A fractional calculus approach for the evaluation of the golf lip-out

Abstract

Golf is a sport in which competing players need to introduce the ball into the hole using the fewest number of strikes. However, this goal can sometimes be compromised when the ball suffers from lip-out phenomenon, that is, when the ball surrounds the hole’s edge without dropping in. Although some techniques may be presented in the literature to assess golfers’ performance (e.g., evaluation of the ball’s final position to the hole), none takes in consideration the putting lip-out. With this in mind, this article proposes a correction metric based on fractional calculus that considers past events in ball’s trajectory, thus slightly increasing player’s performance when putting lip-out occurs. On the opposite of integer derivatives which are considered as “local” operators, fractional derivatives implicitly have “memory” of all past events being well suited to describe the dynamic phenomena of ball’s trajectory. Therefore, this novel correction metric will provide a new virtual position of the ball based on its trajectory induced by the putting lip-out. This metric was evaluated analyzing the performance of 10 expert subjects who performed a total of 30 trials, with the lip-out occurring in 29 out of the 300 considered. Experimental results show an average improvement of 19.6 % in trials where the lip-out occurred and an average overall improvement of 1.82 % in player‘s performances, when applying the correction metric.