In his efforts to address the homeless crisis, Mayor Bill de Blasio has tried over and over to throw something new at it. Then, it seems, he waits to see what sticks.

A piecemeal game of darts won’t work on a critical, complex issue, especially without better leadership.

The clearest example came this week. On Tuesday, Gilbert Taylor, de Blasio’s homeless-services chief, resigned. It was a chance for de Blasio to clean house in an agency long criticized for its bumbling of the crisis.

But Taylor isn’t going anywhere. He’s keeping his $220,000 salary to advise the mayor on overhauling the homeless system and fixing the very agency he led. What’s more, City Hall gave Human Resources Administration Commissioner Steve Banks the unenviable three-pronged task of leading his own agency, heading homeless services, and conducting a review of homelessness operations.

It’s a baffling move. After all, how do you reform a system and make it new while being advised by those who ran it the old way? How do you pay an adviser equal to a commissioner? And how does an insider conduct a credible review and lead two agencies simultaneously?

De Blasio threw a new dart yesterday with Home-Stat, an outreach effort to canvas the city, count homeless people quarterly, and add mapping, data-gathering and staff. It’s a good idea. But without a broader strategy and new leadership and expertise, the crisis will remain unsolved.

City officials defend the strategy, saying current personnel can conduct a review, implement new programs and tackle the problem. But they fail to see it’s not that simple.

The homeless problem is staggering, with up to 4,000 people living on the streets and more than 57,000 living in shelters. Addressing it is difficult and complicated. It has deep roots that predate de Blasio, but for now, it’s his crisis to confront. He should take a step back and stop trying to toss hasty answers at a problem that needs more. He should commit to a true overhaul, bring in new people with new ideas, and let them lead. Perhaps then, the city might arrive at a comprehensive plan that shifts how homelessness is handled.

Perhaps then, de Blasio might finally hit the bull’s-eye.