Among the many features added in yesterday's GTA 5 update are new settings options. One of the most notable is the ability to adjust the "deadzone," for both first-person and third-person gameplay. Thanks to fans on Reddit, you can see the third-person deadzone setting in the above screenshot.

The deadzone, if you're unfamiliar with the term, refers to the amount of time between when you move the analog stick and when movement on the screen actually begins. If you've noticed a tiny delay while aiming, that's the deadzone.
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Some players thought it was a problem, but apparently Rockstar intended it as a feature, since it's now controlled by a slider. According to the update notes, you should lower the deadzone if you want aiming to be more responsive. It's unclear what benefit a higher deadzone has, if any.
This isn't the sort of thing most people would think about changing in the settings, and some of you might have even wondered what it was when it appeared after the update. The deadzone is more noticeable in first-person than in third-person, which is probably why Rockstar decided to implement this setting now.
Other new settings you can now change include the speed at which you aim or move the camera and whether or not the camera will automatically point ahead when you begin to walk forward. Play with all of these settings to make the GTA 5 controls ideal for you.
Deadzone is a feature designed for arcade games. It's a throwback to the time when analog joysticks used potentiometers (pots). Pots tended to be very noisy and progressively more so over time. So dead zone was created for games where the user could see the amount of noise their joystick had around the center position and increase the deadzone until it extended beyond the noise threshold. Modern controllers shouldn't rely on pots, instead using digital or magnetic hall-effect or in some cases (high end flight controllers) - pressure sensing.
The problem is that arcade game programmers tend to be pretty clueless and set default deadzone quite high. The higher the deadzone - the more the analog control becomes akin to a key-press. In other words - increasing deadzone reduces the sensitivity so you have to push the stick further before the vehicle responds.
What you tend to find is that proper simulations (DCS combat sim or FSX, Elite Dangerous) have zero deadzone by default, whereas the more arcade games like Battlefield set deadzone. Setting deadzone is actually bizarre in this age of digital controllers and even more bizarre when you consider how small the thumbstick is on an xbox controller. Yet arcade game programmers still set high deadzone on games. It's bad design and shows the developer doesn't really understand modern controllers or how damaging deadzone is to gameplay.
If you want high deadzone: just use keys.
I literally just found the true reason for dead-zone. OK, I was about to write this whole thing because you said "Pots tended to be very noisy and progressively more so over time", then I typed in Joystick noise and realized it mean what I thought. On the other hand; I want to remove that confusion, so people who were ignorant like me can understand easier.
Dead-zone is all about joysticks. If you use mouse and keyboard, then dead-zone needs to be off. The joystick looses it's stiffness over time. The ability to return the joystick to the true upright position, and when the joystick just leans a little, it's enough (sensitivity) to make your (cursor/reticle) move slightly. I think COD's dead-zone is zero because as soon as my controller joystick started to wear I had this problem.
Look at your joystick, and think of the words dead-zone. You can make a zone on your joystick that is dead, so when your joystick does that slight lean from being wore out, it will not do anything. if you have a brand new controller, dead-zone should be at zero, but as the joysticks wears more and more, the dead-zone setting will need to be raised more and more. This way you will not have this slight movement when you are not even touching the joystick. All you are really doing is, as you joystick wears, you are telling the game to not register that slight movement.
Go to game and turn dead-zone all the way down. Now go out of settings and just stand there. With your right joystick (most important) slightly rub it to the left, the let go. Does you reticle stop or keep moving? Do this in every direction, one direction might be more worn out than others (racing games). Then go back to setting and bump dead-zone up once, and repeat the process, until you have no movement when you ever-so-slightly rub/push the joystick in every direction.
I've been looking for that thing that truly makes mouse and keyboard better than controller and this is it. it is a problem that every controller person will have to deal with.