No sooner had Ronald Koeman been sacked by Everton than a predictable troupe of has-beens, hopefuls and cast-offs were plonked among the favourites to replace him. Inevitably David Moyes was high on the bookies’ list, despite a triad of failures at Manchester United, Real Sociedad and Sunderland. So was Sam Allardyce, a roast-beef-and-potatoes option for a club striving for cordon bleu. Before Sunday’s defeat at Leicester, the academy and under-23 coach, David Unsworth, even became the frontrunner, despite a handful of games on his managerial CV.

Whatever happens at Goodison Park it is a cast-iron bet that some of these men will be in the frame the next time a Premier League job comes up – and the one after. That is how the system goes. Rinse. Recycle. Repeat. These days managers, like Buddhists, accept that death and rebirth is a fundamental part of existence.

Yet while clubs increasingly spend crazy money on decent but not exceptional players – Everton, after all, threw £45m at Swansea for Gylfi Sigurdsson – there is a curious reluctance to adopt a similar approach to prise away a proven manager. We are not talking a million here or there, as is occasionally seen, but proper money, crazy money even.

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According to Omar Chaudhuri – the head of football intelligence at 21st Club, a consultancy that works with many leading sides in Europe – the data suggests such an approach makes sense.

His starting point is that even a star player is worth only about five points a season to his team over an average one in the same position. That might sound absurdly low. But, he explains, imagine replacing every player in a Premier League team at the bottom of the table, who get around 30 points a season, with one from near the top, who will earn closer to 85 points – that averages out at five points a player.

For managers this is trickier, Chaudhuri concedes. “But when we’ve looked at the immediate impact of new coaches on performance – at the change in results accounting for difficulty of fixtures and luck that the old manager might not have enjoyed – the maximum increase is usually up to 10-12 points per season.”

It is often less than that, of course. But the trade-offs are worth considering: if one can spend £10m to bring in someone such as Marco Silva or Marcelino, the coach who has worked miracles at Villarreal and now Valencia, or twice that on an average player, why would one go for the latter?

Incidentally Chaudhuri finds that the majority of improvement occurs in defence, which is to be expected given a manager is often sacked when the team are losing, usually after conceding too many goals.

Meanwhile Ted Knutson, who worked as an analyst at Brentford and FC Midtjylland before setting up Statsbomb Services, which works with clubs across the globe, describes the range of managerial talent as being like a U-curve, with the best and worst coaches having a bigger impact on results than is widely thought – and those in the middle tier relying on the quality of their players, their club’s recruitment strategy and luck to succeed or fail.

Most, of course, fall by the wayside. It seems almost quaint to recall that in the early 90s the average spell of a manager in English football was more than three years. Last season 60 managers left their jobs between September and June – with only a third in situ more than a year.

If insanity really is doing the same thing over and over again while expecting a different outcome, perhaps chairmen should take a leaf out of Blackadder by sticking pencils up their noses, a pair of underpants on their heads and repeat the word ‘wibble’ until the men in white suits arrive. It would certainly be cheaper than paying so much compensation.

So how does one identify a decent manager given that Avram Grant took Chelsea to the Champions League final and Roberto Di Matteo went one better? As Chaudhuri and Knutson concede, it is not necessarily straightforward to distinguish managerial skill from the talent of the players a club has. Yet both believe that by looking at a team’s underlying metrics, budget and results, it is not difficult to identify managers who have outperformed their resources consistently over a number of seasons.

There is more to it than that, of course. When organisations such as 21st Club work with clubs they ask what attributes of a potential manager are most important to them. Is it performing on a tight budget? A certain playing style? Improving young players? They will then scour their database, weighting the various metrics and produce a shortlist.

Knutson, who provides a similar service, explains: “We are not making the choice for clubs; we are just presenting better options. And compared to what they pay if they get rid of a bad manager too quickly, it is the tiniest drop in the bucket. But time and again clubs don’t spend enough money to find the best candidate – and then end up paying a spectacular amount to get rid of them.”

This cycle of perpetual failure continues. Yet, as the transfer market for players approaches Weimar Republic levels of hyperinflation, more clubs should ask whether it makes sense to settle for what they have always done in terms of recruiting managers – or flash the cash for proven quality.