Trig in Tennis!

Many sports are heavily influenced by the power of probability, mechanics and general arithmetic and none more so than tennis! Here are four ways that mathematics is weaved into Wimbledon (and every other tennis tournament).


With over 100 players or teams in each of the men’s, women’s and doubles tournaments, and each match lasting on average two to three hours, clearly the scheduling for a grand slam tournament requires some serious thought. As is often the case, the logic behind this serious thought is in fact just maths. To reduce the number of matches played, most tournaments follow a knockout structure. This restricts the number of competitors to the values in the sequence of the powers of 2, the power to which 2 is raised being how many rounds will then be played. For example, both the men’s and ladies singles competitions at Wimbledon consist of 128 players, and so the tournament will have 7 rounds and 127 matches (each match has exactly one loser, every player but one will lose exactly one match).


Every tennis player and fan will be well aware of the importance of their first serve. Top players will serve at over 100 mph and the very best will be able to do so 75% of the time. In order to perfect this art, mathematics, and more specifically mechanics, is extremely useful. By determining the distance from an extended arm with a racket to the opposite serving line, and the angle required to get over the net, it is possible to calculate the exact optimal angle of projection whilst also taking force into account.

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Hawk-Eye is one of the most sophisticated advancements in modern sport, combining techniques from statistics, geometry and physics to process an image and then predict its position in a chosen frame. In tennis, clearly this is the frame when the ball is going to hit the court. This is done using several cameras placed at different angles that record the ball’s position at high speed. A computer that is programmed to recognise the ball then calculates its position within each frame. This is done continually so that Hawk-Eye can build a picture of the ball’s 3D projection and hence its position in the crucial frame.


The scoring system in tennis is somewhat unorthodox compared with other sports. Each match is broken into sets, the sets into games and the games scored through the bizarre points structure of 15,30,40. Though seemingly illogical, this unique system has quite an impact on the result of the game. It’s possible to win a match despite losing more points than you win but it’s from this that the game gets its excitement. Comebacks are more likely and it also gives some points far more importance than others, keeping the players under pressure and spectators on the edge of their seats!

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