dropped bat

[t2nyval]

Please clarify, an inside pitch, batter ducks to avoid being hit and as he's ducking he lets go of the bat. As soon as his hands come off (instantly), the inside pitch hits the bat. Is this a ball or foul ball (it landed foul). I called ball due to him not having contact with the bat when the ball hit it. Did I get it right? What if the ball goes fair? still a ball? I think so but want clarification. Thanks -Tony