Posted by: zyxo | February 6, 2010

Are Tennis Point Counts Unfair ?

Venus Williams plays Vera Dushevina on the ope...
Image via Wikipedia

Ever wondered about this silly scoring system in tennis ? Me too. I suppose we do not think about the same thing : whether they count 15-30-40 or 1-2-3 does not really make a difference. My concerns here are about the composite system:

  • a game ends at 40+ (or 3+ if you count 1-2-3) if the difference between the two players is 2 points
  • a set ends at 6 if the difference between the two players is 2 games
  • if at 6 the difference is only one game, an extra game is played. This results in either 7-5 or 6-6. In the latter case a tie-break is played. In a tie-break they simply count points up to 7, but there must be a difference of 2. So a tie-break is just a special sort of game.
  • In the last set of the grand slam tornaments tie-breaks are not played. In stead they go on with the games until there is a difference of 2 games.

Now the question : is this a good system ?

But first another question : who wins the match ? Obvious answer : the best of the two players.
OK, but if he is the best, why doesn’t he always win all the sets ?
Or, if he is the best, why doesn’t he always win all the games ?
Or, if he is the best, why doesn’t he always win all the points ?

The answer : variability, noise, variance, standard deviations, standard error, luck, chance …

So let’s rephrase the above.
Who wins the match ? The one who is on average the best in the match (is this true ?)
Who wins the set ? The one who is on average the best in the set (is this true ?)
Who wins the game ? The one who is on average the best in the game (is this true ?)
Who wins the point ? The one who is the best in that point (this is true !)

And : is this a good system ?

Let us look a a game.

a tennis game

tennis quality of the 7 points of a single tennis game

This first chart shows the tennis quality of players A and B during each of the 7 points of a game. Four times player A was the better one and scored. Only three times was player B the better one. Result at 40-30 player A wins the final point and he wins the game. Was he really the best ?
Let us calculate the average quality of the 7 points : A= 5.86 B=5.93. So actually B was the better player, but A was more lucky. Conclusion : in each game there is a portion of luck.

What do we do in statistics ? We repeat the experiments a number of times to “average out” this luck. This is exactly what happens in a tennis set. After 6 (6-0) to 13 (7-6) games we can expect that both players are lucky a number of times and it is only the tennis quality that determines the outcome.
However, consider following set :

Player B wins with 5 – 7, but scores in total three points less then player A. Obviously he was not the best player but nevertheless he won the set.

And a similar discordance between player quality and match outcome may exist.
Look at the mach between Stepanek and Carlovic in the first round of the Australian Open 2010.

Stepanek lost his match, although he was the better player, winning 26 games against only 24 for Carlovic.

It is clear : with the current counting system it is not always the one who played the best, who wins the match.
If we would want this to be the case the counting would be very simple : just keep on counting point per point, up to a maximal number. If chance plays a role … by chance in any point it would be like tossing a coin : the more you toss, the closer you come to 50% heads or tails.
As men play on the average 230.5 points in a match I suppose 150 points would be a good target.

Why don’t they never use a system like that ? Sports is not only fun for the ones who play it, but it is also entertainment for the supporters. The Romans already knew that : Bread & Circuses ! And when do we like a game or a movie ? When tension builds up towards the and and the final outcome is a surprise. This means that in a sports game chance, luck, surprise must be possible untill the end. Games and sets are meant to start chances all over again. Whether you lose a set with 6 – 0 or 6 – 7 , next set still begins at 0 – 0, meaning that a slight difference in your favor during the second set can undo the huge inequality in the first.

Wait ! they do ! In soccer they do, in basketball they do. In waterpolo they do, in handball they do … They just count the number of points.
But in soccer the number of goals are normally so few (1-2, 3-0 are common soccer results) that in most matches we can consider this for a great deal a “chance game”, especially when an erroneous decision of the arbiter can result in a penalty kick, with a large probability of scoring.

Basketball is something different. Its scoring system is just based on averaging. No sets, no games, just one mach with each point adding up to the total score and with a large number of points at the end of the match. So It is obviously the fairest system possible.

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  1. To some extent, I agree, but…your analysis neglects the advantage given by serving; it’s not necessarily true that the best player in a point wins that point, because the starting first advantage can tip the balance. This doesn’t necessarily negate all your points, but it does add to the issue in ways you have not considered.

    Also. part of the reason for the odd scoring, is that tennis was a noble’s sport, with intentionally obfuscated scoring to confuse the lower classes. It is partly this tradition that carries tennis today, distinguishing it from other sports and making it enjoyable to watch by adding tension to points mid-game, rather than it being the fairest possible system.

    • Hi Joe,
      thanks for visiting my blog and for adding this info!

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