While researching a 2008 book on the missile crisis, I plotted the positions of Soviet and American ships during this period, on the basis of United States intelligence records. I was stunned to discover that the lead Soviet ship, the Kimovsk, was actually 750 miles away from the blockade line, heading back toward the Soviet Union, at the time of the supposed “eyeball to eyeball” incident. Acting to avert a naval showdown, the Soviet premier, Nikita S. Khrushchev, had turned his missile-carrying freighters around some 30 hours earlier.

Kennedy was certainly bracing for an “eyeball to eyeball” moment, but it never happened. There is now plenty of evidence that Kennedy — like Khrushchev — was a lot less steely-eyed than depicted in the initial accounts of the crisis, which were virtually dictated by the White House. Tape-recorded transcripts of White House debates and notes from participants show that Kennedy was prepared to make significant concessions, including a public trade of Soviet missiles in Cuba for American missiles in Turkey and possibly the surrender of the United States naval base at Guantánamo Bay.

While the risk of war in October 1962 was very high (Kennedy estimated it variously at between 1 in 5 and 1 in 2), it was not caused by a clash of wills. The real dangers arose from “the fog of war.” As the two superpowers geared up for a nuclear war, the chances of something going terribly wrong increased exponentially. To their credit, both Kennedy and Khrushchev understood this dynamic, which became particularly evident on the most nerve-racking day of all, “Black Saturday.”

By Saturday, Oct. 27, the two leaders were no longer in full control of their gigantic military machines, which were moving forward under their own momentum. Soviet troops on Cuba targeted Guantánamo with tactical nuclear weapons and shot down an American U-2 spy plane. Another U-2, on a “routine” air sampling mission to the North Pole, got lost over the Soviet Union. The Soviets sent MiG fighters into the air to try to shoot down the American intruder, and in response, Alaska Air Defense Command scrambled F-102 interceptors armed with tactical nuclear missiles. In the Caribbean, a frazzled Soviet submarine commander was dissuaded by his subordinates from using his nuclear torpedo against American destroyers that were trying to force him to the surface.

When it was all over, Kennedy aides sought to spin the crisis by depicting their man as fully on top of the situation. Arthur M. Schlesinger Jr. later praised the “mathematical precision” with which Kennedy calibrated his threats of force against Cuba and the Soviet Union and the “composure, clarity and control” the president displayed.