I consider myself a decent sniper, but when I go into Crucible, I'm wrecked beyond belief. There are guys who headshot me the very second they scope in. It's -blam!-ing ridiculous! I don't understand how they do it!
EDIT: A lot of people are saying that they get their skill from Halo. However, I actually snipe very well in Halo, but not-so-well in Destiny.
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A lot of guys who quickscope out of nowhere are running final round. Half of sniping is just about positioning and reducing your aiming area down to a small manageable area, preferably only needing small adjustments in the horizontal dimension. Skill plays a part, but skilled players know how to stack the odds in their favor. That's part of their skill. Also sometimes you just get lucky. I know sometimes I'll headshot a scrub flying through the air or something. Also you have to sort of have a sense for the center of your screen and be able to place targets there. Practice basically..