As a subject matter expert in the history and rules of tennis, I can provide an explanation for the scoring system that uses the numbers 15, 30, and 40. The scoring system in tennis is indeed unique and has historical roots. It is believed to have been influenced by the clock face, where the quarter movements of the hand were used to represent the score. When the hand moved to the three-quarter position, it signified a score of 15, to the half position for 30, and to the three-quarters-to-full position for 45. When the hand reached 60, the game was over. However, to keep the score within the 60 "ticks" on the clock face, the 45 was adjusted to 40. This adjustment was made to ensure that the server would have a chance to win the game before the receiver could achieve a score that would be too close to winning the game outright. So, the progression from 0 to 15 (one quarter), then to 30 (half), and finally to 40 (three-quarters) reflects the movement of a clock hand, with the 40 being a modified version of the original 45 to fit the scoring paradigm. read more >>

However, the origins of this convention remain obscure. It is possible that clock faces were used on court, with a quarter move of the hand to indicate a score of 15, 30, and 45. When the hand moved to 60, the game was over. ... To make the score stay within the "60" ticks on the clock face, the 45 was changed to 40.read more >>