“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.

“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.