How does mario jump?

How does mario jump? that definitelly doesn't seem like a hard question, anybody would simply say, just add a gravity value every frame, this should make him go up and down.

And to be honest that is probably what 99% of the people do, but today I discovered the most amazing thing, I discovered that that 1% was Mario!

believe it or not mario doesn't simply do that, and perhaps this is the little detail that lets all of us realize that most of the games we play are not exact remakes.

below you will find the graph that proves that the jump is not a simple parabola. at the moment I am trying to figure out how to recreate this exactly.

Notice the ladder that the jump creates, my initial idea is that this is a variable that every couple of seconds boosts itself up if you are still pressing the jump button. this explains the different heights you can jump with mario.

And in case you were wondering, I was able to calculate this by importing a recorded run into Adobe Flash and then measuring the distance per frame.
Also notice that mario didn't update every frame, I really don't know what this means.