The 40 in
Why the tennis score is 40 instead of 45
In our opinion the most plausible explanation for the “40” instead of “45” finds its origin in the ancient “jeu de paume”. This predecessor of tennis was initially played without rackets and the ball was hit with the palm of the hand ("paume" in French). It was played indoors by the aristocrats whereas the "peasants" played outside.
The serve for the first point was launched from the “baseline”, at 60 feet from the middle line (initially there was no net). With each point won, the player who served was allowed to approach 15 feet to the middle. That way, after three points won, he would be on the middle line. So after two point won, he was only allowed to advance 10 feet.
The scoring in jeu de paume was in simple numbers but the feet indicating the consecutive distances from the “baseline” for the serve can be “translated” into 0-15-30-40.
Jeu de paume gradually evolved into lawn tennis; for which the rules were first published in 1874.
A different theory suggests that the scoring is linked to clocks.
With each point won, the hour hand was moved a quarter of an hour forward. Ancient clock used to have only one hand, indicating the "hours". The "minutes" could be derived approximately from the position of the hour hand. So 0-15-30-45. But to win a game, you needed two points more than your opponent. So when the score was deuce or 45-45, it became confusing to indicate what we now know as the "advantage" for the player who won the next point. That might be why the third point was marked as "40", so they could use the "45" to indicate the advantage.
This French slant influenced even more in tennis. For instance, the term "deuce" comes from "à deux de jeu", because at that point, you are two points away from winning the game. In turn, the zero score we call ‘love’ comes from the shape of that number: the French word "l'oeuf", for "egg".
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