Lucky the leader who first experienced failure in the ranks. He has a huge advantage: the inclination to consider that other people have different solutions, perhaps even better ones. Top-flight coaches were usually second-division players. Failure was formative, sharpening their observations and developing their empathy. In contrast, great players who become coaches often suffer from over-reliance on the very instinct that once served them so well: it worked for me before, so it must work for everyone.

Andy Flower resigned as coach of the England cricket team on 31 January and he left office with some notable achievements. With personal directness and analytical clarity, Flower oversaw three Ashes series victories and England enjoyed brief spells as the top-ranked team in the game’s three formats. In Australia this winter, however, the England team seemed increasingly cowed by their manager rather than inspired by him. His response was fatal: more work, more toughness, and a narrowly defined emphasis on “character” – the cornerstones of Flower’s highly successful career as a player. He started out trying to modernise English cricket and ended up trying to recast it in his own image. This is a classic process that should become a business school staple.

Playing and managing exact almost opposite psychological demands. All of the top four English football clubs are coached by men who had unremarkable careers as players: Arsène Wenger, José Mourinho, Manuel Pellegrini and Brendan Rodgers. Naturally, there are exceptions. Pep Guardiola, arguably the best manager of all, was previously a superb midfielder. But the wider point stands: playing at the level below greatness hones the most underrated quality in a leader – scepticism. Great managers, despite their ultra-confident press conference personas, constantly reassess their managerial bag of tricks. When they stop evolving philosophically and become predictable, their effectiveness tapers off.

For once-great players, however, it is harder to learn scepticism. All athletes depend on a trained conviction: this is what works for me. Your particular methodology becomes hard-wired into your DNA. It might be to attack when you are under pressure, or to defend; it may be to nurture anger, or to assume calmness. It doesn’t really matter. What matters is the degree of faith that sustains your default position: you need to trust what has worked for you before. The best players have a higher degree of confidence in their routines and patterns of thought.

A manager searches for the opposite position; he must become detached. In his handling of people, he cannot trust one default position as innately superior. Instead of believing he can change everyone’s character, he must see how every player is seeking a personal solution to a unique set of problems.

Behavioural economists would describe this as overcoming a cognitive bias. Great players, who benefit from a narrow and intense focus, are inclined to observe and remember their own methods while ignoring or forgetting the approaches of others. In contrast, managers have to see the whole picture.

The best coach I encountered – once a distinguished player but not a great one – constantly drew on his playing experience in his new role. He advised people how to avoid making the errors he had made. He recast his stock of playing experience as something to be judged and interpreted with total detachment. Having performed at a high level was not a licence to lecture people about “In my day” or “When I was a player”. Instead, it fired his imagination. His management evolved so far from his own playing days that it approached a state of negative capability.

Some great managers pursue the transition too far. They end up with only one blind spot: for their mirror image. George Graham, the successful Arsenal manager in the 1980s and 1990s, had once been a languid, laid-back player. His nickname was “Stroller”. As a manager, far from indulging players cut from his own cloth, Graham revered discipline and control. Too much so: unpredictable playmakers, such as the mercurial Paul Davis, never quite fitted his manager’s template.

It is ironic that Andy Flower once sought to bring the scientific method to cricket by drawing on principles of Moneyball. Michael Lewis’s book portrayed Billy Beane, the general manager of the Oakland A’s major-league baseball team, using statistical modelling to buy and select players who were undervalued by the transfer market. Flower hoped to bring a similar analytical rigour to cricket.

In the final, disastrous months of his regime, it became fashionable to ridicule England’s vast back-room staff of analysts and experts. Surely it was time to go back to instinct and self-expression, perhaps even a smile or two? This theory, though true enough, misses the central difference between Flower and Beane. Flower was a great player, Beane a highly talented failure. Beane’s pursuit of scientific detachment led him to avoid acting on managerial instincts. He became like a trader who sells a stock when it reaches a predetermined price. Indeed, he stopped watching Oakland’s matches because he didn’t trust himself to manage his emotions. Flower, by contrast, loomed large in the dressing room.

Strategy does not exist in a vacuum. It interacts with the person who imparts it. Flower’s theories advocated detached reason, yet in person he became imposingly dogmatic. Between those two forces, there was little space for anything else.

Ed Smith’s latest book is “Luck: a Fresh Look at Fortune” (Bloomsbury, £8.99)