I've never worn mine during sports, but I have worn it during a convention where I was serving/acting in a high-energy dinner-theatre. I was bouncing, jumping, singing, running and playing tag. On the Saturday of the convention, I did 4 hours of panels (basically, teaching, but my style is high energy, with me jumping from chair to chair behind the panelists' tables to illustrate points and talking loudly enough for a whole room to hear and doing walking demonstrations to "walk like a boy" and "walk like a girl" because the bioboy doing the crossplay panel had broken a leg) and then 5 hours of the dinner-theatre thing (see above for what I did there) and then an "impossible positions" contest which consisted of (fully clothed) imitating impossible sexual positions from Japanese comic books (manga) where I took 3rd place.
I wore my binder through all that.
I have lung damage because I had pneumonia as an infant and my lung development went awry.
I had no breathing difficulties at the end of the day (which started at 8 am and went until 3 am the following morning) and no bruising.
I have done the same thing with the "bandage" method of binding--nearly died from that. I recommend ONLY attempting the binders/compression shirts, personally. The bandages left me bruised for weeks and my breathing was damaged for weeks after the bruising cleared.
I use an underworks
Double Panel Compression Shirt and am relatively small chested. I would recommend it to others.