If the ball took a bad hop and hit the fielders glove and then hit the fielder, there would not be an error and the batter would get credit for a hit. However if the fielder had the ball glance of the heel of his glove and come up and hit him in the face because he misplayed it, it should be scored as an error. To answer you question. Like any hit/error decision, this is soley up to the decision the Official Scorer makes. It is his job to determine whether the play should have been handled correctly and recorded an out, or if, the batter deserves a base hit.
** In MLB an injury will not stop the play until the play is over. i.e if an outfielder rolls an ankel going over a ball, they will not stop the play due to his injury, someone else will need to field the ball or all runners will score and then the play will end
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In this case were the ball was directly hit at the second baseman, it would be considered an error because if the ball is playable in your area and could have been made into an out and you deliberatly or accidentaly missed the ball and was unable to make the out, that is an error. A hit is when the ball is hit to a place in the feild were it is not easy to be played or near anyones area and you safely get on base.
In the books it would be considered a hit because it wasn't a routine play. If it were hit hard directly to a player and it bounces out, that would be considered an error because was easily playable.
This would be a hit assuming the ball was fielded and caught cleanly. If a play is so close that a 1st baseman has to stretch to make the out, then it will be a base hit if the runner is safe, even if he stretches off the base.
Now if the ball was bobbled when fielded or the throw was off and pulled the 1st baseman off the bag because of a bad throw, then the fielder would be charged an error and no basehit given, if the batter would have been out on a properly fielded or thrown ball