Which ball flight law has the most influence on a golfer's ability to control the distance of their putts?

The correct answer focuses on how the centeredness of contact significantly affects a golfer's ability to control the distance of their putts. When a golfer strikes the ball with the center of the putter face, it results in a more consistent interaction between the ball and club. This center contact leads to a more predictable transfer of energy from the putter to the ball, allowing for better distance control because the putt will roll more smoothly and evenly.

If the ball is struck off-center, it can lead to mis-hits that affect both the speed and direction of the putt, often resulting in inconsistent distances. Therefore, ensuring centeredness upon contact helps maintain the desired distance control throughout different greens and conditions, which is crucial for effective putting.

While the other factors, such as the path of the putt, face angle, and launch angle, do play roles in overall putting performance, they do not specifically influence distance control as directly as centeredness of contact does. These factors affect characteristics like direction and spin but not the energy transfer as critically as making contact with the sweet spot of the putter face.