What is the advantage of a wide lens diameter?

I presume you really are referring to a large (wide) diameter and not a "wide lens".

It will gather more light in a given time, thereby permitting larger apertures for an exposure. Larger apertures will allow faster shutter speeds, which would be useful in sports Photography. I don't know your definition of "wide", but I would guess you mean relative to "normal" for a given focal length. Check out what a Canon 200mm F2 or 500mm F4 lens looks like to get an appreciation for a wide diameter.