First, learn to shoot with back button focus. If you are going to be shooting sports primarily, the sooner you get that done the better. It will take a little while but it will become second nature fairly quickly.
Second, for the problem you describe, the issue is that the camera is tracking the background too long before changing over to the player on the fast break. You need a greater sensitivity not less. Try 0 first and then perhaps a +1 depending on the sport and situation.
Next, if see that you are not focused on the player you want, put the focus point on the player and "Bump Focus". Bump focus is when you let off the back button (focus) for just an instant and then push it back in just as soon as the focus point is where you want it. That will expedite the re-focusing on the player you want to shoot. In basketball, players are often obscured by other players or the refs temporarily. Learn to bump focus.
Surrounding focus points? I use a few depending on the detail/contrast available to focus upon in the uniforms. A very dark, solid color, uniform may be hard to focus upon unless there is an area of contrast visible to the focus point.
Last, remember that the better your skills are at keeping the focus point exactly where you want it, the less you will need the camera body to guess what you want it to do.