Note that it is wrong to think that David was at a disadvantage. I know that is not how the story is taught today, but slingshot troops of that age we the snipers of their age: very deadly (not at the range of a modern sniper, but...).

If the fight between them was started at some distance, the David should have been the expected winner by pretty much everyone on the field. Think "bright a club to a gun fight" sort of vibes.

David had a sling, not a slingshot. They are very different tools. slings need more skill, but are easy for a shepard to learn. (I suspect more powerful as well but I'm not an expert)