On the day of the big football game between the University of Missouri Tigers and the Cowboys of Oklahoma State, a football scout named Dan Shonka sat in his hotel, in Columbia, Missouri, with a portable DVD player. Shonka has worked for three National Football League teams. Before that, he was a football coach, and before that he played linebacker—although, he says, “that was three knee operations and a hundred pounds ago.” Every year, he evaluates somewhere between eight hundred and twelve hundred players around the country, helping professional teams decide whom to choose in the college draft, which means that over the last thirty years he has probably seen as many football games as anyone else in America. In his DVD player was his homework for the evening’s big game—an edited video of the Tigers’ previous contest, against the University of Nebraska Cornhuskers.

Effective teachers have a gift for noticing—what one researcher calls “withitness.” Illustration by Joost Swarte

Shonka methodically made his way through the video, stopping and re-winding whenever he saw something that caught his eye. He liked Jeremy Maclin and Chase Coffman, two of the Mizzou receivers. He loved William Moore, the team’s bruising strong safety. But, most of all, he was interested in the Tigers’ quarterback and star, a stocky, strong-armed senior named Chase Daniel.

“I like to see that the quarterback can hit a receiver in stride, so he doesn’t have to slow for the ball,” Shonka began. He had a stack of evaluation forms next to him and, as he watched the game, he was charting and grading every throw that Daniel made. “Then judgment. Hey, if it’s not there, throw it away and play another day. Will he stand in there and take a hit, with a guy breathing down his face? Will he be able to step right in there, throw, and still take that hit? Does the guy throw better when he’s in the pocket, or does he throw equally well when he’s on the move? You want a great competitor. Durability. Can they hold up, their strength, toughness? Can they make big plays? Can they lead a team down the field and score late in the game? Can they see the field? When your team’s way ahead, that’s fine. But when you’re getting your ass kicked I want to see what you’re going to do.”

He pointed to his screen. Daniel had thrown a dart, and, just as he did, a defensive player had hit him squarely. “See how he popped up?” Shonka said. “He stood right there and threw the ball in the face of that rush. This kid has got a lot of courage.” Daniel was six feet tall and weighed two hundred and twenty-five pounds: thick through the chest and trunk. He carried himself with a self-assurance that bordered on cockiness. He threw quickly and in rhythm. He nimbly evaded defenders. He made short throws with touch and longer throws with accuracy. By the game’s end, he had completed an astonishing seventy-eight per cent of his passes, and handed Nebraska its worst home defeat in fifty-three years. “He can zip it,” Shonka said. “He can really gun, when he has to.” Shonka had seen all the promising college quarterbacks, charted and graded their throws, and to his mind Daniel was special: “He might be one of the best college quarterbacks in the country.”

But then Shonka began to talk about when he was on the staff of the Philadelphia Eagles, in 1999. Five quarterbacks were taken in the first round of the college draft that year, and each looked as promising as Chase Daniel did now. But only one of them, Donovan McNabb, ended up fulfilling that promise. Of the rest, one descended into mediocrity after a decent start. Two were complete busts, and the last was so awful that after failing out of the N.F.L. he ended up failing out of the Canadian Football League as well.

The year before, the same thing happened with Ryan Leaf, who was the Chase Daniel of 1998. The San Diego Chargers made him the second player taken over all in the draft, and gave him an eleven-million-dollar signing bonus. Leaf turned out to be terrible. In 2002, it was Joey Harrington’s turn. Harrington was a golden boy out of the University of Oregon, and the third player taken in the draft. Shonka still can’t get over what happened to him.

“I tell you, I saw Joey live,” he said. “This guy threw lasers, he could throw under tight spots, he had the arm strength, he had the size, he had the intelligence.” Shonka got as misty as a two-hundred-and-eighty-pound ex-linebacker in a black tracksuit can get. “He’s a concert pianist, you know? I really—I mean, I really—liked Joey.” And yet Harrington’s career consisted of a failed stint with the Detroit Lions and a slide into obscurity. Shonka looked back at the screen, where the young man he felt might be the best quarterback in the country was marching his team up and down the field. “How will that ability translate to the National Football League?” He shook his head slowly. “Shoot.”

This is the quarterback problem. There are certain jobs where almost nothing you can learn about candidates before they start predicts how they’ll do once they’re hired. So how do we know whom to choose in cases like that? In recent years, a number of fields have begun to wrestle with this problem, but none with such profound social consequences as the profession of teaching.

One of the most important tools in contemporary educational research is “value added” analysis. It uses standardized test scores to look at how much the academic performance of students in a given teacher’s classroom changes between the beginning and the end of the school year. Suppose that Mrs. Brown and Mr. Smith both teach a classroom of third graders who score at the fiftieth percentile on math and reading tests on the first day of school, in September. When the students are retested, in June, Mrs. Brown’s class scores at the seventieth percentile, while Mr. Smith’s students have fallen to the fortieth percentile. That change in the students’ rankings, value-added theory says, is a meaningful indicator of how much more effective Mrs. Brown is as a teacher than Mr. Smith.

It’s only a crude measure, of course. A teacher is not solely responsible for how much is learned in a classroom, and not everything of value that a teacher imparts to his or her students can be captured on a standardized test. Nonetheless, if you follow Brown and Smith for three or four years, their effect on their students’ test scores starts to become predictable: with enough data, it is possible to identify who the very good teachers are and who the very poor teachers are. What’s more—and this is the finding that has galvanized the educational world—the difference between good teachers and poor teachers turns out to be vast.

