There is no DPI for analog.
Analog says everything, it calculates the X Y axis of the controller like, lets say for every axis 360 is max, you have 360x360 points where your stick can be also the 0x0 which is center.
It calculates where your analog stick is currently at. https://electronics.howstuffworks.com/joystick3.htm
I ask the question because I couldn't get specification of controllers.
I believe joysticks have various quality of sensors. Xbox one controller might read increment 0.1 degree (it might read 88.1°, 88.2° etc) while xbox 360 controller might read increment 1 degree (it might read 88°, 89° while cannot read 88.1°). And cheap controller might read like increment 5 degrees so feel unsmooth. Do you mean all joysticks have same precision each other from cheap to expensive?