Original post by: Conor Bailey ,
Every controller stick has what's called a "dead zone" and that's the area that the controllers position is registered as 0, or no movement. Over time and with use, the sticks idle position will drift out of the dead zone, an indicator of this is if it seems loose and moves easily, and will seem to move position on it's own because the hardware detects the stick is out of the dead zone. There are all kinds of novel solutions, like super gluing elastic bands to the inside to counter the drift and hitting them straight down with a hammer... I don't recommend. Unfortunately, the only real solution is to replace the stick and it's board level hardware, you'll need a soldering iron. Fortunately, [https://www.amazon.com/Epaler-Controller-Joystick-Analog-ThumbStick/dp/B01AJ0BT0K/ref=sr_1_10?s=videogames&ie=UTF8&qid=1495310757&sr=1-10&keywords=xbox+1+analog+stick+replacement|they're quite cheap] I couldn't recommend this particular product because I've never bought one myself, and I reckon you could shop around and get a bargain somewhere.