These have been some of the most eventful N.F.L. playoffs ever, stuffed with comebacks, tense quarterback duels and games won on final plays. But from a certain vantage point, the biggest play of the N.F.L. season happened back in September, in the fourth quarter of a game between the Los Angeles Chargers and the Kansas City Chiefs.

The Chargers, trailing by 3 points, faced a fourth-and-4 well within range of a game-tying field goal. But instead of sending out kicking unit, Chargers Coach Brandon Staley kept the offense in, and Justin Herbert fired a 9-yard pass to receiver Keenan Allen for the conversion.

Watching at home, Aaron Schatz, the editor in chief of Football Outsiders, a site that specializes in analytical assessment of the sport, perked up. “That was a really aggressive move to go for it,” Schatz said of Staley’s call, which led to Los Angeles reaching the end zone a few plays later — a turning point in what became a 30-24 Chargers win. “That was really, I think, a watershed moment.”

Over the course of the 2021 season, N.F.L. teams were more aggressive than ever in challenging football orthodoxy, attempting fourth-down conversions at historic rates. Offenses remained on the field on 69 percent of fourth-and-1 plays this season, 39 percent of fourth-and-2s and 19 percent of fourth-and-3s, all N.F.L. records.

This season’s aggressive play-calling was also evident in decisions to attempt two-point conversions at game-tilting moments, as the Baltimore Ravens did in December losses to the Browns and the Packers. But despite the trend, this year’s Super Bowl coaches have largely leaned old school: The Bengals’ Zac Taylor and the Rams’ Sean McVay rank 21st and 23rd, respectively, in Edjsports’ Critical Call Index, which tracks how often teams make fourth-down calls, optimized for win probability.

The movement toward more aggressive play-calling started slowly, then hit a Super Bowl flash point. David Romer, an economist with the University of California at Berkeley, published an article in 2006 that asserted that teams could improve their win probability by keeping their offenses on the field for fourth downs.

“For easily the next decade, there was no change,” Romer said. “There was a switch to starting to think about this seriously in 2018 — it’s risen since then.”

That was when the Philadelphia Eagles, led by the backup quarterback Nick Foles, knocked off Tom Brady’s New England Patriots by way of a string of now-or-never play calls.

“It’s a copycat league,” Schatz said. “And that’s the thing people have decided to copy from the 2017 Philadelphia Eagles.”

By now, the low-hanging fruit of short-yardage tries in enemy territory has mostly been plucked, forcing teams at the cutting edge to make bolder calls to stay there. Kansas City Coach Andy Reid, for instance, iced a game away in last season’s playoffs by picking up a fourth-and-2 with a backup quarterback instead of punting the ball to the Cleveland Browns.

But Reid’s risk-embracing approach backfired in this season’s A.F.C. championship game against the Bengals, when Kansas City went for the touchdown from Cincinnati’s 1-yard line instead of taking a sure field goal. The Bengals stopped Kansas City at the goal line to end the first half, then made five consecutive defensive stops to win the game, 27-24, in overtime.

Michael Lopez, the N.F.L.’s director of football data and analytics, pointed out that the tension between optimizing win probability and keeping a score superficially close can be a psychological hurdle for coaches. When a savvier and more ambitious play fails — say, going for it on fourth down in the first half — it can give the game an earlier tipping point, turning what might have been a respectable-looking loss into a blowout.

“When you add in plays that have big, big swings in win probability,” Lopez said, “you’re going to get that sort of impact.”

The backlash against decisions that don’t work out can be noisy. In the December rematch between Los Angeles and Kansas City, the Chargers’ Staley — tops in the Critical Call Index — went for it on fourth down five times, but his team converted only twice and lost in overtime. “Neither of us can spell ‘analytics,’” Fox’s Howie Long said to fellow analyst Terry Bradshaw during the postgame show, “but it took a beating tonight.”

Those who work to integrate analytics with N.F.L. strategy cringe at such statements, which take a small sample of outcomes as a referendum on a large-scale tactic — as if the occasional interception delegitimizes the forward pass. “We don’t want them to be robotic about this,” said Michael McRoberts, the president of Championship Analytics, which advises four N.F.L. teams on in-game decisions. He added that fatigue, weather and emotional momentum swings serve as extra-statistical elements that a coach might consider alongside what the data shows.

“We want them to have wiggle room and freedom,” he said, “while also just telling them, ‘Hey, all things considered, we can give you this recommendation.’”

Analytics-based thinking isn’t just limited to fourth-down play-calling. Despite the Rams’ relative conservatism in those situations, the team employs a so-called “Nerd’s Nest” of data analysts who have contributed to the team’s ranking as the eighth-best offense and fifth-best defense, based on Football Outsiders’ catchall Defense-adjusted Value Over Average. Since 2017, the team has taken a data-driven approach to scouting the draft and has had success building around selections like Aaron Donald and Cooper Kupp.

It has also used data sets to determine how to fold in high-profile acquisitions like linebacker Von Miller and receiver Odell Beckham Jr. in the middle of the season alongside Matthew Stafford, the quarterback for whom the team traded high-round draft picks in January 2021.

The Bengals have an analytics team as sparse as the Rams’ is robust: Cincinnati has just one data analyst, Sam Francis. But like many of his counterparts around the N.F.L., Francis has a direct line into Taylor’s headset and offers counsel on fourth-down decisions.

If the Bengals tend to play it safe in those circumstances, they’ve demonstrated a willingness at other times to go where the data leads. In Cincinnati’s upset of Kansas City in this season’s A.F.C. championship game, Cincinnati saw Patrick Mahomes struggling against coverage packages in which it dropped eight defenders off the line of scrimmage. So, in the second half, Cincinnati doubled down on the approach, jumping from a 24 percent usage rate to 45 percent, according to N.F.L. Next Gen Stats. Mahomes threw an interception and took two sacks against the coverage.

It’s hard to tell how much the decision came down to old-fashioned eyeballing as opposed to newfangled number-crunching. “Every coach draws up a defensive game plan knowing what the offensive trends are,” Lopez said. “Coaches have always been doing analytics, they just might not call them that.”