Yes, batsman is a Scrabble word!
...and is worth 11 points in Scrabble, and 14 points in Words with Friends
batsman
Noun
1. (baseball) a ballplayer who is batting
What Scrabble words can I make with the letters in batsman?
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1 Anagram of Batsman
Words that can be created with an extra letter added to batsman:
O:boatsman