Wright himself admitted he was trying to get a good secondary lead so that he could score from 2nd on a double. If with two outs in an inning where he is running on contact, he is concerned about scoring from 2nd on a double, that should tell you all you need to know about how "fast" Wright is.
“That's why I more like dove, jump backed to the bag vs. slide, because it caught me off guard," Wright said. "I didn't think my lead was that big and I panicked, I just jumped back. My initial reaction was 'don't get picked off.' That's the last thing I wanted to do. If the ball's hit hard — I wasn't going to try to score like other hitters would on a single, I wanted to make sure I had a good enough secondary where if it's a double, I could score. But that's what I did, I jumped back to the bag, and I just happened to land on my arm the wrong way. One of those things at first, I was thinking the worst, I was thinking labrum because of the way I felt, but I'm glad that it's not.”
http://www.bostonherald.com/sports/red_sox/clubhouse_insider/2016/08/steven_wright_hurt_shoulder_pinch_running_replaced_by_clay