The shoes have zero support.  I've been a runner for 10+ years (cross country team in high school and I compete in road races) and I have rolled my ankle on more than one occasion.  If you do use the shoes for running, they are only good for running on a treadmill or track because of the design of the bottom.  If you run outside, especially on trails, little rocks tend to get stuck between the grooves on the soles of the shoes.  it makes it really uncomfortable and annoying.  I had to pick rocks (some which are pretty large) out every time I used them.  I don't use these shoes for running at all anymore.  I'll use them if I'm bike riding or going to the store, but that's about it.