The usual implementation of a game port uses a capacitor and a simple voltage comparator. Both together form a sort of simple ramp-compare ADC. This system is polled periodically and reset at precise moments to read an input. This must be done more than 30 times every second to provide a responsive game input. The actual acquisition frequency and value usually depend on the joystick's resistance inside, noise, CPU speed and the total joystick-capacitor's RC time constant.