After years on the public stage, Mayor Bloomberg is a puzzle even to those who watch him closely. On the one hand he has thrown himself into the mayoralty, winning re-election — and, in political terms, vindication — by a wide margin. On the other hand, his public flirtation with the presidency ended up raising more doubts than it answered. The more the current presidential race grinds on, the greater the impact it appears, at least to the editors of these columns, he could have had had he not pirouetted away.

The answer to how serious he is about the vision he has put up for New York will come with his decision on whether to run for governor. The idea of a run for the governorship is being advanced within the mayor’s inner circle — and also his outer circle, by which we mean a number of savvy unofficial advisers who have grown enthusiastic about his leadership of the city. When one puts the question to his friends, the first thing they retort is that the mayor just doesn’t like Albany. To which one can only say that Audie Murphy didn’t like mud. But he didn’t walk away from the war.

In the case of Mr. Bloomberg, he is now being mocked and chided in public by Senator Schumer, who calls the mayor’s plan for the West Side the “goofiest thing I’ve ever seen.” The mayor turned around and told the senator to mind his own business back in Washington. The New York Times has swung in behind the senator, proposing to give responsibility for Moynihan Station to the very institution, the Port Authority, that has failed so spectacularly at ground zero. The fact is that if Mr. Bloomberg walks away, his detractors are going to have the last laugh. And not just on the West Side.

Earlier this week we issued an editorial in respect of the mayor’s legacy in the city, encouraging him to encourage the best members of his administration — or others — to step forward as candidates to succeed him. But protecting the mayor’s legacy in City Hall is one thing. Protecting his successor is another, and the best way to do that is for the mayor to campaign and win the governorship so that he can follow through on what he’s started. It would put him in a strong position in respect of mayoral control of the schools, of reform at the rolling disgrace known as the Metropolitan Transportation Authority, of the West side, of the charter school movement, and of the budget issues.

It is a pity that the mayor walked away from the Republican Party. It is lying fallow in a state in which it once elevated to high office such figures as Javits, Rockefeller, Pataki, and Theodore Roosevelt, to name but a few. One could see, given the strictures of the Republican Party on the national level, the temptation of an independent or third party run for the presidency. But in New York state the Republican Party would have been a win-win for Mr. Bloomberg and could, we’d aver, yet be. The thing the mayor is going to have to do is decide just how serious he is about the public weal and whether he is the type who is going to finish what he started.