For one thing, jurors are often sympathetic to police arguments. The officers charged with beating Mr. King after a car chase argued that he was uncooperative and making movements they deemed potentially threatening. (Two of the four acquitted officers were later convicted in federal court of violating Mr. King’s civil rights.)

And police have some latitude to use force when making an arrest. Daniel Pantaleo, the officer who applied the chokehold to Eric Garner, narrated three videos taken of the encounter while testifying before the grand jury, saying he intended only to wrestle Mr. Garner to the ground.

Confronted with a video, the police usually “have a version that seeks to explain what you see, not necessarily to contradict what you see, but to explain it,” said John Burris, an Oakland-based civil rights lawyer who worked on the King and Grant cases.

The potential for officers to tailor their testimony to video evidence highlights an ongoing debate over the extent to which police should have control of or access to the videos taken by their body cameras.