Here is my proposed logo for you: every sport is represented with a ball graphic, within an all-encompassing emblem logo. In addition, the balls could be used on their own, throughout your site and/or catalog to designate the specific sport sections.
As promised, here is the alternate idea I came up with. It implies baseball (and all sports for that matter) without having actual balls in the design to hold you back in terms of size issues (balls not reproducing well at smaller sizes)