Joseph Kenny, the Police Department’s chief of detectives, at a news briefing on Friday, said the suspect offered a timeline showing that within roughly an hour of the killing, the suspect likely fled town on a zigzag escape route through Manhattan by bike, foot, cab and bus.

The chief said the suspect arrived in New York City at 10:11 p.m. on Nov. 24 on a bus that originated out of Atlanta. He took a cab to the New York Hilton and spent about half an hour walking in the area of the hotel before checking into a hostel on the Upper West Side, the chief said.

At the hostel, he stayed under fake identification, always using cash, avoiding conversation and hiding his face with his mask even during meals, the chief said. He never spoke with anyone and lowered his mask once to speak, smiling, to the hostel clerk, the chief said.

“We do not have his name,” Chief Kenny said. “At this point, we believe he acted alone.”

The gunman left the hostel at 5:30 a.m. on Dec. 4 and rode a bicycle toward midtown, Chief Kenny said. At 5:41 a.m., he arrived at the Hilton and began wandering the area near the hotel, walking back and forth on West 54th Street, before going into a Starbucks, where he bought a bottle of water and a snack bar.

After shooting Mr. Thompson at 6:44 a.m., he got back on the bike and made it into Central Park four minutes later. He left the park at 6:56 a.m., still on the bicycle. Surveillance cameras captured footage of him, still on the bicycle, two minutes later at 86th Street and Columbus Avenue. By 7 a.m. he was still on 86th street, no longer on the bicycle. He then took a cab northbound to a bus station near the George Washington Bridge.

By 7:30 a.m. he had made it to the bus station, where video surveillance showed him going in but not coming out, Chief Kenny said.

The police have not been able to find the bicycle, he said.

The police have made no arrests in the attack on Mr. Thompson, the 50-year-old executive who led UnitedHealthcare, one of the United States’ largest health insurance companies.

Here’s what else to know:

New details: The news about the suspect likely leaving town came after a series of breaks in the case earlier on Friday, including the disclosure by the authorities that they had obtained DNA from a water bottle at the scene and took it for testing. Chief Kenny said they had a passenger list for the Greyhound bus that brought the suspect to New York but emphasized that passengers did not need identification or a credit card to board the bus, so he could have even boarded as John Doe.

Facial recognition: Experts in facial recognition technology disagree on whether the widely circulated security-camera images of a smiling man wearing a hooded jacket, but depicting his face from a sharply downward angle, would contain enough detail to identify him, since the technology works best with a high-resolution photo of someone looking directly into a camera.

Insurance denials and rage: The killing unleashed a torrent of criticism of insurance companies, in particular UnitedHealthcare. Covering more than 50 million people, the company has battled complaints and investigations from patients, doctors and lawmakers for its denial of claims.

The police have released two surveillance camera stills in which the entire face of a person the authorities are seeking is visible, including one in which he is smiling. Both images are grainy, and his face is captured from a sharply downward angle.

Anil Jain, an expert on facial recognition technology at the Michigan State University, said the photo in which the man is smiling contains enough detail for a facial recognition system to yield potential results.

“The challenge will be which face database to search against,” Dr. Jain said. Law enforcement officials could search the F.B.I.’s mug shot database, the drivers’ license databases of New York State and neighboring states, or public photos on the internet using a system such as Clearview AI.

A facial recognition search would yield a list of people deemed similar looking to the person in the original photo. The police would need to find other evidence to tie a person identified that way to the crime, Dr. Jain said, or run the risk of making a wrongful arrest.

Other experts disagreed about how useful the images could be for identifying the man.

Alessandro Acquisti, a technology and policy professor at Carnegie Mellon University, said that the photos shared with the public would not be enough to uniquely identify the man because they were not full-frontal images. They could, though, help to “restrict the pool of likely suspects,” he said.

Giorgi Gobronidze, the chief executive of PimEyes, a face search engine that anyone can use to find photos of a person on the internet, was skeptical that the poor-quality images would produce reliable results. A facial recognition system performs best with a high-resolution photo of someone looking directly into a camera.

Mr. Gobronidze also said that automated facial recognition would only work if the images of the person were in the database being searched.

“If the person in the image has little to no online presence,” Mr. Gobronidze said, PimEyes “won’t be able to find anything.”

A correction was made on

Dec. 6, 2024

:

An earlier version of this article misidentified the university where Anil Jain works. He is at Michigan State University, not the University of Michigan.

When we learn of a mistake, we acknowledge it with a correction. If you spot an error, please let us know at nytnews@nytimes.com.Learn more

For those who professionally study criminal behavior, though, the shooting was packed with crucial information, with the killer’s every known move providing new opportunities to speculate about who he might be.

