Buffalo Bills quarterback Ryan Fitzpatrick earned the second-highest score ever recorded by an NFL player on the Wonderlic test. (Julio Cortez/AP)

Buffalo Bills quarterback Ryan Fitzpatrick sports the scruffy beard of an outdoorsman, the size and strength of some running backs and the intelligence quotient of your average nuclear physicist.

Fitzpatrick, a Harvard graduate who majored in economics, enters Sunday’s game against the Washington Redskins with impressive totals in a variety of NFL statistical categories. He is one reason the Bills, a perennial disaster, are 4-2 this season.

Yet the result for which he is best known is the 48 he scored on the Wonderlic Cognitive Ability Test shortly before he was drafted in 2005. That number puts him in closer intellectual company with Stephen Hawking than some of his teammates —and probably his coaches. Research indicates that it corresponds to an IQ of about 150.

It was the second-highest score ever recorded by an NFL player on the 50-point test (trailing only the perfect 50 earned by fellow Harvard alum and former Cincinnati Bengal Pat McInally in 1975). It trumps the highly respectable 30 tallied by Redskins quarterback John Beck, the 29 earned by Rex Grossman, and the societal average of about 20.3 — which represents an IQ of about 100.

All of which probably means nothing when Fitzpatrick and his colleagues step on a football field.

A 2009 study of 762 players from three draft classes found no correlation between intelligence, as measured by the Wonderlic test, and NFL performance except for tight ends and defensive backs — whose achievements increased with lower scores. Even at the quarterback position, where brains are generally believed to be critical, there was no significant relationship between high scores and high performance.

“We found in no cases was cognitive ability related to [football] performance,” said John W. Michel, an assistant professor at Towson University who co-authored the study. “We did find a negative relationship for tight ends and defensive backs. For defensive backs, it was the most pronounced; basically, the lower you scored on the Wonderlic, the better you performed.”

That hasn’t stopped NFL executives from continuing to apply the Wonderlic — with a certain amount of discretion — along with increasingly frequent and extensive psychological testing. For three decades, the Wonderlic has been as integral to the NFL’s examination of draftees as the bench press and the 40-yard dash. The NFL is the only one of the major U.S. sports to give prospects an intelligence test.

“It’s of value, because it’s something everyone takes,” said former Redskins general manager Charley Casserly. “You got a history on it. It gives you a red light, which is good to have, and then you work from the red light.”

Fitzpatrick completed the 50-question, 12-minute exam in nine minutes. The scores are not released publicly, but many — especially the better ones — have leaked out over the years.

Says Tim Murphy, Fitzpatrick’s coach at Harvard: “It’s one thing to have a great SAT score; it’s a different thing to be able to make great decisions under pressure when everything is happening around you.” Fitzpatrick, Murphy said, excelled at both.

Team officials say they want players who are savvy enough to absorb a playbook, identify the complex formations of the modern NFL and comprehend the consequences of, for example, tucking a loaded gun into their pants and walking into a crowded nightclub.

“If you get a solid score, show better than average intelligence, that’s going to help you in the long run for myriad reasons, not just retaining the playbook,” said Stanford graduate Lester Archambeau, who played defensive end for 11 NFL seasons and is now a player agent.

Scores in the single digits or low teens, which could indicate a learning disability, generally trigger follow-up measures by interested teams. To give top prospects an edge on the test, and help them avoid scores that generate such scrutiny, some player agencies obtain copies of old Wonderlic exams and offer extensive prep courses before the pre-draft combine, where the test is formally administered.

Of course, some football people look just as warily at players who ace the Wonderlic as those who struggle with it. The exceedingly bright can anticipate having their dedication and aggressiveness questioned more than average scorers.

Longtime agent Frank Murtha, who represented many players from Notre Dame, said scouts jokingly referred to such concerns as the “Domer Mentality.” Archambeau was nicknamed “The Professor” in Atlanta, and recalled getting lambasted by coaches anytime he made a mental mistake.

Gil Brandt, former vice president of player personnel for the Dallas Cowboys,admitted to having a reflexive bias against those who scored exceptionally well on the Wonderlic.

“When you have a player who is really extraordinarily smart, he’s probably not as aggressive as a player with a lesser intelligence quotient,” Brandt said. “I’m not sure that’s correct — but I think it is.”

McInally played nine years with the Cincinnati Bengals. After he retired, he recalled, five-time NFL executive of the year George Young told him his perfect Wonderlic score likely caused him to fall from the second or third round of the draft to the fifth.

“He really did tell me it cost me two or three rounds, because [NFL teams] did not like extremes,” McInally said. “He told me they don’t like ’em low, and they sure as hell don’t like ’em high.”

According to various reports, the Giants’ Eli Manning scored a 38 on the test; his brother Peyton, a 28; Drew Brees and Brett Favre tallied 22; Tom Brady earned a 33; and San Francisco quarterback Alex Smith, a 40.

There also have been some infamously low scores. Murtha said he recalled an offensive lineman from a Southeastern Conference school who scored a 3, and yet went on to a successful NFL career. Brandt said he knew of a Hall of Fame quarterback who scored a 13. Miami Dolphins legend Dan Marino reportedly scored in the mid-teens, then became one of the top signal callers in the sport’s history.

Of 430 businesses that also used the Wonderlic test and reported scores to the company in 2003, executives scored best at an average of 28.1. Computer programmers tallied 27.1, and correctional officers 20.5. Truck drivers averaged 18.7; mechanics 17.1.

The legendary Paul Brown introduced the test to his peers in the early 1960s when he was with the Cleveland Browns. The Dallas Cowboys, under general manager Tex Schramm, Brandt and coach Tom Landry, began testing prospects soon after, seeking an edge in player evaluations.

It wasn’t long before the NFL had entered into a contract with Wonderlic, testing all prospective draft picks who showed up for the league’s annual combine and distributing the results to teams. It is the only non-physical test, intellectual or psychological, that the NFL uses; brevity is considered one of its many advantages. Many individual teams, however, run their prospects through psychological testing, some substantially longer and more involved.

“There are some teams that never consider a player without taking the Wonderlic score into consideration; other teams say it’s interesting, but don’t put a lot of weight into it,” said Michael Callans, vice president for research and development at Wonderlic. “It really comes into play when somebody’s score is so out of line that you wouldn’t expect it.”

Murphy, Fitzpatrick’s coach at Harvard, said his former collegiate star stood out not only for his Wonderlic score, but also for his athletic skills, poise and calm under pressure. Despite what Murphy considered a full package of assets, Fitzpatrick attracted little attention from pro scouts even after putting up incredible numbers for the Crimson.

The St. Louis Rams selected him in the seventh round of the 2005 draft, but only the Green Bay Packers — who ended up drafting Aaron Rodgers in the first round that year — seemed to foresee a certain NFL future for Fitzpatrick, Murphy said.

“They were the only ones that got it with him,” Murphy said. “It was clear they loved this kid. But they were the only ones that loved him.”