Allen, who once disparaged the flanker reverse as a “gimmicky play,” never officially confirmed or denied that he had chosen the play at Nixon’s behest. Marv Levy, an assistant coach for Allen, claimed that before the playoff game, his boss had arranged for Nixon to take credit for the flanker reverse, so that his friend the president would look “very sage.”

Pronouncing football his “favorite sport,” Nixon applied its language to politics. When he was angry over something done or said by some politician, he would write in the margin of his daily news summary, “Get someone to hit him.” Nixon once told Henry Kissinger, his national security adviser at the time, that war should be fought like football: “You give ground in the middle of the field, hold the line and the goal line and then score a touchdown.”

As president, Nixon derived some of his tenacity from his experience with the Poets. Citing his old coach, he would say, “You have got to hate to lose and get up off that floor and come back to fight again.” But there is little evidence that he learned other football lessons, such as teamwork or respect for the rules of the game.

After Nixon was forced to resign in the Watergate scandal, his three-time Cabinet member Elliot Richardson, who had quit in protest during the so-called Saturday Night Massacre of October 1973, said, “His use of football analogies was so revealing — anything was O.K., except what the referee sees and blows the whistle on.”

More than a historical curiosity, Nixon’s intense interest in football continues to affect fans of the sport today. N.F.L. games were regularly blacked out on television in their home markets in an effort to boost ticket sales. In December 1972, the Washington team was to face the Packers in the playoffs on its home turf, and Nixon was incensed that fans like him could not see the games on television.

Secretly recording their telephone conversation (the tape was released in 2012), Nixon ordered his attorney general, Richard Kleindienst, to ask N.F.L. Commissioner Pete Rozelle to lift the blackout for the playoffs. Nixon said, “I’m for pro football all the way,” adding that “I want us to get some publicity” for removing the blackout.

To clinch the deal, Nixon ordered Kleindienst to inform Rozelle that the president would give the N.F.L. “absolute protection” by vetoing any effort by “the damn Congress” to cancel the blackout on regular-season games.