The second- and third-worst decisions were also fourth-and-1 punts from near midfield. Martz and the 2001 Rams, despite having an offense so powerful that it was nicknamed the Greatest Show on Turf, opted not to go for it in the second quarter when trailing the underdog Patriots by 4 points. And Tomlin and the 2010 Steelers, another team with a strong offense, punted to the Packers midway through the first quarter.

That last decision makes for a tidy allegory about the downside of caution. The punt by Jeremy Kapinos went into the end zone, giving the Packers the ball at their 20. Green Bay then moved down the field in nine plays to score a touchdown, a demonstration of why, with today’s high-powered N.F.L. offenses, having the ball usually matters more than where a team starts with it.

Obviously, no one can know what would have happened if the Steelers had instead tried for the first down. But it’s striking that after having forgone a fourth-and-1 early in the game, the Steelers were forced to try a worse risk — fourth-and-5, from their 33 — late in the fourth quarter, while trailing by 6 points. It failed, and they lost.

The years before 2000 are also full of such examples. In 1991, Levy and the Bills punted on fourth-and-1 from around midfield on their opening drive, then watched the Giants march for a field goal; the Bills lost the game on Scott Norwood’s missed field goal as time expired. Landry and the Cowboys, in their two Super Bowl losses to the Steelers in the 1970s, punted a total of six times when they arguably should not have.

Even the so-called Greatest Game Ever Played, the 1958 championship between the Giants and the Colts, was decided in part by fourth-down caution. The Giants’ final two possessions — the second coming in the first overtime in N.F.L. history — ended with punts on fourth-and-1. After each, Johnny Unitas led the Colts on scoring drives.

These days, when coaches are asked to explain their fourth-down decisions, some emphasize that they are coaching individual players, with their own strengths and weaknesses. The 4th Down Bot, on the other hand, is based on league averages. After a Buffalo reporter asked Doug Marrone, then the Bills’ coach, about the Bot this season, he replied that “people on the outside looking in” often do not “truly understand what the data is.”