# Field Equations: The Physics of Baseball

A Q&A with physicist Alan Nathan

### More on this Topic

• #### The Science of Baseball

At long last, Opening Day is nearly here. As with each new season, this one arrives with a slew of major-league questions: Can the Phillies repeat? Can the spendthrift Yankees break their World Series drought? Is this the year the Athletics reclaim their freewheeling magic? But the answers to all those big questions will ultimately arise from countless small interactions, both human (a pitcher facing down a batter, a base runner challenging a catcher's arm, a manager's clever double switch) and physical (a ball meeting the bat's sweet spot, a sharp slider slicing through the air, a pop fly tracing a parabolic arc through the sky).

Alan Nathan, a physics professor at the University of Illinois at Urbana–Champaign, has trained his expert eye on those questions of physics that make up the quanta of the game. Nathan maintains an online repository on the physics of baseball, drawing from his own work and that of other baseball-minded scientists. We spoke to him about corked bats, the mysterious "gyroball," and whether his favorite team has the manpower to grind out another championship season.

[An edited transcript of the interview follows.]

How did you become interested in this subject?

On your Physics of Baseball Web page, I see a lot of information about the spin of the ball. To an observer of baseball, this is something that comes up a lot when we're hearing about pitching but very rarely when we're talking about batted balls. Is this a major factor for balls in flight?
Absolutely. It's one of the determining factors in how far a fly ball will carry, for example. Typically, if you want to hit a long fly ball, you want to put backspin on that ball. The so-called Magnus force on the spinning baseball will be upward for a ball with backspin, and basically it opposes gravity. It keeps the ball in the air longer so it travels farther. So this leads to batting strategies—you actually undercut the ball. You don't want to hit the ball head-on, which would give you sort of a line drive. You want to undercut it a bit, which gives it more of a vertical takeoff angle and also gives the ball backspin. And the backspin is essential if you want to hit a long fly ball.

On the other hand, if you do the opposite—if you hit on the topside of the ball—generally the ball goes down, so it's going to be a grounder, and it's going to have topspin on it. But topspin itself can lead to interesting things happening. Sometimes a batter can hit a sinking line drive; again, it's another hitting strategy. In this case the ball is hit as more of a line drive, but it's slightly topped, so the ball has topspin on it. Topspin makes the ball fall more rapidly, and that's what you might want to do for a line drive so it falls in front of the outfielder. So there are all sorts of hitting strategies that batters can employ, and I suspect that although they don't think of it maybe quite in these terms, they really do understand what it's all about.

While we're on the subject of hitting strategies, I see you have done some work on the pros and cons of corked bats. Could you walk us through that?
The idea of corking a bat is that you drill a hole through the barrel end of the bat—maybe a foot deep, maybe about an inch in diameter—and you backfill it with cork. The cork itself doesn't do anything other than hide the fact that you've done this illegal act. The idea is the following: with less weight of the bat at the head of the bat, in the barrel, you're able to swing the bat faster. But it's a trade-off. Because the business end of the bat has less weight, you can swing it faster, but it's less efficient at transferring energy to the ball. And so there's something of a controversy as to whether the net result is positive or negative from the point of view of the batter. My conclusion from the point of view of getting the highest batted ball speed, which is what you want if you want to hit the longest fly ball, is that it's a net loss for the batter. That is to say, what you gain in swing speed does not quite make up for what you lose in the efficiency in transferring energy.

So then you might ask, well, why do batters do this? There's actually a good reason for why they might do it. It's not to get the highest batted ball speed but to have the best bat control. So with less weight of the bat in the barrel, you're much more easily able to manipulate the bat, to get the bat into the strike zone quicker. Batters make the distinction between bat speed—how fast the bat is actually moving when it hits the ball—and bat quickness, which has more to do with the acceleration, the batter's ability to get the bat from where it is initially on his shoulder into the strike zone as quickly as possible. And that means the ability to be able to even change your swing in the middle of the swing, which happens once you get more information on where the ball is going to end up.

So whereas corking the bat very likely does not allow you to hit a longer home run, it might allow you to make good contact more often.

So even though you're sacrificing your batted ball speed and perhaps your reputation, if you're Sammy Sosa, there are some benefits to be gained there.
Yeah. And I think that this kind of trade-off is very similar to the kind of trade-off that players at the high school and college level make. The same things apply, except they're not using wooden bats. They can actually reduce the weight in the barrel of the bat legally by selecting a bat that's not quite as top-heavy. With nonwood bats you can more easily alter the moment of inertia of the bat, which mostly has to do with how heavy it is in the barrel, almost independent of the overall weight of the bat, and you can do it legally. So the interesting thing is that most collegiate players seem to prefer bats with less weight in the barrel, in a sense sacrificing the highest batted ball speed in favor of more bat control and the ability to put the barrel of the bat on the ball more often.

