When does an umpire throw a ball out of play?

MLB Rule 5.08 states: "If a thrown ball accidently touches a base coach, or a pitched or thrown ball touches an umpire, the ball is alive and in play. However, if the coach interferes with a thrown ball, the runner is out."

MLB Rule 5.09(g) states: " A pitched ball lodges in the umpire's or catcher's mask or paraphernalia, and remains out of play, runners advance one base; If a foul tip hits the umpire and is caught by a fielder on the rebound, the ball is "dead" and the batsman cannot be called out. The same shall apply where such foul tip lodges in the umpire's mask or other paraphernalia. If a third strike (not a foul tip) passes the catcher and hits an umpire, the ball is in play. If such ball rebounds and is caught by a fielder before it touches the ground, the batsman is not out on such a catch, but the ball remains in play and the batsman may be retired at first base, or touched with the ball for the out. If a pitched ball lodges in the umpire's or catcher's mask or paraphernalia, and remains out of play, on the third strike or fourth ball, then the batter is entitled to first base and all runners advance one base. If the count on the batter is less than three balls, runners advance one base."

If a pitched ball strikes an umpire the ball is in play. If a pitched ball lodges in the umpire's mask all runners advance one base.