Power and Influence

In some RPG settings the power and influence level available to the characters is fairly fixed.

Power level is something that’s largely controlled through the system mechanics that are available to the players whereas the influence level is more associated with the actions of the characters and the constraints of the story.
When you kick off a new campaign or set out to play a shorter term game the group will set what the Power and Influence levels will be going in.  As a campaign develops though the opportunity is there to revisit those levels either through organic change or through a larger step change.

Give us an example Dave!

Ok so to give an example I’m going to choose the journey that Han Solo has in the Star Wars movies.

Power level - At the start of the movies Han is a smuggler and a pretty good one at that, sure he’s had some bad luck and made some poor choices but he’s good at being a smuggler.
As the story moves on his power level really doesn’t change that much, sure his “abilities” and “skills” develop as time moves on in the movies.  This is organic change within Han’s power level.
Influence level – At the start of the movies Han is a smuggler who is down on his luck and so his influence level both within the smuggling world and elsewhere is pretty low.
As the story moves on and in particular what happens in between each movie his influence grows in larger steps that what would be normal.  There’s an obvious reason for this, he’s Han Solo and a lead character in a plot.  He moves from being a smuggler with a tarnished reputation to a General in the Rebel Alliance in the space of a few years.

Ok so that’s an Influence step change with a Power organic change.  Can it work the other way? Absolutely.

Superman is an interesting character to walk through this with.

Power level – This continually grows with every day that he spends on Earth.  He gets stronger, faster, smarter and just better overall.  Arguably this is actually an organic change but it’s only organic because he’s Superman.  In any other scale it would be a step change of power level growth.  The largest step is as he’s growing from a child to a man but it doesn’t stop there.
Influence level – From the first moment that he wears the costume to several years later his influence does grow but it’s such a gentle organic growth that it’s almost negligible.  That’s largely offset by the fact that his influence is so high from the starting point.

Which other characters can be used to demonstrate this?  Plus which characters have their Power and Influence scaling the same way?