In case after case, it took only a split second for an officer to pull the trigger.

Adam Toledo, a 13-year-old in Chicago, had tossed away a handgun and begun raising his hands. Ma’Khia Bryant, a 16-year-old in Columbus, Ohio, lunged with a knife at another teenager. Tyrell Wilson, a 33-year-old mentally ill homeless man in Danville, Calif., had a knife in hand when he shouted “Kill me” at an approaching deputy sheriff.

All three were among more than 100 people shot and killed by the police over the previous six weeks.

The officers’ justification for the use of lethal force in each instance differs with the circumstances. But as in almost every other recent case involving questions of police use of force, law enforcement officials defending the officers are relying on a doctrine set forth by the Supreme Court three decades ago and now deeply ingrained in police culture: that judges and juries should not second-guess officers’ split-second decisions, no matter how unnecessary a killing may appear in hindsight.

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Until the mid-1980s, policies on the use of force varied widely across the states. Some allowed deadly action against any fleeing suspect of a felony, even if the suspect posed no imminent threat.

That changed in 1985. The Supreme Court ruled in Tennessee v. Garner that police could shoot only if they had probable cause to believe that a fleeing suspect posed a significant threat of injury or death to an officer or others. The number of police killings steadily declined over the next four years, studies show.

But in 1989, a more conservative court took a different approach in the ruling of Graham v. Connor, establishing the precedent that dominates today.

The case was brought by Dethorne Graham, a Black man the police had stopped in Charlotte, N.C., on suspicion of shoplifting because he had hurried in and out of a convenience store.

Mr. Graham, a diabetic desperate for orange juice to avoid a seizure from low blood sugar, told the police that he had rushed out of the store because of a long checkout line. But as he staggered and briefly passed out, officers assumed he was drunk and forced him into tight handcuffs, leaving him with a broken foot, cuts on his wrists, bruises on his forehead and an injury to his shoulder.