Compromise between indoor shots and superzoom

Sensor size is a HUGE part of the equation, too.  You'll be shooting ISO 3200+ for indoor sporting events at f2.8, regardless of camera.    And on a tiny little sensor like the FZ200 has, you are not going to like the image quality.

You are going to have to crack open the wallet for indoor sports.   It's not cheap and requires fast lenses and a camera with a bigger sensor.  At least 4/3 size if not APS-C.  The cheapest option is going to be something like a Nikon D3200 (or similar) with a 85mm f1.8 lens.