It was fortunate Liverpool emerged victorious against Salzburg on Tuesday because otherwise they might have been out of the Champions League, with speculation growing that Jürgen Klopp was for the axe. I jest, of course, though it’s not quite as an absurd idea as it may sound.

Klopp has worked wonders at Liverpool, creating arguably the finest team in the world at the present time. In all competitions the only side to beat his team so far this season are Napoli. But it should be noted the manager of that Napoli team, Carlo Ancelotti, a three‑times winner of the Champions League, was sacked last week, after his side qualified for the knockout stages alongside Liverpool.

That was in Italy, of course, where they do things differently. Except, what’s the difference? The departures last month of Mauricio Pochettino and Unai Emery from Spurs and Arsenal confirmed the lifespan of elite Premier League managers is akin to those elsewhere in Europe and around the same as that of a mole: three years. At the top end of the myopic Premier League, Pochettino lasted just over five years, and Emery 18 months, but the key thing is that neither could withstand a sustained drop in form.

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Pochettino turned Spurs into a consistent top-four side with serious title aspirations and took them to the final of the Champions League – achievements at a level no one at the club since Bill Nicholson in the 1960s had managed. Emery made less of an impact and his public image was hampered, perhaps, by the fact he sounded like Latka from Taxi.

Still, he was a manager with a track record and he inherited a poor defence. In times past, the club would have stuck with him until he had enough time to turn the tanker round. It doesn’t work like that any more because of two key factors: the players and the fans.

Emery is gone but Mesut Özil remains. Emery was on a whopping £6m a year. Özil’s salary is three times that at £18m. Arsenal can afford to cut their losses with Emery but with Özil, who has underperformed for at least two seasons, that’s a much bigger sacrifice to swallow.

No one wants to buy Özil on those wages. So he is stuck at Arsenal, leaving the manger the option of placing the club’s most expensive asset in the reserves (which won’t please the board) or playing him (which pleases few fans). At the same time, a manager has to be careful not to “lose the dressing room”.

Because, whether or not they admit it, players know their power. If enough of them underperform, it’s the manager who pays. Very soon he will be informed by the fans, who are customers paying a hefty sum for season tickets, that “you don’t know what you’re doing”. This is the inevitable end stage of the foreshortened life cycle of football management.

That cycle invariably begins with the “project” stage. In this honeymoon period there is much bright talk of the future, where everything is possible and towards which everyone is united in wanting to go. The project implies a new philosophy, reorganisation and the time and patience to put it all into practice. The project, in other words, is a fantasy.

The second stage is reality – the desperate need to win. All those ideas about a new way of playing? They’re gone. The project has been placed on the back burner, to be retrieved when the world becomes a kinder, more tolerant place, Brexit is resolved to everyone’s satisfaction and climate change is stopped in its tracks.

And the final stage is the losing sequence. It comes to every manager and team. Even Pep Guardiola’s Manchester City have fallen from their stratospheric heights. The question is, what can a manager do when his team start losing? You hear the same tired cliches: we must work harder, their confidence will return with a victory and give me more money for new players.

Facebook Twitter Pinterest When results began to go wrong for Unai Emery after 18 months, Arsenal were not prepared to give him more time. Photograph: Steven Paston/PA

But managers know what the end is if they can’t quickly reverse the trend. If Pochettino can take Spurs, a team previously with its sights on the Carling Cup, to the peak of European football and then lose his job in his first losing streak, then it will take an awful lot of earlier success to ride out a bad patch.

Players “stop listening”, it’s said. And they do so because they know the ending, too. Hardly any chief executive is going to show resolute support for a struggling manager because it elevates them to a position of importance that modern clubs do not want to accept. There will never be another Alex Ferguson or Arsène Wenger.

Pochettino’s replacement, José Mourinho, has been widely criticised for being a “three-season” manager. He is someone, it is said, whose approach pays dividends for two seasons but by the third he has alienated too many people and he has to move on. But if three seasons is the new normal, if it’s the average lifespan, then where’s the problem? At least he’s usually successful for two of them.

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Critics also say Mourinho’s methods are out of date, that managers such as Klopp and Guardiola make him look like yesterday’s man. Perhaps, but in one sense he’s right up to date. He is a short-termist. His project is now. The future can look after itself.

This outlook is now the consensus. It has bred the unhealthy belief that the “top four” and the “big six” are preordained positions. Yet unless we want a duopoly like Spain, we should think it natural that all clubs, even the biggest, experience periods of setbacks and renewal. In this respect it’s good to see Leicester riding high – managed, of course, by Brendan Rodgers, who lost his job at Liverpool not long after almost winning the Premier League – and Wolves and Sheffield United challenging for top spots.

The longest serving Premier League manager is Eddie Howe. Aside from a brief sojourn at Burnley, he has been doing the job at Bournemouth for 11 years. His finishes in the Premiership are: 16th, 9th, 12th, 14th. He would have been sacked at almost any other club but his is a tremendous achievement. Keeping his small, underfunded club in mid-table is a managerial feat every bit the equal of Pochettino’s series of top-four finishes. That their teams have also played with style and tenacity, and neither manager is a moaner, speaks volumes for both men.

It is often said Howe deserves to go to a bigger club. And so he does, but, alas, I’m not sure that bigger clubs, given the quick-fix way they are run, deserve him.