The psychological processes used to compete in a complex and uncertain world
Tom’s train leaves due North travelling at 60mph. His station is 100miles from his starting point. You are 15miles and 60 degrees Northwest and can travel as the crow flies to meet him at his destination. If you leave now, what speed do you need to travel to arrive at the same time?
This came to mind when I heard Rishi Sunak recently announced plans to ensure all pupils in England study maths in some form until the age of 18. The pseudo-realistic hypothetical scenarios you would be asked to solve that elicited trigonometry or tears. And thank God – if I needed to find out what time I needed to set off to reach a destination at a particular time by train – I would of course immediately reach for my Casio.
Footballers aren’t usually associated with excelling within the education system, but there are some notable exceptions: Frank Lampard has an A in GSCE Latin, Bukayo Saka achieved 4 A*s and 3 A’s, and Matt Le Tissier conducted and communicated secondary research into the efficacy of the Moderna vaccine.
But the scenario presented above isn’t too dissimilar from what footballers frequently encounter in gameplay:
You find space at CAM and notice the left winger making a late run into the box. You need to pass now to ensure he is onside and allow him to intercept the ball before the keeper can claim it. How much weight should you put on the pass?
This involves just as sophisticated a calculation as before to work out the distance and speed of the pass – and more, once you factor in the moving ball, the coefficient of friction, how that may be impacted by environmental factors. Worse, the relevant parameters are estimated, not known.
Oh, and then translate all this into action. How do players perform these calculations with such ease and in short moments of time. Obviously, they can’t be performing the sequential steps outlined in our textbooks.
Cue heuristics: mental shortcuts that allow people to solve problems and make judgments quickly and efficiently. These rule-of-thumb strategies may not be optimal, but provide good enough approximations for achieving goals. A well-recognised example is the FAST heuristic for identifying the signs of a stroke.
Their simplicity does not imply their efficacy. Simple heuristics have been shown to out-perform more complex approaches in a range of contexts, from investment strategy, to healthcare, and even sports prediction. The recognition heuristic: if you have heard of one player, but not the other, predict that the recognised player will win – on average, predicted the winners of 128 Men’s Singles Championship in Wimbledon better than the ATP rankings and the Wimbledon experts’ seeding.
When investigating the behaviour of athletes – we are within the realm of embodied heuristics: rules that require specific sensory and/or motor abilities to be executed. Enabling us to make effective sporting decisions based on uncertain cues.
Let’s look at another example that wouldn't be out of place modelled as an A-level question. When a batter skies one into the outfield – the fielder on the boundary has to judge where to run in order to take the catch. Or in mechanics:
The batsman hits the ball at a 50 degree angle to the pitch at 50m/s. How far from the 80m boundary will the ball land – and how fast must the boundary fielder travel to get to intercept the ball as it lands. Assume g=-9.81m/s^2 and air resistance to be negligible.
Does the fielder – either consciously or unconsciously – estimate the relevant parameters: the initial angle and speed, and then apply suvat equations to solve the vertical and horizontal components motion (made even harder by the presence of an atmosphere which, whilst keeping the fielder alive, will impart friction on the ball). Unsurprisingly, no. But how do they behave appropriately?
Experimental studies have shown that fielders use a heuristic. The angle-of-gaze heuristic ignores all the information necessary for computing a trajectory and attends to only one variable, the angle of gaze.
The fielder fixates their eyes on the ball, runs, and adjusts their speed to ensure the angle between their gaze and the ball remains constant. Once hit, if the ball rises at an accelerating rate, the ball will fall behind you; a decreasing rate, the ball will fall in front of you. (This is reversed for when the ball is dropping). If the image of the ball rises (or falls) at a constant rate, you are at the right speed.
Although some heuristics are derived from experience, boundary fielders did not invent the gaze heuristic – and the reliance on this heuristic by multiple species suggests the gaze heuristic evolved for predatory-prey interaction. This, therefore, is an example of exaptation: a trait acquiring a new function beyond its evolutionary-derived origin.
Embodied heuristic strategies aren’t optimal – but are good enough. And in instances of exaptation where evolutionary adaptive heuristics are culturally appropriated for new purposes – this can lead to mistakes and biases. In certain situations, players run a slight arc to keep the angle of gaze constant, rather than taking the most efficient path.
So consider this: analysis of the 2006 Football World Cup evidenced that headers are more likely to miss when directed to the far than near post. This has been interpreted as footballers demonstrating a naïve concept of impulse integration – failing to fully account for the ball’s impetus prior to heading.
It could be the case that there is a heuristic players use to inform how they redirect crosses, a heuristic that is accompanied, in certain situations, by a bias to underestimate the ball’s velocity. What the heuristic may be is open to suggestion… (answer in the comments below).
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