That baserunning play is like when you're at a yield sign with a car in front of you. You're watching the traffic looking for openings and not necessarily paying attention to the car in front....you see an opening in the traffic and you assume the car in front will go...so you tap on the gas before looking to see if that car went.
I think Cozart was thinking why the heck Ludwick didn't go to third when that ball got away from the catcher.