Can you hit the hand, if it's on the ball?
I need proof that it shows that if you hit the hand, it isn't a foul.
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Just a little further down in the same rule @posdef quotes, is this one:
e. Contact which occurs on the hand of the offensive player, while that hand is in contact with the ball, is legal.
This is significant enough to warrant its own exception in the rules. It also is called out as incidental contact explicitly in the first section of Contact Situations:
... The hand is considered "part of the ball" when it is in contact with the ball. Therefore, contact on that hand by a defender while it is in contact with the ball is not illegal.
While the defender may not flagrantly attempt to injure an opponent's hand, if a defender bats at the ball to attempt a steal and contacts only the hand (not the forearm) of the ballcarrier while it is in contact with the ball, a foul will not be called.
It all depends in what context the contact happens, it's either judged as incidental or illegal contact. Incidental contact is judged if the ball carriers "move" is not effected by the contact. Here's the relevant bit from the NBA rulebook (Rule 12 Fouls and Penalties, Subsection B)
b. Contact initiated by the defensive player guarding a player with the ball is not legal. This contact includes, but is not limited to, forearm, hands, or body check.
(1) A defender may apply contact with a forearm to an offensive player with the ball who has his back to the basket below the free throw line extend-ed outside the Lower Defensive Box.
(2) A defender may apply contact with a forearm and/or one hand with a bent elbow to an offensive player in a post-up position with the ball in the Lower Defensive Box.
(3) A defender may apply contact with a forearm to an offensive player with the ball at any time in the Lower Defensive Box. The forearm in the above exceptions is solely for the purpose of main-taining a defensive position.
(4) A defender may position his leg between the legs of an offensive player in a post-up position in the Lower Defensive Box for the purpose of main-taining defensive position. If his foot leaves the floor in an attempt to dis-lodge his opponent, it is a foul immediately.
(5) Incidental contact with the hand against an offensive player shall be ignored if it does not affect the player's speed, quickness, balance and/or rhythm.
So, no you cannot go and hit the ball carrier's hand to steal or block a shot, that would be a personal foul.
When the hand is touching the ball it considers as part of the the ball, meaning that hitting the hand while it is on the ball isn't considers as foul.
Here the source from NBA.com - Explaining the NBA’s Most Misunderstood Rules
Incidental Contact: The mere fact that contact occurs does not mean a foul has been committed. Players are allowed to contact other players when reaching for a loose ball, or when performing normal offensive and defensive movements. The hand is considered “ part of the ball” when it is in contact with the ball and contact with a players hand when it is in contact with the ball is not a foul.
k. A technical foul, unsportsmanlike act or flagrant foul must be called for a par-ticipant to be ejected. A player, coach or trainer may be ejected for: (1) An elbow foul which makes contact shoulder level or below (2) Any unsportsmanlike conduct where a technical foul is assessed (3) A flagrant foul where unnecessary and/or excessive contact occurs
Marginal/Incidental Contact: While some contact may occur during a game, it does not mean a foul has been committed. Contact which is incidental to an effort by a player to play an opponent or to perform normal defensive or offensive movements should not be considered illegal. Players are allowed normal body contact with opponents when reaching for a loose ball if they both have the same opportunity to get the ball. This type of play shall be ruled incidental if neither illegally gains an advantage. The hand is considered “Part of the ball” when it is in contact with the ball. It is not a foul if a defensive player makes normal contact with a players hand when it is in contact with the ball.