The John McEnroe effect has been unravelled by scientists who say that players really do see things differently from the line judges.
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A comprehensive study of tennis matches shows precisely how much harder it is to see on which side the ball bounces, when it comes down within four inches of the line.
It turns out that in around ten per cent of cases, judges will make the wrong call, showing that McEnroe really did have a point when he said: "You cannot be serious."
Unfortunately, however, when players do complain about a decision their protests are only valid 40 per cent of time, while the judges' decision is right 60 per cent of the time.
The research was conducted by Prof George Mather of Sussex University, Falmer and is reported today in the Proceedings of the Royal Society, Biological Sciences.
The study concludes the arguments could be reduced by making players, umpires and line judges take more care to see what happens to balls that bounce near the ends of the court, rather than the sides.
For years now, audiences watching tennis on television have been able to see the "MacCam" showing the precise landing of the ball to review controversial calls about whether it crossed a line.
The technology is used routinely to shed new light on line call controversies, for instance at Wimbledon and the US Open.
Now Prof Mather has analysed the data recorded by the cameras used by the Hawk-Eye system in professional tournaments.
When a challenge is made, the umpire calls for a review of the Hawk-Eye data to determine whether the ball actually did bounce on the inside or outside of the court line. The umpire either upholds or overturns the line judge's call accordingly.
Based on his study, Prof Mather could come up with a mathematical model to predict performance, based on limitations to how the eye and brain work together. "The model predicts that 8.2 per cent of all line calls involving balls within 100 mm (four inches) of a court line will be called incorrectly by line judges, due to inherent limitations in their perceptual system."
In his paper, Prof Mather concludes from 1473 challenges by 246 players during 15 tournaments organised by the Association of Tennis Professionals that judgements are more difficult on certain parts of the court and he recommends that training and line judge selection should take this on board.
"Players should attempt to make full use of all the challenges available to them because some errors are inevitable, but should bear in mind that both they and the line judge are more likely to be wrong for base and service line calls than for side and centre line calls."
But he concludes that "line call accuracy is sufficiently high" that a rule of two unsuccessful challenges per set "seems reasonable".
He found that 94 per cent of the challenges occurred for balls bouncing within 100 mm (four inches) of the line, a distance less than twice the diameter of the ball.
Both players and line judges are remarkably accurate at judging ball bounce position, with an uncertainty of less than 40 mm (1.6 inches) in its position, which is remarkable given that the ball is moving up to 50 metres per second.
In all, he says, four in 10 challenged line calls turned out to be incorrect.
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