For a president who never made the front line of his college squad, football played a surprisingly large part in Richard Nixon’s life.

Founded by the Society of Friends, Whittier College in California called its football team the Poets, after the college’s Quaker namesake, John Greenleaf Whittier. Despite his relentless efforts, Nixon — who graduated from Whittier, his hometown school, in 1934 — managed only to become a third-string guard for the Poets. Nixon was “cannon fodder,” said one teammate, who added, “He wasn’t cut out to play the sport.”

Although a benchwarmer, Nixon later attested that he admired his head coach, Wallace Newman, more than “any man I have ever known aside from my father.” (When Nixon became president, Newman graciously insisted that he had not been “a very good judge of talent” and gave Nixon an honorary letter in Whittier football.)

Because Newman was part Native American, players on the Poets called him Chief. Nixon venerated him as a “molder of character,” and, decades later, commended the Chief’s exhortation: “You must never be satisfied with losing. You must get angry, terribly angry, about losing.” Few students of Nixon’s political career could say that the scrub player did not absorb this lesson.

As vice president, Nixon made no secret of his delight in rubbing shoulders with renowned football coaches like Woody Hayes of Ohio State, whose support he credited for helping him carry Ohio in the 1960 election against John F. Kennedy. During his wilderness years as a New York lawyer, Nixon analyzed football plays with Y. A. Tittle and Andy Robustelli over cocktails at the apartment of their Giants teammate Frank Gifford...