What ball flight law is primarily responsible for controlling the distance of putts?

The primary law of ball flight that controls the distance of putts is centeredness of contact. When a putter strikes the ball at its center, it ensures that energy is efficiently transferred to the ball. This results in a more consistent distance and trajectory, as a centered hit maximizes the ball's forward motion and minimizes the chances of skidding or being mis-directed.

Factors such as angle of approach, speed of the stroke, and the type of putter certainly influence the way a putt is made, but their impact on distance is secondary to the necessity of striking the ball cleanly in the center. For instance, if the putt is struck off-center, it can lead to inconsistent distances, regardless of how smooth or fast the stroke may be; thus, centeredness of contact is fundamental in achieving the desired putt distance.