Yes. If in the Official Scorer's opinion, the batter would have been out at first base had the fielder chosen to make that play then the play is scored as a fielder's choice. The batter reaches first base safely, but is not credited with a hit and is charged with an at-bat. He's officially 0 for 1 on that play.
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I AM A COLLEGE BASEBALL PLAYER ALL INFORMATION HERE IS 100% TRUE. A fielders choice does not count as a hit for the batter even though the batter reaches base safely. It counts as an out for the hitters batting average but RBI's, runs scored, stolen bases and any other effects of the batter reaching base safely count. In essence a fielders choice counts as an out because the fielder could have chose to get the batter out or another runner which means there was an out on the play. Also, you cannot assume a double play even if the ball hit was the easiest 4-6-3 which the fielders made an error on.
A fielder's choice is just like an out and lower's a player's batting average since the fielder chose to put out another player instead, usually the lead runner... On the other hand, a sacrifice does not count against the batter because his intention was to advance the runner at his own expense.
It was 26 pitches
There is no playing restrictions on what a center fielder may do defensively that other fielders may do.
No. Walks do not count toward batting average. If you get a walk in your first at bat, you will still be 0-0.