# We are all a big hit at maths

The science of sport – what does it matter? Well, says AOIFE McLYSAGHTof Trinity College Dublin, when you play you’re using complex science without even knowing it

What goes through a tennis player’s mind just before they return a serve? Give yourself a gold star if your answer was an equation.

It’s doubtful that many people realise that this is what they are doing as they try to estimate the speed and trajectory of an approaching ball, but research into sensorimotor learning and decision patterns has shown that this is in fact what is going on inside the central nervous system.

Without us really being aware of it, our brains are employing complex probabilistic models as we learn and react to the world around us.

Examine the performance of a successful player and you’ll see that they are particularly quick to anticipate where the tennis ball will land. To an observer like me, it almost seems impossible that they could have the time to see the ball coming and react as accurately as they do. In fact, they aren’t only relying on their eyes to do this. They achieve their lightning-quick responses through a combination of two types of information: one is the visual input that gives them an estimate; and the other is experience, both of tennis players generally, and their specific match opponent. That is why hours of pre-match preparation, watching videos of their opponent, is time well spent. Players even get better at anticipating their opponent’s moves as the match progresses: so they continue to learn, and learn very quickly.

That all sounds like common sense; a far cry from the scary-looking mathematical equation above. But in fact that equation is Bayes’ Theorem, and it describes those common-sense judgements we make many times each day. What you expect is based on a combination of prior knowledge and observation, and it turns out to be one of the most useful statistical models for real-life situations. It accurately describes what is happening as a tennis player gets better with experience. Without knowing it, players are incorporating their experiences into a constantly updating probability distribution of where the ball is likely to land.

They expect the ball to land in certain parts of the court, and react more quickly than could be expected if they relied on visual information alone. Without fully realising what is going on, even those of us who think ourselves to be maths-dunces are finely tuned mathematical machines.