Mauricio Pochettino has been at the club for four years and agreed a new five-year deal shortly before Antonio Conte found it necessary to pack his bags after just a couple of seasons at Stamford Bridge.

Over at Arsenal, no one expects Unai Emery to last anything like the 22 years his predecessor put in, though there is a distinct sense that the board have cast around for a manager suited to the club with a view to replicating the stability achieved under Arsène Wenger.

Chelsea do not seem to do stability. They have made 11 managerial changes in the 14 years since Claudio Ranieri’s four-season stint at the start of the millennium, and though five titles and both major European trophies have arrived in that period, no manager has succeeded in serving for longer than the Tinkerman.

Maurizio Sarri’s chances of proving any more permanent are already being questioned on account of his age – 59 – and the fact that though personable and popular he has not yet succeeded in winning anything in his managerial career. Chelsea have appointed the former Napoli manager in a departure from their normal selection process. Ever since José Mourinho arrived to speed up the process of turning Roman Abramovich’s investment into success on the pitch the club have gone for proven winners when not appointing from within or finding a short-term solution – even André Villas-Boas had the Portuguese league title and a Europa League triumph on his CV when he arrived as a relative unknown. Mourinho came fresh from winning the Champions League with Porto, Carlo Ancelotti had won it twice with Milan and would go on to win it again with Real Madrid, while Conte came direct from managing Italy following three Serie A titles in a row with Juventus.

Ancelotti has replaced Sarri at Napoli and can look forward to Champions League football next season thanks to the latter’s efforts in finishing runners-up to Juventus, though second place is not normally the sort of achievement that would recommend a manager to Chelsea. Sarri has never managed outside Italy, was in charge of obscure lower league sides such as Alessandria and Sorrento until six years ago, and in no way fits the stellar profile of the statement manager Abramovich has been accustomed to hiring. But statement managers can be hard work, as Chelsea have just discovered with Conte.

He did not lose the goodwill of his players, as seemed to happen to Mourinho in his second spell at the club, but he has gone public on numerous occasions with his dissatisfaction over funding and transfer policy. Chelsea managed only fifth place last season after winning the title the previous year. Conte’s side put up a more convincing defence than did Mourinho’s in 2015-16, though missing out on the Champions League every couple of seasons is not something that appeals to the owner and all season long Conte has sounded like someone getting his excuses in first. “After two years the club know me very well,” he said after defeating Mourinho’s Manchester United in the FA Cup final. “I can’t change.”

His departure could be seen as an acknowledgment that the club realise that, just as Sarri might be viewed as a subtle change in direction by Chelsea. Though Conte’s habitual moaning became a pain, he was merely articulating what has become increasingly apparent in the last few years: that not even Chelsea can match Manchester City for money. Or, it seems, for managerial input of the sort that brings in major trophies and attracts the very best players. That was Chelsea’s formula for instant success a decade ago, but it never brought the continuity City are starting to achieve.

Pep Guardiola has signed a two-year extension to his contract, and should he see it out – all the signs from his previous clubs suggest he will – he will have spent five years in Manchester.

The last Chelsea manager to last five years was Dave Sexton, who took over from the equally durable Tommy Docherty. Chelsea have been up and down the divisions since the 1960s, of course, becoming in the process a byword for infuriating inconsistency, but the point is that so have Manchester City. If Guardiola does stay for five years, he will be the first City manager to do so since Tony Book, and before him Joe Mercer.

The two clubs with the most eye-catching financial backing over the last few years have more in common than it might appear, but in their newly-rich incarnation City have long had a plan that they have been diligent and patient in bringing to fruition. Chelsea, admittedly not helped by friction between players and some of the managers at times, are still going through coaches at the rate they were doing when Ken Bates was in charge.

Sarri may not have led Napoli to the title but he rejuvenated his native city’s club, succeeded in playing more attacking football than Rafael Benítez and was voted Italian coach of the year last season. All those things should recommend him to Chelsea, as should the fact that though he initially signed for only a season at Napoli, he ended up with an extension to 2020.

Obviously that did not work out – this is football after all – but after the disappointments of the past few seasons, there might be worse things for Chelsea to aspire to than being Napoli to Manchester City’s Juventus. As Jürgen Klopp has proved at Liverpool, a charismatic and positive manager capable of generating love from players and supporters can take a club a long way.