The Wired article in Geekdad reviews the body structure and alignment required for drawing the bow.
Quote: Now compare the grip; Hawkeye is gripping the bow mostly from the side; his fingers wrapped solidly around the handle, with his wrist off to the side in an attempt to get it out of the way, hence the first arm guard. By contrast, Brady’s hand is holding the bow very lightly, just a couple of fingertips resting on it. The bow is pressed against the base of his thumb, his palm is at a 45-degree angle, and his wrist bones point directly into the center of the bow. This makes for a lot less bow movement and a much more accurate shot.
Quote: Note the lines of force in Jake’s (below) stance; there’s a straight line from his right shoulder to the bow, and another straight line from the tip of the arrow to his right elbow. This is a solid, consistent, repeatable, powerful position. Now look at Renner (Hawkeye,top); his bow arm is nowhere near being lined up with his shoulders, his draw arm is nowhere close to being in line with his arrow. He’s got that weak wrist again. He looks awkward and uncomfortable.
Read the full article at The Avengers:Hawkeye, World’s Worst Archer.