Not much else to add here. What lens are you currently using? If a zoom what focal length is it mostly set to?
It will be expensive, but getting a prime telephoto lens with a wide aperture will help. Others can be more help, but maybe something like the 200mm f/2.8 or 135mm f/2.8. A 3rd party lens like Sigma will save you some money.
At night in a sports stadium using ISO 800 at f/2.8 will get you a shutter speed of 1/250. Kinda slow for what you want. ISO 1600 at f/2.8 will get you a shutter speed of 1/500. Thats better.
If you have just a basic telephoto zoom, chances are its widest aperture at the longest focal length is f/5.6. (Guessing that its 200 or 300mm) That f/stop at ISO 1600 will get you a shutter speed of about 1/125.
Maybe pushing the ISO to 3200 might help? Others on the board with Canon dSLR's will have a better clue on that. I don't know how it will effect fast moving objects.