In fairness, Frigo said, he has never seen a franchise behave quite like the Eagles, one of several teams that subscribes to EdjSports’s predictive tools. The Eagles’ shrewd application of analytics to everything from roster management to in-game strategy helped propel them to a 13-3 record and a berth in Super Bowl LII against the New England Patriots on Sunday.

Analyzing every team’s risk-management style, EdjSports determined that Philadelphia optimizes decisions — on fourth down, especially — better than its peers by a substantial margin.

“The Eagles capture value at every turn,” said Tony DeFeo, the president of EdjSportss, “because they understand where the value lies.”

That understanding saturates an organization that not only accepts counterintuitive thinking but encourages it. The approach pervades every layer, from ownership to the football operations department, and from its analytics team to a coaching staff comfortable with mining statistical analysis for advantages. Philadelphia’s defensive coordinator, Jim Schwartz, who earned an economics degree at Georgetown, has long been one of the league’s leading devotees of statistical analysis — Frigo has known him for more than a decade — and some of his players said this week that they preferred studying probabilities and tendencies even before studying situations or receivers’ routes.

“We’re into the analytics as much as he is,” defensive back Jaylen Watkins said.

The Eagles have empowered Pederson to make decisions rooted in instinct or math, or both. They understand that what may seem a foolish move in the short term may enhance their chances of winning — as that fourth-down call against the Giants did. In a call that was likely to fail, Pederson identified that the upside of going for it outweighed the downside of failing.

Frank Frigo, a co-founder of EdjAnalytics, said the Eagles are “in the Super Bowl for a reason.” He said he had never seen an N.F.L. team apply analytics quite like Philadelphia. Luke Sharrett for The New York Times

“He can do whatever he chooses to do, but when you have the resource of data, why not?” the Eagles’ owner, Jeffrey Lurie, said Monday night at the Super Bowl’s opening festivities in St. Paul. “It’s kind of a no-brainer.”

That is also how Frigo and his colleagues at EdjSports feel about using quantitative analysis in the N.F.L., which has yet to fully adopt it. EdjSports would not divulge how long it has worked with the Eagles or how many other teams are clients, though the logos adorning the walls of its office — of the Lions, Saints and Steelers, among others — offer a hint. Contractual obligations prevented EdjSports from sharing data that could compromise its relationship with the Eagles, but Frigo said many of Philadelphia’s decisions have aligned with EdjSports’s recommendations.

Those recommendations derive from a model drawing on years of play-by-play data, churning it through hundreds of thousands of simulations — sometimes more — to determine the decision that most boosts a team’s likelihood of winning, a metric EdjSports calls GWC, for Game Winning Chance. Because the model cares only about producing the most wins on average, it tends to favor unorthodox moves.

Looking at a chart, Sean O’Leary, one of EdjAnalytics’s founders, noted how it’s mathematically defensible for a team on its first possession of overtime to go for it on fourth-and-1 at its own 10-yard line; not that a coach, facing public pressure to adhere to football norms, ever would.

But fourth downs are embedded with opportunity for those keen to exploit it. Frigo said that on fourth down alone, teams on average give up anywhere from two-thirds to three-quarters of a win over a season on what Edj classifies as high-confidence mistakes — that is, decisions that EdjSports’s model has deemed with certainty to be an error. The worst offenders might lose as much as a game and a half.

Using the Patriots, who are not an EdjSports client, as an example, Frigo cued up on a screen one of the company’s postgame reports, which allow a team to evaluate its decision-making. The report of New England’s A.F.C. championship victory against Jacksonville revealed that Bill Belichick, perhaps the best coach in history, committed four of those high-confidence errors when he elected to punt instead of go for it. To Frigo, those mistakes confirmed coaches’ susceptibility to conservative thinking from a purely game theory standpoint.

By contrast, although the Eagles have not acted perfectly at every turn, DeFeo said they were “almost unblemished” this season in critical junctures, such as 2-point tries and fourth downs.

