THE JOHNSON PROBLEM

Russell Domingo, South Africa's coach, never played first-class cricket. But he is a whizz with numbers. "I am," Domingo told Firdose Moonda, "very driven by technical and strategic aspects and analysis." AB de Villiers says of Domingo: "He likes his stats." No doubt, then, that his team thought they were well-prepared. Hashim Amla said before the first Test with Australia: "I don't think in this series there's too many surprise factors." Mitchell Johnson? "We've played against him before," said Faf du Plessis. "It's nothing we haven't seen … we're ready." All Australia's talk, Graeme Smith said, was just so much "bull". South Africa's batsmen had their plans, ones based on experience and analysis. "Everyone has a plan," as Mike Tyson put it, "'til they get punched in the mouth."

At 85mph, a ball takes 0.52sec to travel 22 yards. That's less time than it takes Usain Bolt to complete his first stride, and a little more than it takes you to blink. It's how long a batsman has to spot the length and line of the delivery, pick a shot to play, and then pull it off. To do it right, he needs to judge the position of the ball to within around three centimetres, and time the arrival of the bat to within three milliseconds. Any further, any sooner, any slower, and the ball misses the sweet spot. Put like that, hitting a cricket ball begins to seem like a preternatural act, as impossible as pinching a fly from the air with a pair of chopsticks.

They say it takes a minimum of 100 milliseconds for the brain to produce even the simplest action, and around double that to do something only a little more complex, like flicking a light switch. Benjamin Libet, a physiologist at the University of California, found that it took between 400 and 500 milliseconds for the brain to complete all the processes needed to produce a subjective experience. In cricket, the time constraint imposed by the speed of the delivery often exceeds the time available to process information. Against fast bowling, a batsman operates at a speed that outstrips his own consciousness. So how is it done?

It's not that the best Test batsmen have quicker reactions than anyone else. As Peter McLeod, a member of Oxford University's Department of Experimental Psychology, explained to John McCrone in the New Scientist: "There is surprisingly little difference between top-class athletes and good, fit ordinary people. In laboratory tests of reactions using unskilled tasks, most people show much the same reaction time of about a fifth of a second."

In his book Wait: The Art and Science of Delay, Frank Partnoy breaks that half a second down into still smaller chunks. Roughly, the first 150 milliseconds is seeing the ball. The last 100 milliseconds is spent playing the shot. In one of his studies, McLeod found that it is impossible for any batsman – he tested Allan Lamb, Wayne Larkins, and Peter Willey – to correctly react to any deviation the ball makes in the final 200 milliseconds of its flight. What matters then, is that chunk in the middle, the 150 milliseconds between seeing the ball and playing it. Partnoy calls this the "ball identification stage", a phrase he borrowed from the tennis coach Angel Lopez, who says similar processes are at work when a player returns a serve. It's what happens in this little window that separates the best from the rest.

When the ball is released, you and I might see a blur and have time enough to think through the first two letters of the curse we'll finish when the ball has passed. A batsman sees an ordered set of possibilities. He draws on information he has about the pace and style of the bowler, the condition of the pitch, and his own form. Add to that what he gathers from the anatomical position of the bowler during delivery, and finally, most importantly, what he observes during the first few milliseconds of the ball's flight.

After that, it is all anticipation. No one, despite everything your school coach ever told you, actually watches the ball on to the bat. Instead, the batsman's eye vellicates to the spot where he thinks the ball will bounce. The skill of a batsman, McLeod says, "lies in how they use visual information to control motor actions once they have picked it [the ball] up". It can't be taught, but is honed over hours of practice and play. We call it muscle memory.

At 95mph, a ball takes 0.47sec to travel 22 yards. That extra 10mph robs the batsman of 0.05sec. Which seems like nothing at all. But it's not. McLeod found that 0.05sec is the difference between a club and a Test cricketer. "We precisely measured how long different players took to swing and when they began their swings," McLeod explained. He looked at a range of players, from "true amateurs to top professionals". And he found that the professionals were quicker, "though not by much – just in the range of tens of milliseconds quicker". McLeod says: "What matters crucially is just a tiny time window of about fifty milliseconds in all. That makes all the difference."

Fifty milliseconds. The difference between an amateur and a pro, between 85mph and 95mph, between Mitchell Johnson and Jimmy Anderson. "There is," Kevin Pietersen tweeted last week while he was watching the Test, "a HUGE difference when facing someone at 140kmh compared to 150kmh … When you are facing someone as quick as Mitchell, your instinct occasionally makes you do things you shouldn't. PACE causes indecision."

The process must be disrupted, too, by the fear of being hit. The instinct to avoid being injured is even more ingrained than that of hitting the ball and the two can pull in opposite directions. It was telling that De Villiers, the one batsman who played Johnson well, explained afterwards "once you don't have that fear of getting hurt then I feel you play a lot better."

You could see that indecision in the first innings dismissal of Graeme Smith, who spotted the short ball, shaped to hook it, then changed his mind, and ended up spooning the ball to slip. It's only a little more speed, and a little less time. But it's enough to skew the complicated subconscious calculations of the best batsmen, accustomed as they are to having 50 milliseconds more to work with. Such slender margins, but such significant differences.

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