Analog movement mechanics create more interesting outcomes and are one of the biggest contributers to delightful movement.
With analog movement, precision is key and constant improvement is possible.
As Frosty T. Snowman always says: "I jumped 3.459 units high there. I made it to the platform, but bonked my old top hat. I can do it faster if I jump 3.48 units next time!"
Vary jump heights based on the length of time the "jump" button is held. Scale the movement speed based on how far the analog stick is held. Build acceleration into the movement. How long does it take the player to reach top speed? How long does it take to change directions?
Warning: Tweak acceleration values responsibly as having too much buildup can lead to a game feeling unresponsive.
Example: Vehicle acceleration based on amount trigger is pressed. Vehicle steering based on how far stick is held.
Example: Jump Height based on how long jump button is held.
Example: Power build up based on how fast button is tapped.
In Super Mario Sunshine, Mario can jump to different heights and accelerates into his movement.
In Sonic 2, a range of spindash speeds can be achieved based on the rate at which the player taps the button.