I shot a fair amount of sports with the D1h and the D2x, cameras with only moderately-sophisticated, yet pretty capable AF modules "for their era". Using a user-selected, group AF approach was the best producer for me with the 70-200 VR I, and the various other lenses I used. "sometimes" center point-only AF was not very good, and besides, a LOT of the time, I want the focus to be a little ways off to the side of the center of the frame, or in the top 1/3 of the frame and NOT in the middle.
One thing I can tell you is it pays to really understand, as in totally understand, exactly HOW the camera is actually designed to work. For example, the Nikon term "lock-on"; chances are good you have it set wrong. Chance are good that 90% of users set lock-on incorrectly. Many people think it means the AF system will lock-on FASTER if they set the delay to the shortest option....but NO, what the lock-on interval does is sets the delay for seeking new focus points when the target is lost or when something intervening comes into the field of view.
Many people will go through the custom function menu and not have a fricking clue on how the camera actually works, or could work, so they stick it in center-point and throw away the camera's amazing AF ability and instead of using multiple data points to compute focus and rate of target speed, they throw all that out and use it like it's an old Canon, where ONLY the center AF point is reliable...big mistake much of the time. Not "always", but for a less-experienced user, it can actually help a LOT to allow the camera's AF module to actually acquire,lock, predict,and track focus.
Apparently, the way you are doing it now is not working. If you are in single-shot AF, you'll have nothing but headaches.