The police said the shooting was a targeted attack by someone with experience with firearms. But was that someone acting on a personal grudge — or a hired hand? And if the killer was a hit man, was he an amateur or a seasoned professional?

The consensus among experts following the killing of Brian Thompson, the veteran chief executive of one of the nation’s largest health insurers, was that the shooter could indeed handle himself around a gun, but that everything else suggested that he was unlikely to have been hired to commit the crime.

“Forgive me for saying too much on too little evidence, but it looks like the kind of guy that made up his mind that he was doing the right thing,” said David Shapiro, a professor at John Jay College of Criminal Justice in New York, and a former F.B.I. special agent. “He didn’t look like a guy that was fearful.”

He added: “In terms of a professional hit man, that seems unlikely. It would be very hard to get somebody to do something like this. It’s very high risk.”

The gunman waited by a specific entrance to the New York Hilton Midtown and fired his weapon with confidence. He also appeared to have outfitted his gun with a silencer, which are rarely used in murders.

But silencers have become more popular, and while the shooter may have had military or law enforcement training, experts pointed out, he could just as easily be an avid hunter or have practiced at a range.

The culprit did appear to have a getaway plan: jumping on a bicycle, perhaps electric, and riding it toward Central Park, the last place where he was spotted. But again, experts were skeptical. “That’s not much of a plan — on a bicycle,” said Dennis Kenney, also a professor at John Jay College. “Even an electric bicycle.”

“I mean, the whole problem is doing the whole thing in Midtown Manhattan, even though it’s in the morning,” he continued. Not only are there “cameras everywhere,” he said, “there’s too much of a possibility of other people intervening, of a cop happening to walk by.”

He added: “There’s just too much that can go wrong and there’s too little that you control.”

And the shooter left a trail of clues.

On Thursday, the police released images of a man they said was wanted in connection with the shooting, and revealed that bullet casings collected at the scene had been inscribed with messages, including the words “delay” and “deny.”

Before the shooting, according to the police, the man stayed in a hostel some miles away, on the Upper West Side of Manhattan, where he shared a room with other guests and where his smiling face was captured by a surveillance camera. He went to a Starbucks near the Hilton before the shooting, where a camera again recorded his actions.

After the shooting, the police found not only the shell casings but also a cellphone that they are examining.

None of this looks like the work of a professional, the experts said. (Assassinations occur but are usually ordered by governments or criminal groups like drug cartels, and rarely leave behind much evidence, they said.)

On Thursday, when authorities revealed that the bullet casings collected at the scene were scrawled with “delay,” “deny” and other words, they did not suggest the meaning of the messages. But some experts wondered if the shooting could have been motivated by frustration over common problems people have with health insurers — problems for which Mr. Thompson’s company, UnitedHealthcare, was often criticized.

At this point, all signs point toward a person who is not a professional, according to Gary Jenkins, a former police investigator from Kansas City, Mo., who now hosts the “Gangland Wire” podcast. Instead, it was likely “somebody that has an ax to grind,” he said.

In rare cases, Mr. Jenkins said, people who are upset tap their networks for a hired gun. An angry spouse, a jilted lover or a duplicitous business partner might ask a bartender, hairdresser or a friend if they know someone who knows someone.

But like the other experts interviewed in the wake of the shooting, Mr. Jenkins speculated that in this case, it was the shooter himself, or someone close to him, who was “disgruntled,” possibly over something related to insurance coverage.

Others brought up the possibility, however remote, that the messages on the shell casings — words that could be perceived as a reference to the tactics used by insurers to avoid paying claims — were written to throw investigators off track. “Is that a great red herring?” asked Mr. Shapiro, the former F.B.I. special agent.

Time will tell.

But like red herrings, the idea that someone can easily hire a hit man is “more the stuff of movies and fables,” said Michael C. Farkas, a defense attorney who has worked as a New York City homicide prosecutor. “I’m not saying it’s never happened or that there aren’t mercenaries that can be hired,” he said. “But this doesn’t seem to be such a situation.”

It is far more likely, he agreed with the others, that the shooter acted alone. “I think he planned this as meticulously as his abilities allow,” said Mr. Farkas. “And he’s probably intelligent enough to know the odds of evading capture indefinitely are not in his favor,” he said.

“He clearly wanted to send a message, and he is trying to get away.”

The killing, however, stunned business leaders, some of whom were already concerned about safety. Over the last five years, there has been a sharp rise in targeted attacks, digital and offline, of executives and their families, said Chris Pierson, the chief executive of BlackCloak, a digital executive protection firm. Health care, biomedical and pharmaceutical leaders tend to be targeted more often than executives in other industries, according to the firm’s data.

