First, let’s establish that games (at least ones with DoF settings) generally work by only drawing what you’re looking at. Whatever is “behind” you (or even just out of view to the sides) is not being drawn until you turn that way. By not drawing most things, this makes what the computer does have to draw faster (higher FPS) since it doesn’t have to constantly draw the entire world, and can focus only on what you’re looking at.
With the DoF setting, the game does not have a “blurry” version of everything that it just switches to because that would be way too complicated, especially if it’s a good/true DoF that has levels of blur that fall off into the distance. Instead, what the computer has to do is still draw everything that it normally would (i.e. the clear version) and then add the blur on top of that based very specifically on where you’re standing, the direction and angle you’re looking, the amount of light, etc. In almost all cases, especially in any first person type game, DoF being on is adding work, not taking it off, which will always reduce FPS as there is by definition more work to do per frame.
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