Goliath and David ran towards each other (1 Sam. 17.48). We have no idea how close they were when David fired, but it's reasonable to assume he was still out of sword's reach. Obviously, the closer he was, the bigger his target and the more force of his missile.

Walton, Matthews, & Chavalas, in "The IVP Bible Background Commentary: Old Testament" write, "The text offers no information concerning the range between David and Goliath when David took his shot. The slingstone is capable of delivering a killing blow, but only when striking a few strategic areas of the head (which was protected). David’s shot targeted one of the few vulnerable areas that could render his opponent unconscious. This allowed him to approach and secure Goliath’s sword that he then used to kill his unconscious victim."

It seems to me that, militarily and practically speaking, the battle could have gone in either direction. Goliath was well protected and a trained soldier. He had a long-range weapon (a spear). David had a long-range weapon that he could wield with some expertise and precious, but slingshots were common in battle and Goliath had no doubt faced them before. Militarily, it was anybody's victory, but Goliath probably had an advantage. Theologically and spiritually speaking, the battle belonged to the Lord (about which David was quite confident).

Goliath was a melee fighter and needed to be far closer than David would ever allow. David was an expert marksman with a sling and slingers could easily fire a rock as effectively as a gun. We know he had killed lions and bears with his sling and Goliath was certainly a big target. David was prepared to also kill Goliath's 4 brothers too if needed (he picked up 5 rocks as he approached Goliath.)

Note: David chopped off Goliath's head after he killed him. The prize for his efforts.