how much better are the fills on NYSE when using a floor broker route than without a floor broker? how pronounced is this advantage at the close as opposed to other times of the day?
Most orders on the close are MOC, so all your Floor Broker does is drop it on the book. The ONLY advantage of a broker is if it is after the "MOC" cutoff and you are on the opposite side of the order imbalance. The NYSE is really just a landmark building now, not much is executed on the floor these days.