The
trade-off between performance and accuracy is a problem faced by a lot of
different animals in a variety of situations. For example, consider a squirrel
running along a bare branch to get from one tree to another; the faster it
runs, the less time it spends exposed to predators. However, as the squirrel
runs faster, it also increases its chances of mis-stepping and falling to its
potential doom. So, to get the best of both worlds, the squirrel needs to
optimise its running speed depending on its chance of slipping (the width of
the branch) and the cost of falling off (the height from the ground).
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| Squirrels know what’s going down (or do they)? Image source: Wikimedia commons. |
These sort of performance/accuracy trade-offs are also
commonplace in the human world. How fast should you smash out a text message to
your supervisor asking him (politely) to email back your latest draft before
the number of typos makes the whole thing unintelligible? In particular, these trade-offs are of a
great deal of interest in elite sports. An awesome example of a sport where
this trade-off is of utmost importance is in singles tennis.
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Serving hard:
Heather Watson, Roger Federer and David Ferrer. Image source: Wikimedia
commons.
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In tennis, it’s pretty well accepted that if you serve
really hard, it’s more difficult for your opponent to return the ball. But the
harder you serve, the more likely it is that you’ll miss the service area and
fault. So, players will usually belt it out on their first serve, but if they
miss the first serve they’ll hedge their bets and serve softer the second time
round to make sure they don’t double fault.
A/Prof Robbie Wilson, Dr Chris Brown and I have been testing this idea about performance trade-offs and
optimal strategies using data from the men’s singles in the 2013 Australian
Open. We’ve found this observation to be generally true: the probability of
winning the point increases as the serve speed approaches its maximum, but the
probability of faulting increases as well (for most players – some players are
really consistent at getting it in regardless of how fast they serve). This was
reflected in the frequency of high serve speeds in the first and second serves.
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Jérémy
Chardy, Andy Murray and Janko Tipsarevic. Image source: Wikimedia commons.
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We’ve
also constructed an optimality model which predicts the optimal serve speed
taking into account the probability of faulting and the cost of a fault. An
optimality model is, in essence, a mathematical model where you input the risks
and rewards of a specific situation for a given individual, and it will tell
you the optimal response for that individual if it wants to both minimise the
risks and maximise the rewards. Optimality modelling is useful because it
allows us to calculate the optimal response of specific individuals to any situation. We are looking at whether
their opponent’s world ranking (ability to return a fast serve) and the point
they’re going for or defending against (normal, game, set or match) affects
their serve speed in relation to their optimum, but more on those results
later.
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Rafael Nadal,
Caroline Wozniacki and Jérémy Chardy. Image source: Wikimedia commons.
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We hope that our research can teach us more about how
animals optimise their behaviour and physical efforts to improve their chances
of successfully performing a given task. Depending on what we find, we might
even be able to offer specific recommendations to tennis players wanting to
improve their service game – who knows what the future might hold!
Andrew Hunter, a PhD student in our lab, is looking at
performance/accuracy trade-offs in soccer. Will the results be similar between
an individual and a team sport? We don’t know yet, but it will be interesting
to find out.
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Novak Djokovic,
Agnieszka Radwańska and Venus Williams. Image source: Wikimedia commons.
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