Rules References
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If a fielder catches a fly ball and then falls over the fence it is a homerun.
As long as the fielder is not touching the ground in dead ball territory when he catches the ball, it is a legal catch if he holds onto the ball and meets the definition of a catch. If the catch is not the third out and the fielder falls down in dead ball territory, all runners are awarded one base. If the fielder remains on his feet in dead ball territory after the catch, the ball is alive and he may make a play.
Rules:
2.00 CATCH,
6.05(a), 7.04(c) Official Baseball Rules
The ball is dead anytime an umpire is hit by the ball.
If an umpire is hit by a batted ball before it passes a fielder, the ball is dead. On any other batted or thrown ball, the ball is alive when the umpire is hit with the ball. Umpire interference also occurs when the plate umpire interferes with the catcher's attempt to prevent a stolen base.
Rules:
2.00
INTERFERENCE, 5.09(b), 5.09(f) Official Baseball Rules
The home plate umpire can overrule the other umps at anytime.
The umpire who made a call or ruling may ask for help if he wishes. No umpire may overrule another umpire's call.
Rules:
9.02(b, c)
Official Baseball Rules