It was a scene almost designed to show the folly of the N.F.L.’s first-down measurement system.

Late in the fourth quarter of the game between the Dallas Cowboys and the Oakland Raiders on Sunday, Dak Prescott barreled into his offensive line on a fourth-and-1 quarterback sneak.

As is often the case in such plays when the ball carrier is swallowed in a mass of large human bodies, it was difficult to tell precisely where the ball should be placed.

But officials made their best guess and brought the yardsticks out to measure. Even then it was too close to call with the naked eye, so a referee, Gene Steratore, used a folded piece of paper to see if it could slip between the ball and the yardstick.

When it touched the ball, Steratore signaled a first down. The Cowboys would go on to kick the game-winning field goal, keeping their playoff hopes alive and effectively ending Oakland’s.