Greek elections: Where did Alexis Tsipras go wrong?

As Kyriakos Mitsotakis spoke to his cheering supporters after victory, he paused for a moment of reflection.

"I feel the spirit of my parents protecting me," he said.

For Greece's new slick prime minister-elect, talk of his family is not just a personal issue.

He is a scion of one of the country's most powerful political dynasties: his father, Konstantinos, was prime minister, his sister is a former foreign minister and his nephew is the new mayor of Athens.

No other European country has the tradition of family politics like Greece.

• Centre-right regains power in Greece

• Mitsotakis and the return of a Greek dynasty

• Five things that matter in Greek election

• Young Greeks lean to conservatives for future

That is one of the reasons behind its financial crisis - the culture of nepotism that plagued successive post-war governments.

Kyriakos Mitsotakis's party has won an outright majority in the Greek parliament

But Kyriakos Mitsotakis has deftly managed to present himself as a new face in spite of his heritage, reinvigorating a party swept from office in 2015 for embodying the corrupt old guard.

Back then, Alexis Tsipras seemed like the figure of change.

In his firebrand rallies, the left-wing populist vowed to tear up Greece's bailout programme and end austerity.

He brought in a finance minister, the leather jacket-wearing, motorcycle-driving Yannis Varoufakis, who goaded the EU and made enemies in Brussels and Berlin.

He led Greece into a referendum on rejecting Europe's budget cuts, despite warnings from its creditors that it was hurtling towards leaving the eurozone.

Outgoing Prime Minister Alexis Tsipras (centre) will now try to regroup in opposition

And he hopelessly overpromised.

Under pressure from the EU, capital controls on its banks and the threat of "Grexit" - departure from the euro - he was forced into a humiliating U-turn, signing up to a third, €89bn (£80bn; $100bn) bailout, and more austerity.

His support base began to ebb away.

"The fact that Tsipras managed to stay in power for four years despite breaking his pledges is a testimony to his political talent," says Professor George Pagoulatos of the Athens University of Economics.

"His party, Syriza, now carries an ideology so different from the policies he's applied that it's meaningless - the main thing holding the party together is Tsipras," Prof Pagoulatos says.

"We set the bar high - and we didn't reach it," admits Syriza's Dimitris Rapides

Dimitris Rapides, a representative of Syriza in Brussels, agrees.

"I understand 100% why people are disappointed with the party," he tells me in a bustling Athens cafe.

"People had high expectations - we set the bar high - and we didn't reach it."

Yet Alexis Tsipras has achieved some success over his time in office:

• Unemployment, which peaked at 28% during the crisis, has edged down to 19%

• Greece has formally finished its bailout programme - though the country remains under strict supervision by its creditors

• Tourists are flocking back to Greek beaches, helping the economy return to modest growth last year

• And some of the 500,000 young minds who left during the crisis are beginning to return, spurred by start-ups and a feeling that Greece has turned a corner

But Mr Tsipras also fell foul of scandal, seeming to break his "people vs the elite" rhetoric as he was pictured on a luxury yacht of a Greek shipowner last year - just weeks after mismanaging the response to deadly wildfires.

"Tsipras actually came up with very anti-European politics", says Pavlos Eleftheriades, a New Democracy supporter who came back from the UK to vote.

"He reminds me of Nigel Farage [the leader of the Brexit party in the UK], even though one is left and one is right. This result is a victory for a European Greece and I'm very excited."

Mr Mitsotakis has promised tax cuts and job creation, with an agenda of privatisation and sound political management.

He'll benefit from New Democracy being part of the largest bloc in the European Parliament, painting his victory as an end to Greece's populist experiment and a return to the political mainstream.

"He has a good chance of doing much of what he promises, with a more competent team around him," says Prof Pagoulatos.

"And his victory shows that populism is a cyclical phenomenon, more than a trend.

"When populists are tried in power, they face the same constraints of mainstream governments - and don't necessarily respond more successfully. In Greece's case, they were inept and brought the country to the brink of economic collapse."

The legacy of Alexis Tsipras is, indeed, to have shed the populist demagoguery that first swept him to power.

And in concrete terms, his biggest foreign policy legacy is one which cost him support within his own country: to have reached a deal accepting Greece's northern neighbour under the name North Macedonia, ending a two decades-old dispute by Greeks who claim ownership over Macedonian identity.

• North Macedonia deal: Greek PM Tsipras in 'historic' visit

• Greek bailout crisis in 300 words

• How crisis helped Greeks open their eyes to mental illness

That normalised relations between the two countries, but prompted cries - from Mr Mitsotakis among others - of betrayal.

As the (young) Mitsotakis era begins, one of Europe's iconic leftist leaders of the past four years departs the stage.

But he'll regroup in opposition and wait in the wings to seize on any misstep by Greece's new leader.

This is by no means the last Greece will hear of Alexis Tsipras.