Story lines about New York’s mayors are like the soiled wads of gum that polka-dot our sidewalks. They get ground in quickly and are pretty hard to ever remove. David Dinkins, for instance, is widely remembered as the mayor who presided over an alarming crime wave before Rudy Giuliani rode in to restore order. Only true city-nerds recall that the murder rate began its fall under Dinkins, or that the increase in the size of the police force—which facilitated some of the aggressive crime-fighting strategies of the Giuliani era—was set in motion by New York’s first black mayor.

Sometimes these mayoral story lines get written even before a mayor takes office. Mike Bloomberg’s reputation as a great manager colored the lens through which his mayoralty was seen from the beginning. Now Bill de Blasio’s lack of managerial experience is being set up as the Achilles’ heel of his administration.

This is especially true among observers outside New York, among whom the conventional wisdom is that the mayor has been extremely successful as a manager, and that his successor could learn something from him. So said E.J. Dionne in The Washington Post this week:

To achieve his goals, de Blasio will need the evidence-based approach and crisp management style that Bloomberg championed. Bloomberg told the New Yorker’s Ken Auletta that he wanted to be known for having set “a tone that the city can be well run and can invest in the future.” That’s not a bad description of what de Blasio needs to do.

It certainly isn’t. Nor is it a bad description of what Bloomberg did… sometimes. Indeed, to watch Bloomberg give a budget presentation was to witness a public official with full fluency in the issues he was discussing—a frighteningly rare treat. But for better and worse, Bloomberg was never the manager-in-chief some observers paint him as.

On one hand, the manager-in-chief label sells the mayor short: he was in many ways, from the rezonings to the school reforms to the health stuff, more visionary—whether we liked the vision or not—than a mere bean-counter.

More importantly, the Bloomberg management record was sometimes distinctly un-crisp.

CityTime was a massive boondoggle, and it was far from the only technology project that could have done with better management. The 2010 snowstorm was a dangerous lapse in supervision, and the aftermath of Superstorm Sandy, when power outages kept tens of thousands of people in the dark and trapped in high rises, was a management disaster. The selection of Cathy Black as schools chancellor was deeply irresponsible. The conditions that developed in New York’s public housing over the Bloomberg years were not anyone’s idea of good management in action, nor was delegating so much authority to NYPD commissioner Ray Kelly over arresting protesters and spying on Muslims. And if the evidence-based approach was so beloved by Bloomberg, why did the city double down on stop-and-frisk despite ample evidence that it was not effective, or expand the conditional cash transfer despite middling results on its trial run?

The point isn’t that Bloomberg was a bad manager; actually, he was a decent one. The point is that operating the enormous and complex city bureaucracy is bound to result in some management failure. So when de Blasio screws up, as is inevitable, let’s be careful about labeling him a bad manager or comparing him unfavorably to Bloomberg just because that’s what the script says.

Because in the end, we don’t just need our mayors to be managers. We need them to be leaders. Bloomberg himself recognized this with his reference, to Auletta re-quoted by Dionne, about “investing in the future.” Investment isn’t just about efficiency; it’s about being guided by your values in assigning resources to benefit people you may never meet. Bloomberg didn’t invest nearly enough attention or political capital on the growing problem of income polarization in the city. Hopefully, de Blasio will manage to.