[colmack2 (OP)]

Trivial but puzzling: After exercising on my Swiss Ball (on carpet), I stand up and after a few seconds the ball starts to roll. The floor is level. Any hypotheses?

[chris]

Can you post a video?

[Kryptid]

The ball is made of rubber, right? Maybe static electricity has something to do with it. Does it always move in the same direction?

[RD]

...After exercising on my Swiss Ball (on carpet), I stand up and after a few seconds the ball starts to roll. The floor is level. Any hypotheses?

The weight of the air-valve will give it a bias ...

[chris]

...After exercising on my Swiss Ball (on carpet), I stand up and after a few seconds the ball starts to roll. The floor is level. Any hypotheses?

The weight of the air-valve will give it a bias ...

The simplest explanations are always the best, and usually right! Thanks @RD for pointing out the obvious!

[evan_au]

When you stand up, the back of your knees give the ball a slight backwards push?