The difference is not trivial. The ticket would not have cost Mr. Welfare a job that paid him about $40,000 a year. He was arrested on Aug. 16, the first time he had ever had any trouble with the law. That was a Saturday. By Monday, the bus company he worked for had been notified, and he was fired on the spot. His experience was chronicled last month in this column. (At the time, Mr. Welfare asked that his last name not be revealed.) Since then, the charge against him has been dismissed and his record is once again clean. But he has not yet been able to regain his old job, and to date, he has lost nearly $10,000 in wages.

“Now the change goes into effect — after what I just been through,” Mr. Welfare said.

For the most part, the policy change won’t affect white pot users, who were not likely to be stopped and told to turn out their pockets, or to be accused of openly displaying marijuana — or its residue — in the center console of a car. Pot in someone’s pocket is mere possession, not a crime; having it in the open is a misdemeanor. Tricking people into displaying it was called manufacturing misdemeanors. For much of Mayor Michael R. Bloomberg’s administration, such misdemeanor marijuana arrests took place at the rate of one every 12 minutes, or 50,000 a year. Overwhelmingly, those charged were black, like Mr. Welfare, or Latino. Most had never been in trouble with the law.

Mr. Bloomberg and his aides scoffed at the notion that the arrests were a big deal, saying most of those cases were dismissed and sealed. Indeed, that is what happened with Mr. Welfare’s case — after he was fired. A pot charge can cost people jobs that require clean criminal records, like security guards for city and state agencies, or home health care attendants. For immigrants, there can be other harrowing consequences: A Liberian man was held in an immigration jail for a year pending deportation on a marijuana case before the charge was downgraded, said Mitch Briskey, a lawyer with the Legal Aid Society.

How did this go on so long? Part of it, Mr. Bratton said, is that a large number of public complaints come to the police about open pot dealing or smoking.

But there is more. During the stop-and-frisk era, police precincts set numerical goals for “activity” by officers, a standard management productivity tool in all lines of work. It was an article of faith that the stops would help drive down crime. But the numbers became an end unto themselves, a toxic force propelling a machine that devoured the people it was supposed to keep safe.