In a written statement to The Post, D.C. Police Chief Cathy L. Lanier did not distinguish between warrants based primarily on training and experience and those based on more-extensive investigation. She said that all of the warrants the department executed last year were constitutionally sound and that each warrant was reviewed by a police lieutenant as well as prosecutors and ultimately approved by a judge.

“In the vast majority of those warrants, contraband and evidence was recovered in furtherance of criminal prosecutions, and gave MPD [the Metropolitan Police Department] the ability to bring closure to multiple victims of crimes in our city,” she said. “During that same time frame, MPD received very few complaints regarding the execution of those warrants.”

Lanier said residents who are dissatisfied with police should speak with a supervisor at the department or the Office of Police Complaints. “We remain committed to unbiased constitutional policing,” she said.

The U.S. Attorney’s Office said in a written statement that its prosecutors carefully review thousands of warrants each year to determine whether they meet the standards for probable cause.

“Probable cause merely requires that the facts and circumstances available to the officer provide the basis for a reasonable person to conclude that evidence of a crime exists at a location,” the statement said. “Although no system is perfect, the law and the multiple layers of review provide safeguards to minimize the potential for errors.”

Lee F. Satterfield, chief judge of the D.C. Superior Court, declined to comment, citing pending cases.

Karakatsanis studied a year of warrants in which police searched for drugs based on training and experience and found that they recovered drugs one-third of the time. In response to Karakatsanis, then-D.C. Attorney General Irvin B. Nathan argued in 2014, “While Plaintiffs treat this success rate with contempt, finding drugs in one-third of similar police searches is strong evidence of probable cause.”

Nathan also pointed out that the Supreme Court has held that probable cause cannot be reduced to a “precise definition or quantification.”

In January, U.S. District Judge James Boasberg allowed the first of Karakatsanis’s cases to go forward, saying that “a talismanic invocation” of “training and experience” does not automatically satisfy constitutional requirements.

The raids for which police do more investigative work appear to bring better results, The Post found. In February 2015, police searched a house in Southeast and seized an AK-47 assault rifle, two semiautomatic handguns and 100 grams of marijuana. In April 2014, police in Northwest found 25 grams of heroin, 330 grams of marijuana, a revolver and an assortment of ammunition. They also found $60,000 in cash.

Perhaps the most successful raid among the 284 identified by The Post occurred after police made a traffic stop and found a revolver and four hollow-point bullets in the glove box. A search of the suspect’s house turned up two shotguns, a semiautomatic handgun and an assortment of ammunition. The suspect received a 10-month suspended sentence for firearm charges and served no time in jail.

Most of the time, police find much less.

Police told a judge that their training and experience investigating drug cases led them to think that they would find evidence of a PCP-trafficking operation when they raided the house of Margaret Brown in April 2014.

Brown’s son had overdosed on PCP at a building across the street from her apartment in Northwest Washington. A vial containing a small amount of the drug, an eighth of an ounce, was found in his clothes. Police arrested him for possession of PCP, a felony, and he was later sentenced to four months in jail.

The evening after his arrest, police in body armor burst through Brown’s front door.

“They slammed me to the ground,” said Brown, 47, who had just returned home from her job in billing at a hospital and has never been convicted of a crime. “They were fully armed — guns pointed in my face like there was a major drug deal going down.”

Brown said she sat handcuffed while police went through her belongings, knocking over furniture and even opening an urn containing her mother’s cremated remains.

The search turned up a partially burnt marijuana cigarette. Brown told police that it belonged to her son, who she said has a marijuana card allowing him to legally possess the drug for medical reasons.

They arrested her for misdemeanor possession, and she spent five hours in jail.

Eight weeks later, prosecutors dropped the charge against her.