This is how I do it. In my opinion, in sports photography, there are two main things to consider to achieve the result you want in your photo: Do you want to completely freeze the motion, or do you want to capture some motion blur? For example, when shooting karate—if I'm photographing a kata—there’s often a moment when the person's body is still, but their hands or legs are moving very fast. In these cases, having some motion blur in the moving parts is perfectly fine. It helps convey the action.
Here’s an example where the subject’s face and part of the body are sharp, but the kicking leg is blurred.
To achieve this, I set the camera to Aperture Priority mode, selected an aperture of f/2.8, and let the camera calculate the shutter speed and ISO. In this case, the shutter speed was 1/320 and the ISO was 1250. A shutter speed of 1/320 isn’t fast enough to freeze the motion of his leg. I could have used Manual or Shutter Priority mode with the same 1/320 shutter speed, but using Aperture Priority allows me to control the depth of field and achieve a better blurred background.
From experience, I know that using the EF 70-200mm f/2.8 in Aperture Priority mode, under the typical lighting conditions at these competitions, usually results in a shutter speed that isn’t fast enough to freeze the action. This is why it’s so important to know your lens and its capabilities.
When shooting fights I love to freeze the image and in that case I set the camera to use Shutter Priority Mode using the speed of 1/800 to 1/1200 with Auto ISO. In very little occasions I set the speed at 1/2000. All depends on how bright is the room where I'm shooting.
Here is a picture using these settings.
In this case, the shutter speed was set to 1/1000 to freeze the motion. The ISO ended up at 12,800, which years ago was considered high and often resulted in noisy images. However, thanks to applications like DxO PureRAW and the camera’s excellent dynamic range, this is no longer a significant issue.
Here is another example where I used a shutter speed of 1/1250 to totally freeze the image.
I see many professionals using Manual mode when shooting sports, but I don’t find it comfortable to adjust three settings while photographing such fast-paced action. What works for me is either Aperture Priority with Auto ISO or Shutter Priority with Auto ISO. Manual mode with Auto ISO is another option, but I prefer using the C1 to C3 custom modes. These allow me to quickly switch between Aperture and Shutter Priority modes, each preconfigured with the aperture and shutter speed I plan to use throughout the event. That's my last trick, use the C# custom modes.