The Turks are generally considered to have traditionally produced the bows with the longest range, at least in terms of competition, before the rocket science age. These bows however, would not likely see battle because they were lightened to retract faster and thus prone to self destruction. Bows that have light limbs and thin strings retract to their original shape faster and thus allows the arrow to leave the bow at higher speeds. Draw weight, arrow weight, bow & arrow materials-construction and last but not least a perfectly angled release, all contribute to greater distances. In fact one of the biggest distance gains an archer can achieve is to learn to shoot at exactly 45 degrees.
As for draw weights they are part of the equation, but not the biggest part. Modern materials have outstripped the traditional bows and arrows in terms of stiffness and weight. I would have loved to see one of those great Turkish archers shooting just a modern carbon fiber arrow with razors blades for fletchings, that would have been something.