Flat serve geometry

The difference between good and fantastic ability to serve in tennis makes the practical difference between top pro tennis doubles players. The best doubles player in recent ATP Tour Finals in London, Henri Kontinen, is a good, even the best example of it.

Especially in doubles, the second serve makes the difference. Always the serving team is clear favorite winner of the rally when the 1st serve is in (even over 80% probability). When forced to serve 2nd serve the question is how dominating position you have after that. The start position of not-receiving player of the receiving team may reveal the expected outcome.

Henri’s 2nd serve is almost as good as first one. The receiver’s chances to score, even bypass the John Peers (on net) remains minimal. Some double faults are not remarkable when he may still trust on next serves. Henri even served one match in London without giving a single point to the opponent on his serves. And I guess his serve was not broken any time in the Finals (or was it?).

Henri’s ability to variate spin is great. Also as 191 cm tall, he has courage to use almost flat serves. When a fast serve has no top spin at all, its trajectory can be simplified to a straight line. If we presume that the contact point of the ball with the racket is at height of 1.5 times the height of the player¹, the height becomes crucial when choosing to use flat serve. If we draw the lines from the serve contact point to the top edge of the net and the back line of the serving square, we are able to limit the area where the successful serve should be targeted. With simple triangle geometry, the following numbers disclose the advantage of a tall server:

  • 180 cm tall player’s target area is approx. 3 cm area above net on middle of court
  • 191 cm (Kontinen) -> margin is 9 cm
  • 200 cm ->  margin is 14 cm

Although the presumptions are strongly simplified the message stands: the relative height of the target area multiplies when the server has advantage of being tall.

¹http://www.popularmechanics.com/adventure/sports/a2072/4221210/

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