Our perception of distance is highly reliant on the specific way in which the image of the target enters and lands on the receptive field in the back of the eye (called retinal disparity). A closed stance aligns the head in a way that diminishes this effectiveness. As one's stance opens up the head typically turns more toward the target which enhances depth perception.
At close range this is not much of an issue for two reasons. First, the image disparity is greater which allows accurate calculations even if the image is not entering at an optimal angle. And second, the trajectory of the arrow is less critical.
As distance increases, there is less disparity and accurate calculation becomes more difficult, especially if the image is entering the receptive area at an angle. Also, we now have the added problem of increased trajectory.
Research has shown that subjects facing an object are good at accurately guessing distances out to 40 yards. After that distance accuracy begins to quickly diminish. When we turn our heads at an angle, accuracy drops proportionately.
An analogy would be the old 35mm camera lens. Focusing (depth) is easy (large movements of the focus ring) at close ranges and becomes increasingly more difficult (more minute chances of focus ring are required) as distance increases until one reaches a distance where "infinity" is hit and all images beyond that point are in focus.
Did I explain that well?