In several videotaped and recorded interviews and interactions with the police that were played for the jurors, Mr. Routh gave at times puzzling explanations about why he shot Mr. Kyle, 38, and Mr. Littlefield, 35. He spoke of fearing for his life and believing that they were going to kill him or take his soul. He said that Mr. Littlefield was not shooting at the range and that “that’s what got me riled up.” He said he was offended that Mr. Kyle had not shaken his hand when they met, was bothered by the smell of cologne in Mr. Kyle’s truck, and was annoyed that the two men did not talk to him on the drive to the range.

“It smelled like sweet cologne,” Mr. Routh told a reporter for The New Yorker in 2013, in a phone call from jail that was recorded. “I was smelling love and hate. They were giving me some love and hate.”

In finding Mr. Routh guilty and not legally insane, jurors appeared to have sided with the prosecutors, who portrayed Mr. Routh not as a sympathetic, troubled veteran but as a callous killer who stopped at Taco Bell shortly after fleeing the scene and who knew his actions were wrong, a crucial part of the legal test of insanity.

Mental health experts who examined Mr. Routh told the jurors that he had not been directly involved in combat in Iraq and that he had lied about putting the bodies of babies in a mass grave in Haiti as part of an earthquake-relief deployment. Two experts who evaluated him for the prosecution testified that Mr. Routh was not insane and questioned whether he had exaggerated the trauma he experienced while in the Marines to get disability benefits and had tried to sound schizophrenic to get out of prison.

Mr. Routh had made bizarre statements that he believed people around him were half-pig, half-human, and that his co-workers at a cabinet shop were cannibals who wanted to cook and eat him.

Image Chris Kyle in 2012. Credit... Brandon Thibodeaux for The New York Times

But one of the prosecution’s experts who examined Mr. Routh, Randall Price, a Dallas forensic psychologist, testified that Mr. Routh’s statements about pig people may have come not from psychosis but from TV shows, including an episode from “Seinfeld” and a reality show called “Boss Hog,” two of Mr. Routh’s favorite programs. The prosecution’s other expert, Dr. Michael Arambula, a San Antonio forensic psychiatrist who is president of the Texas Medical Board, said that the delusions of schizophrenics often had structure and details, but that Mr. Routh’s statements about cannibals lacked specifics.