LAS VEGAS — The man who killed 49 people at an Orlando nightclub last year pledged allegiance to the Islamic State, in a 911 call, as the massacre unfolded. The sniper who shot to death five police officers in Dallas told the police that his goal was to attack white people. The man who attacked a black church in Charleston posted a racist manifesto online.
In one mass shooting after another, gunmen have offered telling evidence of their motives: complaining of “baby parts” after a shooting at Planned Parenthood, sympathizing with the Islamic State with a Facebook post on the day of the San Bernardino shooting, asking members of Congress if they were Republicans before pulling the trigger at a congressional baseball practice.
But in the four days since Stephen Paddock’s attack in Las Vegas — a shooting rampage that left 58 dead and hundreds seriously wounded — what drove him has remained a mystery, vexing the public and putting enormous pressure on federal and local investigators to find answers.
“In the spirit of the safety of this community or anywhere else in the United States I think it’s important to provide that information, but I don’t have it,” Sheriff Joseph Lombardo of the Las Vegas Metropolitan Police Department said in an interview Thursday. “We don’t know it yet.”
No grandiose manifesto has been found. No account of Mr. Paddock behaving dangerously or holding extremist views has emerged from neighbors or relatives. Unlike past killers, Mr. Paddock did not dial up the police to explain his actions.
The F.B.I. took Mr. Paddock’s computers and cellphones to its laboratory in Quantico, Va., for review, law enforcement officials said. Agents interviewed his girlfriend, Marilou Danley, in an attempt to determine his mental state at the time of the shooting, but Sheriff Lombardo said he was “not at liberty to say” what information had been learned.
Of course, investigators could at any time come across evidence that reveals Mr. Paddock’s thinking. “I’m pretty confident we’ll get there,” Sheriff Lombardo said.
Agents have fanned out across the country, interviewing family members and friends and looking for signs of mental illness.
Mr. Paddock left a trail of clues that are, so far, more cryptic than revealing: There was a note in his hotel room whose exact contents the authorities have yet to reveal. Sheriff Lombardo said that it contained numbers that were being analyzed for their relevance, and that it was not a manifesto or suicide note.
Mr. Paddock may have scouted other locations, including Fenway Park in Boston, Lollapalooza in Chicago and the Life is Beautiful music festival in Las Vegas, before finally checking into a suite at the Mandalay Bay that had clear sight lines to Route 91, and a massive gathering of country music fans. He stockpiled expensive firearms over the course of many months.
Investigators have identified 47 firearms belonging to Mr. Paddock, including a dozen in his hotel suite that were enhanced to fire at an accelerated rate, and discovered a system of cameras Mr. Paddock set up to monitor the area around his location.
Mr. Paddock struck a jet fuel tank near McCarran International Airport with two rifle rounds, said Chris Jones, an airport spokesman, though a police official expressed doubt that he targeted it intentionally.
Despite the huge scale of the attack, why Mr. Paddock carried it out remained a huge and haunting question mark, said Steven B. Wolfson, the district attorney in Clark County, Nev., where the killings occurred. He estimated that in “99 percent of the cases,” the perpetrator of a drastic killing offers some kind of justification, however twisted.
“Most of the time, you don’t defend it, you don’t accept it, but you hear the why,” Mr. Wolfson said in an interview on Thursday.
“I’ve been doing this a long time and I can’t remember another homicide — and then you multiply what I’m about to say by 58 — where you don’t know why.”
Had Mr. Paddock been taken into custody “maybe we would have found out why,” Mr. Wolfson added. “Maybe he would have said, ‘this is the reason why I did it.’ But because he killed himself, we don’t know and it’s frustrating.”
Katherine W. Schweit, a former senior F.B.I. official, co-wrote a lengthy 2013 F.B.I. study that looked at 160 mass shootings in the United States. The study did not specifically examine motivation, but Ms. Schweit said many of the underlying reasons for the shootings were apparent to investigators. “A jilted lover, race or religion, someone who was fired,” she said. “Other times the motive is more elusive. This isn’t the first guy who seemed to have found a target for his anger who we can’t understand where the anger came from. Anger manifests itself in a lot of different ways.”
“I think everyone wants an answer because they are grasping to understand the senselessness of the shooting,” she said. “It reminds me exactly of the conversations we had after 9/11.”
