The potentiometer replies are wrong, but they’re more correct about how it’s generally done in modern controllers.
The N64’s thumb stick was light based, actually the N64’s stick was Digital, it’s not an analogue stick. Inside the N64’s stick there were light sensors and LEDs, and 2 wheels with holes in them. The stick would cause the wheels to rotate and that would block and unblock the light sensors, by counting how many times the light sensors were blocked and unblocked the N64 could determine how much movement of the stick happened. It’s a similar mechanism to how an old school ball mouse worked.
These answer are wrong, it doesn’t use potentiometers, it uses optical encoding disks to determine its position.
As the stick moves it rotates a disk that has gaps in, as the gaps and solid wheel pass a light sensor, it knows that the stick has moved a tiny amount.
[Here](https://www.reddit.com/r/EngineeringPorn/comments/9htfei/n64_analog_stick/) is a great animation that shows how it translates the tiny movement to big rotation of the wheels.
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