I used my 1DMklll for track and field. I always chose the af point i wanted. Most of the time it was center point but I did move it around depending on composition. There were many times I enabled the assist af points (C.Fn III-8-1) or the surrounding af points (C.Fn III-8-2). I also changed the tracking mode for certain events.
Try manually setting the af point and keep that on your subject. I think you will get better results.
Here are two links to pdf's explaining the custom function and setting up the 1DMKlll.
Ok, I've been fooling around with this and have a question or two. Originally, I had manually selected the center af point and kept that on the subject. C.Fn III 8-2 was set but I didn't get any other focus points to light up-just the manually selected one. I'm not convinced this is correct.
AF tracking was at zero.
If I let the camera select an af point, well, it selects a lot of focus points and usually one or more is the right one. Edit-scratch this. It only applies when using one shot. When using AI and automatic af points, none of the af points light up if I'm reading the information correctly. I'm going to bed and I'll play with this again tomorrow. Much to learn and get used to.