Learning how to quickscope in Modern Warfare and Warzone is no easy feat, because while quickscoping has been a thing for over a decade, each new Call of Duty game changes up the process somewhat. Back in 2011, the first Black Ops game tried to eradicate quickscoping by changing how the snipers scoped in, but that was swiftly reverted to allow quickscoping as a viable method of playing the game. Quickscoping is once again a popular pastime in both Call of Duty Modern Warfare (opens in new tab) and Call of Duty Warzone (opens in new tab), but for any newbies, here are some tips on how to quickscope in Modern Warfare.
The key thing with learning how to quickscope is crosshair placement. When you're aiming down the scope quickly, you don't want to also be moving the mouse/right stick to adjust your aim. Keep your crosshair around chest-height when running around and if you run into someone, it's a case of aiming down the sights and firing the split second the in-scope reticle appears. You don't want to shoot before you see the reticle, because the bullet won't go perfectly straight; at that point, it's more like a slightly targeted noscope.
If you're trying to quickscope someone running across your screen, learn to lead your shots. Sniping in Call of Duty doesn't have bullet drop, but if someone is 30 feet away and you quickscope exactly on their character model, chances are they'll be past your reticle when you scope in. Leading is when you aim slightly in front of them, to ensure you connect when you fire.
Finally, anticipate flinch. if you get shot at while you're in the middle of aiming down the scope, your aim will shoot upwards. You can counter this by pulling down on the scope right before you fire, which should recenter your aim.
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