New Official (Almost) with a Question

[FeetBallRef]

Originally Posted by AtlUmpSteve

If the batter hits an out-of-the-park home run, it is a dead ball with all four bases awarded. If the outfielder throws his glove to knock the home run down, or a fan reaches over the outfield fence to keep the ball on the field, it is still a dead ball with all four bases awarded.

To understand the intent of the rule is that if a fan touches the ball, it is dead. If a batter throws his glove and hits the ball, it is dead. If the ball goes over the fence, it is dead even though it hasn't touched anything yet.

It appears that the first two deal with hitting something while the last one (the fence) deals with a plane boundary (like the goal line in football or a foul ball while in the air), are these correct assumptions on my part?