Baseball, by the Rules
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Infield Pop Up Not Caught
The batter hits a lazy pop-up that drifts over the infield. The fielders converge underneath it… and then, something goes awry. Either none of the fielders takes charge— each of them assumes one of the others is going to catch it— or too many of them try to take charge, and they run into each other. Or, maybe it's just a day game, and the infielders lose the ball in the Sun. The important part, though, is that the catch is not made. The batter is safe, as long as they run out the play; most pop-ups linger in the air long enough that once they drop, there’s no chance for a throw.
Whether the batter is credited with a hit, or not, really depends on if the defense managed to get a glove on the ball before it fell in. If it’s the classic “no one calls it, and the ball isn’t caught” blunder, the fact that no one actually touched the ball means that no one can be charged with an error1, and that means the hitter winds up with an incredibly cheap single, or potentially more. But if the defense does touch the ball, and it still drops? Almost always an error.