Eric Hanushek, an economist at Stanford, estimates that the students of a very bad teacher will learn, on average, half a year’s worth of material in one school year. The students in the class of a very good teacher will learn a year and a half’s worth of material. That difference amounts to a year’s worth of learning in a single year. Teacher effects dwarf school effects: your child is actually better off in a “bad” school with an excellent teacher than in an excellent school with a bad teacher. Teacher effects are also much stronger than class-size effects. You’d have to cut the average class almost in half to get the same boost that you’d get if you switched from an average teacher to a teacher in the eighty-fifth percentile. And remember that a good teacher costs as much as an average one, whereas halving class size would require that you build twice as many classrooms and hire twice as many teachers.

Hanushek recently did a back-of-the-envelope calculation about what even a rudimentary focus on teacher quality could mean for the United States. If you rank the countries of the world in terms of the academic performance of their schoolchildren, the U.S. is just below average, half a standard deviation below a clump of relatively high-performing countries like Canada and Belgium. According to Hanushek, the U.S. could close that gap simply by replacing the bottom six per cent to ten per cent of public-school teachers with teachers of average quality. After years of worrying about issues like school funding levels, class size, and curriculum design, many reformers have come to the conclusion that nothing matters more than finding people with the potential to be great teachers. But there’s a hitch: no one knows what a person with the potential to be a great teacher looks like. The school system has a quarterback problem.

Kickoff time for Missouri’s game against Oklahoma State was seven o’clock. It was a perfect evening for football: cloudless skies and a light fall breeze. For hours, fans had been tailgating in the parking lots around the stadium. Cars lined the roads leading to the university, many with fuzzy yellow-and-black Tiger tails hanging from their trunks. It was one of Mizzou’s biggest games in years. The Tigers were undefeated, and had a chance to become the No. 1 college football team in the country. Shonka made his way through the milling crowds and took a seat in the press box. Below him, the players on the field looked like pieces on a chessboard.

The Tigers held the ball first. Chase Daniel stood a good seven yards behind his offensive line. He had five receivers, two to his left and three to his right, spaced from one side of the field to the other. His linemen were widely spaced as well. In play after play, Daniel caught the snap from his center, planted his feet, and threw the ball in quick seven- and eight-yard diagonal passes to one of his five receivers.

The style of offense that the Tigers run is called the “spread,” and most of the top quarterbacks in college football—the players who will be drafted into the pros—are spread quarterbacks. By spacing out the offensive linemen and wide receivers, the system makes it easy for the quarterback to figure out the intentions of the opposing defense before the ball is snapped: he can look up and down the line, “read” the defense, and decide where to throw the ball before anyone has moved a muscle. Daniel had been playing in the spread since high school; he was its master. “Look how quickly he gets the ball out,” Shonka said. “You can hardly go a thousand and one, a thousand and two, and it’s out of his hand. He knows right where he’s going. When everyone is spread out like that, the defense can’t disguise its coverage. Chase knows right away what they are going to do. The system simplifies the quarterback’s decisions.”

But for Shonka this didn’t help matters. It had always been hard to predict how a college quarterback would fare in the pros. The professional game was, simply, faster and more complicated. With the advent of the spread, though, the correspondence between the two levels of play had broken down almost entirely. N.F.L. teams don’t run the spread. They can’t. The defenders in the pros are so much faster than their college counterparts that they would shoot through those big gaps in the offensive line and flatten the quarterback. In the N.F.L., the offensive line is bunched closely together. Daniel wouldn’t have five receivers. Most of the time, he’d have just three or four. He wouldn’t have the luxury of standing seven yards behind the center, planting his feet, and knowing instantly where to throw. He’d have to crouch right behind the center, take the snap directly, and run backward before planting his feet to throw. The onrushing defenders wouldn’t be seven yards away. They would be all around him, from the start. The defense would no longer have to show its hand, because the field would not be so spread out. It could now disguise its intentions. Daniel wouldn’t be able to read the defense before the snap was taken. He’d have to read it in the seconds after the play began.

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“In the spread, you see a lot of guys wide open,” Shonka said. “But when a guy like Chase goes to the N.F.L. he’s never going to see his receivers that open—only in some rare case, like someone slips or there’s a bust in the coverage. When that ball’s leaving your hands in the pros, if you don’t use your eyes to move the defender a little bit, they’ll break on the ball and intercept it. The athletic ability that they’re playing against in the league is unbelievable.”

As Shonka talked, Daniel was moving his team down the field. But he was almost always throwing those quick, diagonal passes. In the N.F.L., he would have to do much more than that—he would have to throw long, vertical passes over the top of the defense. Could he make that kind of throw? Shonka didn’t know. There was also the matter of his height. Six feet was fine in a spread system, where the big gaps in the offensive line gave Daniel plenty of opportunity to throw the ball and see downfield. But in the N.F.L. there wouldn’t be gaps, and the linemen rushing at him would be six-five, not six-one.

“I wonder,” Shonka went on. “Can he see? Can he be productive in a new kind of offense? How will he handle that? I’d like to see him set up quickly from center. I’d like to see his ability to read coverages that are not in the spread. I’d like to see him in the pocket. I’d like to see him move his feet. I’d like to see him do a deep dig, or deep comeback. You know, like a throw twenty to twenty-five yards down the field.”

It was clear that Shonka didn’t feel the same hesitancy in evaluating the other Mizzou stars—the safety Moore, the receivers Maclin and Coffman. The game that they would play in the pros would also be different from the game they were playing in college, but the difference was merely one of degree. They had succeeded at Missouri because they were strong and fast and skilled, and these traits translate in kind to professional football.