Related rules:
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Rule 4 Sec. 6 Courtesy Runner: The player in the batting order where the last out was recorded or any player not currently in the game may replace the current (the player physically playing the position when the 3rd out was recorded) pitcher or catcher as a courtesy runner at any time. The pitcher or catcher will remain in the game and the courtesy runner will retain all substitution rights (if the courtesy runner has substitution rights). A player can be used only once per inning as a courtesy runner. Should the player that made the last recorded out be on base for any reason or is the pitcher or catcher, or batting or has already been a courtesy runner in that inning; the new courtesy runner would be determined by going back previous outs to the next allowable courtesy runner or to any player not currently in the game. If in the first inning a courtesy runner is used for either the pitcher or the catcher (who are listed in the line up when the line ups are turned in) and there are no outs recorded, the courtesy runner will be the player furthest removed from the pitcher or catcher needing the courtesy runner or any player not currently in the game.
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Quote:
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Rule 7 Sec. 3 No baserunner shall be removed from the base she is occupying to bat in her proper place. She merely misses her turn at bat with no penalty. The batter following her in the order becomes the legal batter.
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relevant case play:
Quote:
4.6 FP, 4.10 SP R1, a courtesy runner, who was the last out, is on third base and due up to bat.
Ruling: Coach has following options: 1) Courtesy runner remains on base, and loses turn at bat with no penalty, and next batter is batter following that position. 2) Courtesy runner may be replaced on base by the player being run for, and then taking their turn at bat. (See also Rule 7.3)
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Your local NSA is applying the rules properly.
When reading/searching the NSA rulebook remember that it includes sections for slow pitch, fastpitch and many other sub-sets (for church and industrial leagues for example). Make sure you are reading the proper section.
The rule book and case book can be DLed free from playnsa.com.