Tennis stars serve up performance grounded in mathematical theory

When Andy Roddick returns a 149mph serve, he is performing a feat normally reserved for the best mathematical brains, according to a study into the science of tennis.

Scientists have found that the sort of movements and judgements performed by the world's No 1 tennis player closely match a mathematical principle first formulated in the 18th century.

The study demonstrated that tennis players unconsciously follow the 1763 theorem of the Rev Thomas Bayes, whose rules of probability state that the likelihood of an event occurring depends on prior knowledge.

Konrad Körding and Daniel Wolpert of University College London designed an experiment where people had to judge the movements of a cursor on a computer screen in relation to their own hands in a similar way that tennis players have to judge where an opponent's ball is likely to land in relation to their own position on court.

The study, published in the journal Nature, found that people estimated where a tennis ball was likely to land using information drawn from what they saw and from what they had judged from past experience, Dr Körding said. He added: "They have these two sources of information - what they see and what they know from before - and, in this experiment, I measure how much do people rely on what they see and how much do they rely on prior knowledge."

A statistical method, called Bayesian integration, gauges the probability of something taking place based on the known probability of something happening before it. This is precisely how the brain of an experienced player judges the position of a fast-moving tennis ball that can hardly be seen, he said.

The researchers were able to introduce a level of visual uncertainty into the experiment to mimic what would happen when tennis is played in poor light, when the better players would rely more on their experience than on what they see.

The scientists found that the human brain compensates in poor light by relying more on the judgements which fit the predictions that a computer might make if it was programmed to work in a Bayesian manner.