My rule of thumb is to blow the whistle when the injury would interfere with play, unless it is a severe injury, then the whistle is blown immediately.
For example, A1 has the ball, B1 steals it and begins a fast break. A1 twists his ankle and falls to the floor. I let B1 finish the fast break before I blow the whistle. If Team B doesn't make a basket on the fast break and go into its offense, I blow the whistle.
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