Angela Merkel’s approach to a problem, wrote one of her biographers, is “to sit it out”. Rather than entertain grand ideas of a “historic mission” or “strategic vision”, she aims to “solve today’s problems, in a way that ensures she stays in power”.

The German chancellor, once described by Forbes as the world’s most powerful woman, managed that for 13 years. She has been measured, cautious, methodical, pragmatic, sometimes maddeningly noncommittal and seemingly always in control.

But this week, weakened by plummeting polls, an unpopular and ineffective coalition, dire performances in recent state elections and increasingly acrimonious in-fighting among her centre-right alliance, she conceded defeat.

The dignified, matter-of-fact announcement of her coming departure, however, was Merkel all over, as was the orderly two-stage exit she plans, first surrendering her 18-year leadership of the Christian Democratic Union (CDU) next month, then stepping down as chancellor in 2021, at the end of her fourth term.

It might not work. The election of a conservative Merkel critic such as Friedrich Merz, the current frontrunner, as the party’s head would see her go before election day, many believe. Further big losses by the CDU’s coalition partners, the Social Democratic party (SPD), in coming state elections could also mean her government collapses as early as next year.

But whether or not Merkel sees out her last mandate, a battle royal is under way over her legacy. For her defenders, the chancellor is a calm, unflappable, non-ideological consensus builder who brought stability to her country and the EU in a string of major crises.

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She is, they say, a fundamentally decent politician who fought for democratic values; whose civil, level-headed persona represents all that the posturing populists now challenging Europe’s unity in countries like Hungary and Italy – and the one in the White House – do not.

Her critics say that on major policy questions she is indecisive, unknowable and panders to public opinion. They describe her as a tactician but not a strategist, with no real vision; unwilling and unable to challenge old German orthodoxies or change the political weather.

Perhaps most damningly, they suggest that her analytical, rational, non-partisan and ultimately technocratic style of leadership may, in the end, have actually precipitated the collapse of Europe’s political centre and helped pave the way for the populists.

“Politicians have to be effective and credible, and Merkel has been both,” says one of her supporters, Constanze Stelzenmüller, of the Brookings Institution. “She built relationships of trust – she had a relationship of trust even with Alexis Tsipras.”

At the peak of the eurozone crisis, when most of northern Europe wanted the Greek prime minister to be told his country had to leave the common currency, Merkel demurred, Stelzenmüller says, saying it would have been “a betrayal of the European project. She gains people’s trust because she has clear values.”

Those values are plain, supporters say, in Merkel’s determination to impose sanctions after Russia’s annexation of Crimea, her decision to welcome more than one million migrants into Germany in 2015, and her response to Donald Trump’s election (she pointedly offered him cooperation “based on the values of democracy, freedom, respect for the law and the dignity of all human beings”).

Facebook Twitter Pinterest Merkel and Trump hold a joint news conference in Washington in March 2017. Photograph: Jonathan Ernst/Reuters

And that thorough, lead-from-behind, won’t-be-rushed style? “It’s exactly what you want running a major power in the centre of Europe,” insists Stelzenmüller. “You have to build support, you can’t just ‘decide and do’. Imagine if you tried.”

Others, however, are not so sure. “Much of what we think we know about Merkel is either spin or speculation,” says Hans Kundnani, senior research fellow at Chatham House. “The extraordinary thing is, after 13 years in the chancellery we still don’t really know who she is.”

Certainly there is something about Merkel’s unremarkable personality that resonated with many Germans, who have sound historical reasons for disliking excessive political passion. As one diplomat puts it: “Policies were never the point of Merkel. What Germans knew about her character outweighed what they didn’t know about her ideas.”

For Jan-Werner Müller, professor of politics at Princeton university, many Germans saw Merkel as “an eminently reliable and highly analytical civil servant, not as a politician who has ever systematically staked out a vision for the country”.

Her frequent U-turns (on nuclear power after the Fukushima disaster, for example), “could only have been pulled off by someone seen as more of a civil servant-in-chief, who chose the most seemingly reasonable course of action, beyond partisan commitments,” Müller argued in Foreign Policy magazine.

But this managerial style of politics is not just out of step with a populist age, says Kundnani, but helped create it. The radical far-right party Alternative für Deutschland (AfD) emerged “in direct response to Merkel’s statement, regarding the Greek bailout, that there was ‘no alternative’,” he says. “It basically said: ‘Yes there is’.”

Merkel’s hard line on enforcing austerity was popular in Germany but almost certainly helped fuel support for populist movements in southern Europe, while her 2015 open borders policy – based, Kundnani believes, as much on a misreading of German opinion as on compassion – boosted the German anti-immigration party.

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Kundnani sees Merkel as a cynical operator, who is “Machiavellian” in her ruthless sidelining of political opponents and who acts generally in the way she believes will most appeal to voters. (Her statement on Trump can also be seen in that light, he says: “There are points to be scored in Germany by standing up to a US president.”)

As Europe’s de facto leader for so many years, her failure to do more to create a real architecture for European integration, or – more recently – to take bold steps to secure with France’s president, Emmanuel Macron, the institutional future of the euro, will not be viewed kindly by future historians, critics say.

Merkel’s defenders note the constraints placed on German chancellors, who have far less real power than French or US presidents, by their country’s political structure and strong constitutional court. “She’s not inscrutable; you just have to know her,” says Stelzenmüller. “Nor is she a populism enabler. She’s been a bulwark against it.”

But it could just be that her style of politics has left voters feeling deprived of real democratic choice - and encouraged the ongoing splintering of Europe’s politics. “We don’t yet know,” says Kundnani, “whether Merkel will go down in history as the woman who destroyed Europe, or saved it.”