As for the physics of pitching, two years ago everyone was hearing about the "gyroball." Have we seen one of these in Major League Baseball, or is it a myth?
I won't go so far as to say it's a myth. I don't think it is a myth. But it certainly is seldom used. As you say, two years ago, when Daisuke Matsuzaka was first making his entrance to Major League Baseball from Japanese baseball, that's when all the discussion took place about the gyroball. A gyroball is a ball thrown with what you might call bullet spin, sort of like a spiral for a football. So the spin axis is aligned more or less with the direction of motion. The way that the Magnus force works on a spinning baseball is that the force is largest when the spin axis is perpendicular to the direction of motion. When they're in the same direction, there is no Magnus force. So the ball might be spinning, but that spinning does not give rise to any deflection of the ball. And so it would seem that it's a useless pitch. But when I analyzed it, I concluded that when used judiciously, it's not a useless pitch. And the reason why is that most pitches thrown are spinning. If the batter sees a ball coming out of the hand that looks like a four-seam fastball, which is sort of the straightest pitch and the pitch that drops the least because it's got a lot of backspin, the batter is expecting the pitch to come in more or less at a certain elevation. If instead this is actually a gyroball—for the sake of argument let's say that it's thrown just as hard as a fastball—then it doesn't have any upward Magnus force on it. It's falling freely from gravity, so it ends up dropping more than a typical four-seam fastball would drop, and that's a perfectly useful pitch if the batter is expecting it to do something else.

The old adage, as the great left-hander Warren Spahn said, is that "batting is timing; pitching is upsetting timing." You don't have to throw the fastest ball to get people out—all you have to do is throw something they're not expecting. The really good pitchers know how to do that.

Witness Jamie Moyer, for instance.
Greg Maddux is another great example of someone who has made a career out of not necessarily always throwing his best stuff but always mixing things up in such a way that the batter doesn't expect it.

Now, when I looked at Matsuzaka's pitches from the 2007 season, I concluded that if he threw the pitch, it wasn't being thrown very often. Maybe once or twice per game at most. There is a pitch-tracking system called Pitch f/x that is installed in every major league ballpark, and all the data are completely free for the world to look at. Well, you have to know where to find it and how to interpret it. The signature of the gyroball would be a ball that doesn't break, that has neither a horizontal nor a vertical break. So I've looked for such pitches from Matsuzaka, and you sort of see a few every now and then that look like they might qualify. If he does throw it, it's not the sort of pitch you would want to give people a steady diet of, because once they figure it out and catch on to it, it's an easy pitch to hit. So you have to throw it judiciously, and if he does throw it—nobody knows for sure—he is certainly throwing it judiciously.

Moving over to Matsuzaka's teammate Tim Wakefield, could you give us a rundown on his signature pitch, the knuckleball?
Well, I have to admit that I understand one that the least.

I think that's true of everyone.
The key to understanding the knuckleball is that if a ball were perfectly smooth, the air would flow over it in a fairly smooth fashion. But the stitching on the ball disrupts the flow of air, causing the ball to break. It's not at all the same effect as the effect due to the spinning baseball—it's different altogether. So the key to throwing a knuckleball is that if you throw a ball that's spinning, one way to think about it is that the spinning baseball is averaging over different seam orientations, so there's no net effect due to the air interacting with the seams. But if you throw the ball with almost no spin at all—maybe it rotates a half or even a quarter of a revolution on its way to home plate—then as the air moves over the ball, it's the interaction of the air with those seams that changes the character of the airflow, making it go from a nice, smooth flow to sort of a turbulent flow. That causes local pressure variations which make the ball break, and it breaks in a more or less unpredictable way.

If you use this Pitch f/x system to look at any other pitcher and you plot each pitch on sort of an x-y diagram where x is the break in the horizontal direction and y is the break in the vertical direction, then the pitches fall into nice, neat little clusters. You have a nice little cluster showing a four-seam fastball, a curveball, a cutter. But you look at Wakefield and it's all over the place. There is no nice, neat cluster, which means that the ball doesn't have what you might call a characteristic break to it. It really is quite literally unpredictable. Everyone knows it's coming, but all you have to do is look at what the catcher is doing to realize that nobody knows where it's going—I mean, the catcher's having a heck of a time dealing with it also. [Editor's note: In 2006, the Red Sox reacquired catcher Doug Mirabelli specifically for his ability to catch Wakefield's knuckleball.] It's a tough pitch to hit. It's really funny with Wakefield; he is the closest I've seen to a bipolar pitcher. He gets on the mound, and either he has it that day or he doesn't. When he's on, he's just totally unhittable. And when he's not on, they whack him around. Sometimes that ball is really dancing around and sometimes it's not. And then there are times that it's dancing around so much that he can't control it, and then he's walking people and has a bad day. He's almost a .500 career pitcher; he wins half the games he pitches. It just reflects the fact that sometimes it's on and sometimes it's not.

The Red Sox. I'm from Maine originally.

Do you see them going all the way this year?
I think they have the possibility if things fall into place. There is tough competition in their division. Although hitting this year won't be quite as good as it's been in years past, the pitching looks to be very strong if people stay healthy. They'll be in the mix. Check back with me in October.

Rights & Permissions