Digital platforms have made it easier to obtain information about executives’ identities and locations, while social media has fanned the flames of vitriol directed at these corporate leaders.

Businesses have been increasing their spending on protection: The median amount spent on executive security among the S&P 500 companies that disclose that information doubled from 2021 to 2023, according to Equilar, an executive compensation research firm.

Because of how frequently threats circulate online, companies and security firms must spend time and effort sorting threats by the severity of threatened harm, the likelihood of an attack and the capacity of the individual making the threat, Mr. Pierson said.

While some social media users responded to the news of Mr. Thompson’s killing with anger and schadenfreude, posting their frustrations about being denied reimbursement for crucial medical treatments, many corporate leaders shared a sense of fear at seeing a not particularly prominent executive fatally gunned down on a Manhattan street.

“My wife was like, ‘Why would someone kill a C.E.O.?’ I’m like, any C.E.O. has people who don’t like them. C.E.O.s have to let people go. C.E.O.s have people competing with their business,” said Seth Besmertnik, chief executive of a software company whose office is also in Manhattan.

Brad Karp, chairman of the law firm Paul, Weiss, said, “It was chilling and disturbing to see the assassination captured on video, two blocks from my office.”

For some chief executives, the shooting is a wake-up call: Political leaders aren’t the only ones who need to be on high alert about their personal safety. Many are now scrambling to do more.

Leaders at Allied Universal, which provides security services for 80 percent of Fortune 500 companies, said their phones were “ringing off the hook” on Wednesday with potential clients. Allied covers a wide spectrum of services — including stationing guards outside offices, chauffeuring executives, surveilling their homes and tracking their families.

Protecting a chief executive full time costs roughly $250,000 a year, said Glen Kucera, who runs Allied’s enhanced protection services.

This month, dozens of Fortune 1000 chief executives will gather for a summit in Midtown, at the Ziegfeld on 54th Street, steps away from where United Healthcare’s chief executive was shot.

Jeffrey Sonnenfeld, who runs Yale’s Chief Executive Leadership Institute and will convene the summit, received a barrage of phone calls on Wednesday with questions about safety at the event. Mr. Sonnenfeld said city police and private guards would be stationed at the summit, a decision that was made before Wednesday’s shooting, though in the past he has not worried about a security presence at the event, which has been held for more than 30 years.

“From the left and the right we’ve seen the frightening, uncanny conversion of angry and deranged people,” Mr. Sonnenfeld said. “Leaders in the corporate world are convenient targets.”

Ranjay Gulati, a Harvard Business School professor, noted that while people were often frustrated with businesses — take Purdue Pharma and its role in the opioid crisis or BP and the Deepwater Horizon oil spill — it was shocking to see that anger lead to violence.

“There’s a latent undercurrent here of how frustrated people are with the health care industry,” Mr. Gulati said. “I’m not condoning the action in any way, but there’s a lot of soul-searching we have to do about an industry that consumes nearly 20 percent of our G.D.P. and yet our outcomes are not nearly as good as countries that spend half as much.”

The police said bullet casings found at the site of the killing appeared to have the words “deny” and “delay” written on them — terms familiar to people seeking coverage for medical procedures.

Kathryn Wylde, the chief executive of the Partnership for New York City, a nonprofit representing the city’s business community, said Mayor Eric Adams called her early Wednesday and told her that the shooting appeared to have been targeted rather than random, asking her to notify members of the partnership.

Next week, the Partnership for New York City will host the city’s new police commissioner, Jessica Tisch, at its annual meeting. Ms. Wylde said that business leaders had been focused on public safety in the city more broadly, but that the shooting of Mr. Thompson could prompt a deeper conversation about the personal security of chief executives.

“It’s reasonable to think that violent rhetoric can lead to tragic results,” Ms. Wylde said.

As is typical for public rewards offered by the department, the money would be supplied not by the N.Y.P.D. itself but by the donor-funded New York City Police Foundation, an independent nonprofit that also provides safety equipment and other resources.

The Police Foundation has bankrolled the department’s payments for public information since 1983, and says it has covered more than $3 million in rewards over those four decades.

The payment program, called Crime Stoppers, maintains a tip hotline and offers up to $3,500 for any information that leads to an indictment for a violent crime.

But the foundation said that it had approved a request by the Police Department for an additional $6,500 — nearly tripling the normal offer — to seek information about the killing of Brian Thompson, the chief executive of the UnitedHealthcare.

