A different approach. Try to get a picture showing the ball from the top (As close as you can get). Use a projection node to project this from straight above onto a sphere (Keep the default UVs that are created by Maya for the sphere.) and bake it out. That will give you an idea of what the lines should look like for the top half of the sphere. The bottom half of the sphere is a mirror image of the top in the x and y axis with the colors swapped.

Tinker with that in Photoshop using paths and you should end up with something close to what you are looking for.

I did notice that there is a lot of logos and writing on the ball including the top and bottom. The standard spherical mapping is going to bite you there. The top and bottom have the most distortion.