lot, but given there are 60,000 people in the stadium and millions watching on TV, its not really that big of a number.