Hi, Schnitzl,
I started into the hobby with a Powershot and I had exactly the same problem. I thought it was a bad camera. After getting more into photography through books and web research I at least understand what was going on.
You are not getting enough light into the camera to give you enough shutter speed to deal with 1.) camera shake, and 2.) subject motion blur.
Camera shake is just your hands jiggling. This is magnified when you are zoomed in, and these Powershot cameras have crazy long zoom. If you want to know how this works, get a laser pointer and point it at a wall that is 1 foot away from you. The red dot will be nice and steady. Then try aiming it at a wall that is 50 feet away, and you will see that the dot is jiggling all over the place. Same thing when you're trying to take a picture of something when you are zoomed in like a telescope. That makes blur in your photos. You need a very fast shutter speed to freeze the image the more it is zoomed in like that.
The other kind of blur is subject motion blur. You say you're shooting sports, so I assume that people are moving in the pictures. The cure for that is also having a high shutter speed to freeze the action.
The problem with your camera is two things. One is that the lenses on a PowerShot camera do not let much light in compared to a wide aperture DSLR lens. The other problem can come from shooting in automatic modes. The camera may not always pick the best combination of shutter speed, aperture, and ISO to make a tough picture come out right.
Set your camera to TV mode. Then set a high shutter speed. If I have time I will try to look up the equivalent between an SX 50 zoom and a normal 35mm lens focal length. The rule of thumb is on a full frame 35mm equivalent camera, you need a shutter speed that is the inverse of the focal length of millimeters. In other words if you have a 200 mm camera lens, you need to be shooting at 1/200 of the second shutter speed to stop Camera shake blur. If you're shooting action however regardless of what ever focal length you're using, you need to set a shutter speed is fast enough to stop the motion. For most sports that would be about 1/400 to 1/640 of a second.
Does that help answer your question at all?
Scott
Canon 5d mk 4, Canon 6D, EF 70-200mm L f/2.8 IS mk2; EF 16-35 f/2.8 L mk. III; Sigma 35mm f/1.4 "Art" EF 100mm f/2.8L Macro; EF 85mm f/1.8; EF 1.4x extender mk. 3; EF 24-105 f/4 L; EF-S 17-55mm f/2.8 IS; 3x Phottix Mitros+ speedlites
Why do so many people say "FER-tographer"? Do they take "fertographs"?