EdjSports’s data indicates that the rest of the league treats fourth-down calls as a novelty, going for it mainly toward the latter stages of a game out of desperation, but the Eagles have shown unrivaled aggressiveness. Not so much in their frequency of attempts (26, second in the league to Green Bay’s 28) or their success (65.4 percent conversion rate, third behind New Orleans and Jacksonville), but in their timing. Of their 26 attempts, 11 came before halftime.

In that Week 3 victory against the Giants, the Eagles converted a fourth-and-1 from their own 47 late in the first quarter and went on to score a touchdown. A few weeks later in Carolina, trailing by 10-3 with about four minutes left in the first half, the Eagles passed up a short field goal to go for it on fourth-and-1 from the Panthers’ 3-yard line, a decision that increased their win probability by 2.9 percent. Three plays later, they scored a touchdown, and they eventually won, 28-23.

The Eagles leveraged the odds to their benefit in Week 14 in Los Angeles against the Rams, when they were down by 28-24 late in the third quarter but had fourth-and-goal at the 2. Again, they eschewed a field goal, which would have made it a one-possession game, and again they were rewarded with a touchdown. That call improved Philadelphia’s win probability by a whopping 7.0 percent, and the result helped the Eagles defeat Los Angeles.

Frigo cued up a postgame report, which assesses a team’s decision making, for the Patriots’ victory over the Jaguars in the A.F.C. championship game. Luke Sharrett for The New York Times

“Teams march down the field and feel like they’ve got to get something for their efforts,” Frigo said. “I think when they view a field goal, they’re already chalking it up in their heads. Humans put an undue amount of weight on something that they’re giving away versus something that they could acquire. But the problem is, that’s counterintuitive to win probability.”

The Eagles further distinguished themselves with aggressive play-calling on short-yardage fourth downs, when the high-percentage call is often a quarterback sneak (and indeed, Wentz, before tearing a knee ligament against the Rams, converted all seven sneaks on fourth-and-1). But Pederson also mixed in handoffs and passes.

“The Eagles still might run it up the middle, but they might not,” Frigo said. “That’s exactly the right way to use this information.”

It is a mandate from Lurie, who said he started believing in analytics about 20 years ago, heading into the 1999 N.F.L. draft. That investment led to selecting Donovan McNabb, who would go on to take Philadelphia to five conference championship games and a Super Bowl appearance, with the second pick.

Last season, the Eagles led the N.F.L. with 27 fourth-down attempts, but in the off-season, evaluating his performance as a rookie coach, Pederson resolved to grow more comfortable with data. Much as a chess player practices against a bot, Pederson can conceive different scenarios and adjust the variables — ball position, score, time remaining, to name just three — to ascertain how to react.

“I do feel like it can be overwhelming at times, trying to crunch all those numbers, and I wanted to kind of sift through everything and find the ones that are right for the football team,” Pederson said Thursday at a news conference in Bloomington, Minn.

Heading into games, Pederson speaks daily with the coaching assistant Ryan Paganetti, who joins Jon Ferrari, the team’s director of football compliance, on the coaching headset during games. When the Eagles are on the field, they relay advice and discuss potential fourth-down plays as early as second down.

Teams are prohibited from using computers to process information during games, but with no ban on charts or graphs, the Eagles can plot strategy based on hypothetical situations run in the off-season or customized reports based on that week’s opponent.

O’Leary, the EdjAnalytics co-founder, said those at the company do not speak with teams during the season to see how they integrate data into their workflow every week. But as curiosity morphed into delight among the EdjSports staff back in Week 3, something occurred to DeFeo.

EdjSports, he said, never would have conceived that fourth-and-8 situation against the Giants. It was something that the Eagles deemed valuable on their own. And when confronted, Pederson did not hesitate.

“The Eagles are the right group at the right time to embrace risk-management on a level that we haven’t ever seen,” Frigo said. “They’re in the Super Bowl for a reason.”