If you are only skidding on one side you should have 17 skid patches for a full rotation of the crank. Just as you said. If you were skidding on both sides you would actually have 34 patches, but skidding on both sides only adds patches if you have an odd number of patches. Why you only have patches on half of your tire is probably a matter of chance.

My ratio allows for only one skid patch so if I do have to skid I rotate the wheel after riding. Fortunately this comes up very rarely.

edit: I'm pretty sure I got the doubling thing wrong. As I said I have one patch but it will stay as one patch even if I skid on both sides. So pretty much ignore everything I said and go find one of the old threads to find out about this stuff.