Mr. Thompson, 50, was shot by a masked gunman early Wednesday morning outside the New York Hilton Midtown, which was hosting his company’s annual investors day.

The reward could grow if the Police Foundation approved an increase, and the reward could also be boosted through other sources, including government funds or private contributions.

The Police Department said that it never uses its own funding for rewards, and that the policy helps ensure that tipsters can remain anonymous.

Tips to Crime Stoppers have helped solve more than 5,000 violent crime cases, according to the police.

The department has at times offered five-figure rewards for information about unsolved homicides or the attempted murder of a police officer.

The offer of $10,000 for information on the killing of Mr. Thompson is on the “upper end” of the reward scale and could motivate people to come forward, said Richard M. Aborn, the president of the nonprofit Citizens Crime Commission.

“It means there’s a very high-profile shooting that is being taken incredibly seriously,” Mr. Aborn said, adding, “Information is the life blood of policing, and cops are going to do whatever they can to get information.”

Eli B. Silverman, a professor emeritus at John Jay College of Criminal Justice in New York who has written extensively about the city’s police, said he was initially surprised by the size of the reward. But he said the prominent location of the shooting, the high profile of the victim and the intense news coverage explained the offer.

“This person is more than a statistic,” Mr. Silverman said. “This stands out. This attracts attention. And so I think that’s why they’re going that way.”

While the words “deny” and “delay” have multiple meanings, they could be a reference to the tactics used by insurers of all kinds to avoid paying claims. The words are so linked to those practices that they were used in the title of a 2010 book probing them, “Delay, Deny, Defend: Why Insurance Companies Don’t Pay Claims and What You Can Do About It.”

“An insurance company’s greatest expense is what it pays out in claims,” wrote the book’s author, Jay Feinman, an emeritus professor at Rutgers. “If it pays out less in claims, it keeps more in profits.”

No one knows how often private insurers like UnitedHealthcare deny claims because they are generally not required to publish that data. People who bought coverage under Obamacare, a government-funded plan, had 17 percent of their care denied in 2021, according to KFF, a health policy group. Other surveys have found that denials are more prevalent among those with private insurance than those who carried government coverage.

UnitedHealthcare, part of the giant conglomerate UnitedHealth Group, reported more than $16 billion in operating profits last year and employed roughly 140,000 people. The company is a frequent lightning rod for criticism over how it handles claims.

Earlier this year, a Senate committee investigated Medicare Advantage plans denying nursing care to patients who were recovering from falls and strokes. It concluded that three major companies — UnitedHealthcare, Humana and CVS, which owns Aetna — were intentionally denying claims for this expensive care to increase profits. UnitedHealthcare, the report noted, denied requests for such nursing stays three times more often than it did for other services. (Humana had an even higher figure, denying at a rate 16 times higher.)

UnitedHealthcare did not respond to a request for comment about its history of claim denial.

Journalists have also scrutinized United’s denial practices. In January, the health news outlet Stat published a detailed investigation into how a UnitedHealthcare subsidiary, NaviHealth, used algorithms to deny care for seniors enrolled in the company’s Medicare advantage plan.

The Stat investigation noted specific instances that troubled United employees, like when an older woman who had a stroke was only covered for half the nursing days typically required for recovery.

UnitedHealthcare and its parent company now face a class-action lawsuit over its use of the algorithm. In response to the Stat article, the company issued a statement that “the assertions that NaviHealth uses or incentivizes employees to use a tool to deny care are false.”

A 2023 story from ProPublica dived deep into the experience of one United patient, a college student who racked up $2 million in medical claims a year to treat a severe case of ulcerative colitis. The story showed United disregarding an internal report finding the expensive treatment to be necessary. The patient eventually sued United and received an undisclosed amount in a settlement.

Insurance denials are rarely appealed, with some studies finding appeal rates of roughly 1 percent.

UnitedHealthcare, in response to the ProPublica story, said that the patient took his medication at dosages that “far exceed” Food and Drug Administration guidelines, which led the insurer to “review treatment plans based on current clinical guidelines to help ensure patient safety.”

Since the news of Mr. Thompson’s death on Wednesday, some individuals on social media have expressed frustration over the company’s history of denying claims. Others have gone even further, celebrating the death of a top insurance executive.

The insurance industry has pushed back against the outrage. “The people in our industry are mission-driven professionals working to make coverage and care as affordable as possible and to help people navigate the complex medical system,” said Michael Tuffin, the president of AHIP, a major trade group, on LinkedIn. “We condemn any suggestion that threats against our colleagues — or anyone else in our country — are ever acceptable.”