What is the method called when you point a shotgun at a moving target and pull the trigger when you think the target will be?

The method you describe involves anticipating the movement of a target and pulling the trigger at the right moment, effectively leading your shot to where the target will be. This technique is known as "lead shooting."

In lead shooting, a shooter must account for the speed and direction of a moving target, estimating where the target will be when the shot reaches that point. This allows for better accuracy since a moving target will not be in the same spot when the projectile arrives.

While various terms apply to different shooting techniques, snap shooting refers to taking quick shots without extensive aiming, and follow-through involves the continuation of the shooting motion after the trigger has been pulled to ensure accuracy and control. Swing shooting pertains specifically to the smooth motion of the shotgun along the target before firing. None of these other methods focus specifically on anticipating and leading the moving target as lead shooting does.