Official scorer
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In the game of baseball, the official scorer is a person appointed by the league to record the events on the field and to send this official record of the game back to the league offices.
The official scorer never goes on the field (he typically watches from the press box), and in some cases the person's identity may be nearly unknown.
The official scorer has discretion to make judgement calls about certain aspects of the score that do not affect the final disposition of the game. For example, when a fielder fails to catch a ball in play, and the runner reaches base safely, the official scorer decides whether the ball "should" have been caught. If so, the fielder is charged with an error; if not, the batter is awarded a hit. Note that this decision can never affect the outcome of the game; the runner is safe at the base either way, and the decision of whether the fielder is charged with an error has no bearing on who eventually wins the game. The only effect is on the official statistics for players that are compiled later.
Other decisions that the official scorer makes are the identities of the winning and losing pitchers, whether a relief pitcher is awarded a save, and if so, who gets it, and whether a ball not properly received by the catcher is a passed ball (charged to the catcher) or a wild pitch (charged to the pitcher).
The players on the field all have a number. That way the scorer does not have to write out # 1 batter grounded to the shortstop and the shortstop threw the ball to the first baseman; he can just write 6-3 .
The numbers are: