In Arkansas, a preparatory school won the past four state football championships in its class led by a coach who doesn’t punt on fourth down, does onside kicks at almost every opportunity and goes for nearly every two-point touchdown conversion.

At West Point, Army has won its way back to respectability with a dependence on the running game and statistical analytics that make it college football’s most likely team to go for a first down on fourth down. And it’s working: The Black Knights have converted 88 percent of fourth-down plays.

And in the NFL, Philadelphia coach Doug Pederson proved himself both bold and smart when he guided his Eagles to last season’s Super Bowl title, while again leading the league in fourth-down attempts. This season, undefeated Los Angeles Rams coach Sean McVay is trying to take Pederson’s place with a decisionmaking philosophy he calls “aggressive.”

The math long has said coaches skew too conservative — according to fourth-down probability and win probability logic — in a game where conventional thinking and fear of being second-guessed have weighed heavy for so long.

“Go for it” has never been a more common call, seemingly at all levels. Deep dives into stats show some NFL coaches have reconsidered the concept of risk. The Vikings’ opponent Sunday night, the New Orleans Saints, have converted seven of their eight fourth-down attempts this season.

The crunched numbers say going for it on fourth down is advisable in many occasions, including fourth-and-10 on your opponent’s 40-yard line when a long field goal’s odds are just that and pinning the opponent deep in its own territory with a punt isn’t guaranteed.

Or even on fourth-and-1 inside your own 10, now that the math values maintaining ball possession over cherished field position.

Few, if any, coaches would “gamble” in such a situation, but sheer statistics say chances to succeed by keeping the ball — instead of punting and allowing the opponent near scoring range — are the better odds.

Some coaches play the odds, often following a sheet that details the probabilities of any given situation. Some go by their instincts.

Some do both at the same time.

“It’s hard when you’re the head coach making decisions, because you know your team better than anybody,” Gophers coach P.J. Fleck said. “Statistics are statistics for a reason. That’s kind of an average for everybody. But we’re not everybody. We’re us.”

In Saturday’s 53-28 loss at Nebraska, Fleck went for the touchdown on fourth-and-goal from the 3-yard line to start the fourth quarter. It was the logical choice given the time remaining and situation — trailing by two touchdowns (36-22) — even though the pass into the end zone fell incomplete.

The Gophers are going for it more often this fall. The next time they try to get a first down or touchdown on fourth down, they’ll equal last season’s 13 attempts. They also were wildly successful on fourth down last season, converting 77 percent (10 of 13). Only Alabama had a higher conversion rate. Minnesota is more aggressive this year (12 attempts in only seven games), but less successful (six of 12).

“I’m huge into the statistical part, but there are times when you trust your team or not,” Fleck said. “You’re fourth-and-1, you go for it. You fake a punt, you fake a punt and trust them to get it done. … I’d like to go for it on four downs, I’d like to do that more than not.”

Gambling redefined

On a Sunday earlier this month, McVay ordered a quarterback sneak on fourth-and-1 from his own 42 with 1:39 remaining at Seattle. Jared Goff leaned forward with the ball, reached the first down and the Rams ran out the clock for a 33-31 victory.

Afterward, McVay told reporters he saw belief in his players’ eyes, so he trusted them.

“Ultimately, it’s a good decision because they made it right,” said McVay, whose Rams are 7-0.

That same night, Dallas punted on fourth-and-1 from Houston’s 42-yard line with the score tied and six minutes left in overtime. The Cowboys’ Jason Garrett did what coaches have done for time infinitum: He gave the opponent the ball back at its own 10, but the Texans merely drove 72 yards and kicked the winning field goal for a 19-16 victory.

Cowboys owner Jerry Jones later called the situation a “time for risk.” But going for it might have been anything but that.

Overall, NFL fourth-down attempts (roughly two per game, on average) and conversion rates (usually around 50 percent) have held steady the past decade. But the stats site Football Perspective recently dug deeper on decisions near midfield in close games (margin of 10 points or fewer). From 1994 to 2004 in the first three quarters of games, teams went for it on fourth-and-1 situations between the 40-yard lines 28 percent of the time. From 2005 to 2014, it rose to 35 percent, and from 2015 through this season, offenses stayed on the field for these fourth downs 46.5 percent of the time. Using only 2017 and 2018 games, it’s more than 50 percent.

Pederson’s Eagles have gone for it on fourth down 10 times this season — as much as any NFL team — and converted seven of them. Last season including playoffs, the Eagles led the league with 29 attempts — including two important fourth downs, one for a touchdown, in their Super Bowl LII 41-33 victory over New England at U.S. Bank Stadium.

Fifteen years ago, on a stage a little smaller than a Super Bowl, an Arkansas high school coach put all his trust in probability-based math. Pulaski Academy’s Kevin Kelley has won seven state championships since then. He’s the contrarian who seldom punts and is fond of trick plays.

“People always say, ‘You’re a gambler,’ ” Kelley recently told the Washington Post. “No, I’m not. I’m the house.”

Playing the percentages

Vikings offensive coordinator John DeFilippo has worked for six NFL teams since 2005, including last season when he was Pederson’s quarterback coach. He coached teams that didn’t use analytics at all or a little and in places such as Philadelphia, where the Eagles rely upon them. He doesn’t know where the number-crunching stops and Pederson’s personality begins.

“I know he really used that information and came to his own conclusions how to use it,” DeFilippo said. “How much of that was analytics and how much was Coach’s gut, I’m not sure. I never asked him.”

DeFilippo said he reads everything given to him and uses some of it. Fleck said he pores over “books upon books” of “stats, percentages and numbers” every week.

Coaches at high schools and Division II and III colleges don’t have the same technology and detailed information, but the way coaches contemplate the game is changing.

Eden Prairie coach Mike Grant played the “percentages” when his team scored two touchdowns on fourth downs and beat rival Minnetonka by a touchdown two weeks ago.

Division II’s Southwest Minnesota State coach Cory Sauter keeps probabilities only in his head, but the former Gophers and NFL quarterback has come to believe a converted fourth down equals an intercepted pass or recovered fumble.

“The game is all about probability,” Sauter said. “It’s like working in insurance: You have to decide how much risk is in this thing. Some coaches are very conservative and others just look at the odds. I’m not a guy who goes to the casino or gambles, but you’re always searching for an edge.”