Experts and law enforcement veterans caution that it can take time to establish a killer’s real motivations, piecing together electronic data with interviews and other shards of a life twisted into extreme violence.
Officials involved in the Las Vegas investigation have said they expect it will take an exhaustive search into Mr. Paddock’s past, spanning multiple states and decades of his life, to deduce what brought him to the windows of the Mandalay Bay hotel with such an elaborate plan for murder. In F.B.I. speak, they want to understand his “pathway to violence.”
Andrew Bringuel, a former member of the F.B.I.’s behavioral analysis unit, said investigators were undoubtedly exploring a range of motives that include personal, economic, social or political.
“He could have been seeking revenge,” said Mr. Bringuel, who retired earlier this year. “This could have been a personal grievance. He could have been a sore loser. Gamblers like to talk about their winnings, but not their losses. I worked for the F.B.I. for a long time. The F.B.I. is pretty good at looking at the nooks and crannies of someone’s life. The bureau will end up with a hypothesis. Whether the bureau can prove it is a separate question.”
Mr. Paddock would appear, in several respects, to be an unlikely perpetrator: An affluent man in his seventh decade, Mr. Paddock was both older and wealthier than the typical mass murderer, who is usually a young and isolated white man, often with a history of violence or mental problems.
Mr. Paddock’s father, Benjamin Hoskins Paddock, was a veteran criminal who was placed on the F.B.I.’s most wanted list, which described him as “diagnosed as psychopathic.”
But his brother Eric Paddock said his sibling was not a politically motivated person and had no apparent financial problems. He said he recognized Stephen Paddock’s methodical personality in the planning of the attack, but nothing else.
“He was able to plan this, to do this,” Eric Paddock said. “That is the person Steve was.”
Andrew G. McCabe, the deputy director of the F.B.I., acknowledged in a television interview on Wednesday that insight into Mr. Paddock’s frame of mind had been elusive so far. He declined to rule out the possibility that there was no rationale for the violence, or that investigators might never establish one.
“This one is somewhat different than many of the ones we’ve dealt with in the past,” Mr. McCabe said of the Las Vegas attack, on CNBC, “because we don’t have any immediately accessible thumbprints that would indicate the shooter’s ideology or motivation.”
Mr. Paddock, he said, was “not on our radar, or anyone’s radar, prior to the event.”
Many killers, however, are unknown to law enforcement before their attacks, and some experts caution that the mystery around Mr. Paddock may be less aberrational that it seems. A number of massacres in recent decades have gone largely or completely unexplained.
Investigators never found a convincing motive behind a 1966 massacre at the University of Texas, often described as the first modern mass shooting, in which a sniper, Charles Whitman, fatally shot 14 people from a clock tower after killing his family.
Other attacks have taken months to explain in depth, like the killing of 12 people at a movie theater in Aurora, Colo., in July 2012.
George Brauchler, the district attorney who led the prosecution of James Holmes, the Aurora gunman, said it was not until prosecutors obtained Mr. Holmes’s journal and a thorough psychiatric evaluation that they felt confident laying out an explanation. That information, Mr. Brauchler said, convinced them Mr. Holmes had turned to violence amid a shattering sense of professional failure and sexual rejection. Mr. Holmes was also being treated for mental health issues, and his defense described him as schizophrenic.
Still, Mr. Brauchler said, his office had meaningful clues about Mr. Holmes’s mind-set within days of the shooting, including information about a breakup with his girlfriend. The Las Vegas case was plainly different, he said.
“The scariest part of this,” Mr. Brauchler said, “is to not find or know a motive.”
Adam Lankford, a professor at the University of Alabama who has studied mass shootings, said a killer’s professed motive can also represent incomplete or self-serving information. He cited Orlando as an example: If Omar Mateen, the Orlando gunman, was driven by fundamentalist views, he also pledged loyalty to the Islamic State and expressed affinity for Hezbollah — clashing militant groups.
“In a lot of cases, even when they give a motive, what they’re saying is for public effect,” Mr. Lankford said, “not necessarily the true explanation behind their actions.”
An earlier version of this article misstated the circumstances of the death of Charles Whitman, the gunman in the 1966 University of Texas massacre. He was killed by the police; he did not kill himself.
Reporting was contributed by William K. Rashbaum from New York, Mitch Smith and Sabrina Tavernise from Las Vegas, and Rebecca R. Ruiz from Washington.