The Physics of the Bat Flip

The postseason is upon us, and we can count on clutch hits, critical walks, epic homers, and – of course – the associated theatre of championship bat flips. One of the most famous postseason bat flips belongs to Jose Bautista of the Toronto Blue Jays after his three-run seventh inning blast in Game 5 of the 2015 American League Division Series against the Texas Rangers (Tom Lawless certainly has a case though).

Bat flips are similar to the designated hitter and the no-pitch walk. Fans either love them or hate them. There is no middle ground. Many players also seem to place themselves in one camp or the other. Kris Bryant explained why he won’t toss the lumber, “It’s enough of a disgrace to the pitcher when it’s halfway up the video board.”

David Ortiz is enjoying the newfound freedom to speak his mind as a retired ballplayer. He told the Boston Globe, “Whenever somebody criticizes a power hitter for what we do after we hit a home run, I consider that person someone who is not able to hit a homer ever in his life. Look at who criticizes the power hitters in the game and what we do. It’s either a pitcher or somebody that never played the game. Think about it. You don’t know that feeling. You don’t know what it takes to hit a homer off a guy who throws 95 miles per hour. You don’t know anything about it. And if you don’t know anything about it, [expletive deleted].”

Surprisingly, the fiercely competitive Jake Arrieta has a more diplomatic view, “If he’s a vet and earned it no prob. If he’s a young guy he might wear the next one in the ribs.” MLB itself takes no official position on the bat flip, but they are more than happy to have an article on their website entitled, “Flip your lids with the 10 best bat flips of 2016.”

Here we’ll take a look at this Hanley Ramirez classic stick twirl. I chose it because the camera caught all of it, the camera was not zooming in or out, and the bat was mostly moving in a plane perpendicular to the camera direction.

Below is a sketch that is based upon the position of the bat in each frame of the video. The images are numbered in time sequence. You see the motion appears to be wildly complex with little discernible pattern. I have taken some liberties in this sketch because the exact position of the bat was often difficult to discern in a few of the video frames.

At heart, baseball is straightforward endeavor involving just a few fundamental elements as once described by manager, Joe Riggins, in the film Bull Durham, “This is a simple game. You throw the ball. You hit the ball. You catch the ball. You got it?”

Yet, despite this underlying simplicity, the game unfolds into a myriad of complex, dramatic, and beautiful scenarios. Physics works the same way. The underlying ideas are simple, but they explain everything that is explainable about the known universe. The key underlying idea to explain the complex motion of the bat flip is called the “center-of-mass” or CM.

There is of course a detailed mathematical description of the CM, but let’s be more practical. The way to find the CM of a baseball bat is to balance it on one finger as shown below. The red spot in the dead center of the bat directly above your finger is the CM. You might note the CM is on the barrel side of the bat because the barrel contains so much more of the bat’s mass than the handle.

Below is the same collection of images of the motion of the bat except the CM has been marked in each image.

Now, let me remove the images of the entire bat leaving just the location of the CM. You’ll see that the motion of the CM of the bat is exactly the same as the motion of a ball thrown with the same initial speed and direction of the CM of the bat.

That’s a pretty amazing simplification of the intricate motion of the bat, but it ignores the rotation of the bat. Focusing just on this rotation, I’ll take the images of the bat, but I’ll align the CM’s from each image. The result is shown below.

The bat rotates like clockwork about its CM! So, the complex and stirring motion of the bat during a bat flip can be explained by looking at the overall motion of the center-of-mass which is the same as the motion of a baseball with the same initial speed and direction combined with the steady rotation of the bat about its center-of-mass.

So, love the bat flip or despise it, perhaps we can all agree that the motion of the bat is beautifully complex and, at the same time, delightfully simple.