No one would claim that the New Orleans Police Department is in great shape.

Troop strength is at its lowest level in decades, with the force having shrunk about 30 percent in four years. Embarrassments are routine: Just last week, the department failed to alert the public that one of its officers had shot a man in the head. Morale among the rank and file is thought to be low.

All that said, many observers say that departing Superintendent Ronal Serpas did an admirable job in playing an almost impossible hand.

“I think he did more with less than any chief in the past 36 years,” said Metropolitan Crime Commission President Rafael Goyeneche, a member of the search committee that recommended hiring Serpas in 2010. “I think not too many people could have matched his accomplishments, given the circumstances he inherited in this department.”

Goyeneche and other Serpas admirers noted that the chief’s authority, like that of any police chief, was limited. It was Mayor Mitch Landrieu and the City Council, not Serpas, who trimmed the NOPD’s budget and instituted a hiring freeze that shrank the ranks and inflated response times. The Civil Service Commission, meanwhile, often overturned discliplinary actions meted out by the chief.

Despite all those obstacles, Serpas was able to achieve real progress, his supporters say.

Michael Cowan, chairman of the New Orleans Crime Coalition, pointed to the biannual surveys measuring citizen attitudes toward the NOPD that his group has conducted since 2009, when Warren Riley was still chief. Back then, 33 percent of those polled said they were satisfied; the number now is 60 percent.

“I would attribute most of that to Serpas’ leadership,” Cowan said.

Murders, too, are down steeply. The 156 homicides in New Orleans last year were the fewest the city has seen in decades, and if trends hold up, this year will see a small drop from there.

Granted, New Orleans’ murder rate is still among the highest in the nation, and how much of the credit for the drop should go to Serpas is an open question. Landrieu has made homicide reduction the centerpiece issue of his tenure, and he has portrayed the progress as a vindication of his broad NOLA for Life initiative, which stretches well beyond policing.

While murder is the metric that gets the most attention in New Orleans, both Cowan and Goyeneche pointed to a large increase under Serpas in the percentage of felony arrests that result in convictions. That number has nearly doubled, going from 24 percent in 2007 to 45 percent in 2012, according to the MCC’s research.

“That’s been accomplished by the district attorney and the Police Department working as partners rather than adversaries,” Goyeneche said. “That’s a concrete, tangible accomplishment. As the dust settles and we look back, we will see that the District Attorney’s Office and the Police Department made a quantum shift.”

Then there are the gee-whiz reforms, like the body cameras Serpas unveiled at a news conference last year — a measure now being phased in that goes beyond the mandates of a federal consent decree governing NOPD reforms. Recording all officer contacts with the public should deter misconduct, the chief said.

Serpas consistently championed technology and introduced a data-driven crime analysis program, his supporters say, though critics often argued that he cared more about the statistics than the reality on the ground.

“It seemed to me that he knows the best things going on in contemporary policing, and he was always ready to adopt those,” Cowan said.

“He brought the department into the 21st century,” Tulane University criminologist Peter Scharf said.

Scharf also said the chief deserves credit for taking a harder line on officer honesty than some of his predecessors.

“I think his legacy will be known for addressing issues of integrity, which have built public confidence in the department,” Scharf said. “He took the department from mass opprobrium to quite a sense of strong integrity.”

Not everyone was a fan of Serpas, of course. He didn’t get much of a grace period, in part because the nationwide search process that resulted in his hiring was criticized as a sham in which the hometown boy always had the inside track.

Four members of the search committee quit or were removed by Landrieu, but that hardly quieted things. Critics began calling for Serpas’ resignation early on, and the calls surfaced repeatedly over the next four years as one controversy or another flared up.

“We’re glad the resignation has happened,” said Tamara Jackson, director of the grass-roots group Silence Is Violence. “Our organization had issues with his selection as chief five years ago. We believe he was not the right person to lead the department from the beginning.”

Among the problems Jackson laid at Serpas’ feet: poor morale, depleted staffing and uneven discipline, including “unfair” reprimands given to several officers.

Norris Henderson, of the group Safe Streets Strong Communities, said he was “very excited” Serpas is leaving, in large part because he doesn’t think he has done enough — or anything — to stem the tide of bloodshed.

“He was hired to decrease the murders going on in the city,” Henderson said. “We have people shot in bunches now; we’re not just having the solo incident. We’re having incidents where five or six people are being injured, and we’re fortunate when maybe only one or two of them are dying.”

Henderson said he doesn’t believe the crime rate has changed much, if at all.

“It’s just how it’s being reported. Like when the police shot someone a week ago and didn’t tell anyone about it. We’re not seeing all the information the public should be privy to. They’re trying to pad their books. I’m glad he’s gone.”

Questions about the accuracy of the NOPD’s reported crime statistics cropped up repeatedly during Serpas’ tenure, with newspaper reports questioning whether some assaults were being downgraded to lower the city’s violent crime rate, and Inspector General Ed Quatrevaux issuing a report that found many French Quarter thefts were improperly classified as “lost or stolen property.” That category does not count as a crime in the statistics the NOPD sends to the FBI.

Serpas strongly denied any effort to fluff the department’s numbers, saying any errors in crime reporting were honest mistakes.

Serpas had plenty of enemies, in no small part because of his attitude. Critics said he could be a bully, and he was often seen as aloof. But Goyeneche said he believes the chief earned some of the hostility by doing the hard things. He portrayed Serpas as almost a martyr, a leader whose tenure was bound to be short.

“Someone in law enforcement who I respect told me, when Mitch was looking for a chief (in 2010), ‘Mitch needs to be looking not for one but two chiefs,’ ” Goyeneche said. “ ‘Because the first one is going to be so unpopular, because of the things that have to be done, that at some point it’s going to be necessary to make a change.’ ”

Staff writers John Simerman and Jim Mustian contributed to this article.