Battting
 

Fourth and five at Team B’s 30 yard line. A1 fumbles at Team B’s 20. The ball rolls to Team B’s 16 yard line where B3 bats the ball out of bounds at B’s six yard line.
What do we in force for illegal batting? Team A will decline the penalty and take the ball 1st and goal at Team B’s six yard line???

I’m not sure about NFHS, but NCAA this is not a foul because B batted it backward. This is just a fumble forward out of bounds and will come back to the spot of the fumble. Since that is beyond the line to gain, it will be A’s ball 1/10 @ B-20.

In Fed it's illegal batting because the ball has touched the ground ("The ball rolls"), and it's not a loose ball foul because the fumble was from beyond A's line. Enforcement would be half the distance from the end of the run (where the fumble occurred).

There's no such thing as "new force" in determining who put the ball out of bounds, so if A declined the penalty, the spot of forward progress would be where the fumble occurred, and they wouldn't get the extra distance of the fumble and bat.

I’ve never worked Fed for rules (and at this point probably never will), but just for clarification. In NFHS, you can’t bat a loose ball in any direction after it hits the ground even in the field of play?

...unless you're on the kicking team and you're batting a scrimmage kick backward from beyond your line.

Another situation where this is likely to come up would be by a player of R at a free kick that K is threatening to recover. It would be to R's advantage if a "muffed" ball went out of bounds, know what I mean, say no more? Even if the kick hasn't been grounded, it's illegal to bat.