Funny you mention badminton since that's my sport.

I've been suffering from TOS on my right side for four years and just had the rib resection 12 days ago. This TOS had caused me to give up a lot of things that I enjoyed. About a year ago I said be damned with it, I was frustrated that my lack of activity was adding to my overall downward spiral of well being. I decided to try badminton again, something I hadn't done for a few years. Much to my surprise it didn't add to my TOS pain.

Although many tasks and movements are very difficult (computer, shopping cart, etc) I found badminton doesn't cause me any pain, in fact, it helps by keeping me in shape. Nothing better for the body and mind than to get a good sweat going. It did nothing to alleviate my TOS symptoms but didn't add to them.

I don't understand physically why badminton doesn't hurt. I'm left handed, so play with my left, and have right side TOS. I'm sure if I was right handed it wouldn't be possible to play.