It is Rocket Science

By Paul Hamann

You’ll take every advantage you can get in your game, right? What if the laws of science, physics especially, could help you improve your play calling? As with most officials, you’d follow along. Science can play a vital part in what is seen, in how the ball may bounce and whether a player is safe or out.

Officials and scientists don’t have much in common. Scientists do their work under controlled conditions and can take as much time as they need to reach their conclusions. Officials have almost no time to make their decisions, and they do so under conditions that are both uncontrolled and unpredictable. But officials and scientists share one trait. Both are called upon to explain why and how a physical phenomenon occurs.

Is there any way that science can help an official make the right call?

Of course, your goal is always to see the whole play. If you see it, you can call it. 

But for tougher plays, science can be a part of what is seen, and Professor Timothy Gay took some time to help interpret some of the visual data officials see in the line of duty.

Gay’s unique resumé weds sports and science. Gay, a professor of physics at the University of Nebraska, played football as an undergraduate at CalTech. On top of his research and teaching duties, he has collaborated with NFL Films to demonstrate how the laws of physics explain the tooth-jarring hits and gorgeous spiral passes in NFL games. He is the author of The Physics of Football, which explains gridiron physics to non-scientist couch potatoes.

Gay says that a few scientific laws can help us lay down the law during games.              

Football: Conservation of Momentum

     A wide receiver stands in the middle of the field, facing the quarterback, waiting for the ball to arrive. He concentrates on the ball, blissfully unaware of the fast and vicious defensive back about to drill him between the numbers on his back. Ball and defender arrive very nearly simultaneously and the pass falls incomplete. The covering official is left with an extremely difficult call. Did the defender arrive before the ball and commit pass interference? Or did he arrive just after the ball and make a great play?

Gay says to watch how the ball behaves.

“Let’s take the simple case of a player standing stock still,” Gay says. But instead of the receiver being hit, “He’s fumble- fingered, and he just drops the ball.” Gay tells us that the ball won’t likely rebound very far because a stationary player won’t apply much force to the ball. However, if the receiver has started his rapid, unwelcome forward motion because of the force applied to him by a violent defensive back, that force won’t end with the receiver’s movement. It will transfer into the ball, and the ball will go flying.

Make no mistake — there are many variables preventing that from being a clean-cut case. If the receiver is moving, for instance, or if he juggles the ball at all, things get far more complex. But if it’s a razor-thin margin between the ball’s arrival and the player’s arrival, an official should know that science tells us the ball will travel away from the player faster if pass interference occurred.  

Soccer: Torque

What clues can we get as to whether a running player with the ball has been tripped or has taken a dive?

Consider the definition of tripping, Gay says.

“How does tripping work?” he asks. “Tripping works because there is a quasi-immovable object which is preventing your feet from going forward when they want to go forward.” Think about the last time you tripped on the curb. Your feet stayed at the curb, because the curb was immovable. Your center of mass, however, traveled forward and landed the same distance from your feet that it always is; probably about three feet away, depending on your height. The sudden stop has applied torque, or a rotational force, to your body.

So if the offensive player’s feet are still back where the defender is, odds are, there was a trip.

However, there’s a little difficulty with that. The player may be jumping to avoid the tackler, and a tackler/ tripper’s foot or shin isn’t an immovable object — it has a little give.

Don’t panic, Gay says. The offensive player’s body will still give clues as to whether she dove.

“The hallmark of a trip is that her torso will keep going forward, but her feet don’t,” he says. That is because torque, or rotational force, has been applied to her body. “Therefore, she becomes unstable and she falls down.”

On the other hand, Gay says, “If she’s faking it, she’s going to start to crumple, but her feet are going to move as well. Feet have forward momentum.” That momentum will continue unless something like a tripper slows or stops it by applying torque. 

If the offensive player is faking, she will not be able to decide in mid-air to go horizontal. So if the line between the player’s feet and her torso are close to vertical, she’s probably faking a foul. If it’s closer to a horizontal line, something had to apply that torque. “She can’t really apply any torque to herself,” Gay says, so it’s likely her opponent applied the torque with a trip.

Basketball: Newton’s Second Law

Can science help us determine if a defender got ball or arm?

If it’s an exceedingly close play, Gay says, the ball might help to give answers.

Isaac Newton’s second law states that force is equal to mass times acceleration. Force and acceleration are called “vector quantities,” which means they have direction associated with them. A defender’s arm trying to swat a shot is a vector quantity; he’s attempting to apply force to the ball in a certain direction.

Therefore, if a defender goes to block a shot, and the ball shoots off in the direction that his arm was traveling, it’s almost undoubtedly a clean block. If the ball goes in a different direction from the arm, that’s almost undoubtedly a foul.

The defender, Gay explains, will apply an impulse, defined as a sharp force over an interval of time. If that force is applied to the ball, the ball will travel in the direction of that force. However, “if you apply it to the arm, then the arm gets out of the way of the ball, and the ball will keep going up, roughly speaking.”

In other words, “if the ball keeps going up, it’s almost certain that the guy was fouled. It’s kind of counterintuitive, but it’s true. If the ball doesn’t seem to have suffered anything, the player has.”

Baseball: Coefficient of Restitution

The batter hits a long drive deep to the outfield. The ball heads to the top of the wall, where it ricochets off of either the yellow line on top of the wall, thus staying live and in play, or off of a guy in a yellow shirt in the front row, thus becoming a dead ball and a home run. How can science help us with that call?

Easily, Gay says. Just consider the coefficient of restitution — otherwise known as “bounciness.”

“Guys are deader than walls,” Gay says. “So the ball will bounce back harder if it’s hit a wall than if it’s hit a guy.” If you don’t believe him, first throw a baseball at a wall. Next, throw one at an inattentive friend. You’ll see that the coefficient of restitution of a wall is much higher, resulting in a bigger bounce.

“There are two things at play,” Gay adds. “First of all, the guy is drinking beer, so he’s got a big beer belly. That absorbs a lot of the energy of the ball.” Also, Gay suggests that the fan in the front row will likely not be throwing himself enthusiastically forward toward the ball. “If anything, he’ll be cowering backwards.” That, too, means that the ball won’t travel quickly if it ricochets off a fan.

To put it another way: A lively ball is probably a live ball. A deader ball is probably a dead ball and a home run.

When all is said and done, of course, it’s best to see the play. Officials don’t have time to do all the calculations Gay does. But if a few select scientific rules are in the back of our minds, they can enhance our visual input and help us to make the right call.

Even Einstein would approve.

Paul Hamann has officiated high school basketball since 1996. He is a high school teacher who lives in Vancouver, Wash.