Really doesn't matter which arm you put your shooting sleeve on, although some Basketball players like to put it on their right hand if they are right-handed, or thier left if they are left-handed.
Try it with both and see.
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you put the shooting sleeve on whatever arm you shoot with, if you are a righty put it on your right hand if your a lefty put it on your eft hand. the wide end goes up by your shoulder and the thin side goes by your wrist.
i just wear one on my left all the time but either one it really don't matter some people wear one on both arms