Patriots coach Bill Belichick will look for more than just physical talent when the team enters training camp this week.

New England’s professor of pigskin also will look for players smart enough to study among the ivy walls of the NFL’s finest intellectual institution.

The Super Bowl champs finished the 2014 season No. 1 on the ColdHardFootballFacts.com Intelligence Index, our measure of team-wide efficiency in all phases of the game. The Patriots, in other words, were the smartest team in the NFL.

Smart football is core curriculum at the University of Foxboro, where the Patriots may not always be the most talented team in the NFL but usually are among the brightest. We began tracking team intellect in 2004. Since then, the Patriots have finished No. 1 on the Intelligence Index in 2004, ’10 and ’14.

No coincidence that the Patriots won Super Bowls in 2004 and ’14 and were a dominant 14-2 team in ’10. The Patriots since 2004 finished in the top six on the Intelligence Index every year except for the doomed ’05 season and the Tom Brady-less ’08 campaign.

The Intelligence Index is simply a measure of how well teams play in situational football in all phases of the game. It gauges special teams proficiency, field position, third- and fourth-down success, red-zone success, penalties and turnover differential, among other factors, and tells us how efficiently teams and their opponents score points.

Defensively, smart, efficient teams make opponents work hard to score points — they bend but don’t break, in other words. We call it Bendability. Offensively, smart, efficient teams convert few yards into a lot of points. We call it Scoreability. The Intelligence Index combines the two factors.

Take a look at the C-student Steelers, No. 18 on the 2014 Intelligence Index. They generated 731 more yards of offense last year than the Patriots — but scored 32 fewer points.

The stupid Saints, meanwhile, finished No. 25 on the Intelligence Index, largely because of gross inefficiency on offense. Drew Brees & Co. produced 293 more yards of offense than the Patriots, yet parlayed all that production into just 370 points — 98 fewer than the Patriots.

The Steelers and Saints, in other words, had plenty of physical talent. But those teams did not have the mental talent to convert all that production into points.

The teacher’s-pet Patriots consistently win games other teams lose because they do all the smart, little things well. Take, for example, the Patriots’ Week 16 battle last season over the class-clown Jets.

New York outgained the Patriots, 307-231, in total yards, 116-85 on the ground, and 191-146 through the air. The Jets were the better team physically, averaging 5.0 yards per play to just 3.7 for the Patriots. But the Patriots eked out a 17-16 victory because they were the better team mentally.

The Patriots converted 6-of-13 third downs (46 percent); the Jets 5-of-13 (38 percent). The Patriots returned three punts for an average of 21.0 yards; the Jets returned three punts for an average of 11.7 yards. The Patriots netted 45.6 yards per punt; the Jets 31.5 yards.

The Patriots scored two TDs in four trips to the red zone; the Jets scored zero TDs in three trips there. Patriots kicker Stephen Gostkowski nailed his only field goal attempt; Jets kicker Nick Folk hit three field goals but missed his final go-ahead attempt late in the fourth quarter when the ball was partially blocked.

The dumb Jets, in other words, did all the little things wrong and lost a game they physically won; the smart Patriots did all the little things right and won a game they physically lost.

That game was a perfect microcosm of the difference between the Patriots and Jets in recent years, and much of it comes down to the coach.

The Intelligence Index is, at the end of the day, a measure of coaching. Smart teams are well-coached teams. Dumb teams are poorly coached teams. The poorly coached Jets fired Rex Ryan after finishing the season No. 30 on the Intelligence Index.

Professor Belichick and the valedictorian Patriots marched off the field in Arizona a month later with a fourth Lombardi Trophy in hand — again winning a game that less studious teams would have lost.

The talented Seattle Seahawks (No. 10 on the Intelligence Index) dominated the Super Bowl physically, averaging 7.5 yards per play to just 5.2 for the Patriots.

But the more mentally proficient Patriots won the game, 28-24, making smart plays at critical moments and proving that victory in the NFL is often a matter of brains over brawn.