The Physics of “Monsta Shawts”

I suppose every ballpark has a unique element or two. Yet no other stadium has the wealth of iconic features possessed by Fenway Pawk. Off the top of my head, I can name four–the Red Seat, Pesky’s Pole, the Fisk Pole, and the Green Monster.

Just in case there is some horrible gap in your baseball knowledge, let me explain. The Green Monster is the name of the 37.2 feet-high left field wall at Fenway, home of the Boston Red Sox. The wall begins 310 feet from home plate down the line and continues about 225 ft into almost straightaway center field, staying roughly parallel with the right field line.

To wrap your head around the physics of the wall, imagine if it were just behind the shortstop. I suppose for some defensive shifts, it is essentially. Anyway, hitting a round-tripper would require a pop-up as opposed to a line drive.

Indeed, as John Walsh pointed out in “Making the Most of Fenway,” the Monster does eliminate many line drive-type home runs. In addition, there are fewer outfield flyball outs and more doubles. Just because they are more fun, let’s just look at the physics of the Fenway homers–“Monsta Shawts” as they say in “Bahstin.” First a bit of geometry.

The sketch above shows that, despite the dominating presence of the wall, it is only 6.8˚ above the horizontal as seen from home plate down the right field line. The angle is even smaller as a batter looks toward left-center. Typical dingers have a launch angle around 30˚. So, the height of the wall would, in this light, not seem to be a big factor.

Indeed, if a batter could hit a ball at an unrealistically high exit velocity of thousands of miles per hour, the minimum launch angle for a homer would be this 6.8˚. The ball would be moving so fast it wouldn’t have time to have its trajectory bend back toward the ground very much before it cleared the wall.

At realistic exit velocities on the order of about 100 mph, the track of the ball is an arc. So, the launch angle must be greater than 6.8˚, but how much more? That depends upon the exit velocity. If the exit velocity is high, there should be a variety of launch angles that will clear the wall. As the exit velocity drops, there will be fewer and fewer launch angles that will work.

The combinations of exit velocities and launch angles that just clear the wall should create a curve above which you get a homer and below which you don’t. The “limiting curve” of EV versus LA should look something like this.

Notice there is an optimum LA at the minimum EV, in this case 30˚. At 30˚, any ball hit harder than 95 mph (in this case) will “put one up on the board.” At any given EV over 95 mph, there is a range of angles that will do the trick, and this range of angles grows as the EV increases.

Before we go into the actual mathematical trajectory calculations, we should take this opportunity to watch the most famous right-handed home run ever to clear the Monster. From Game Six of the 1975 World Series, here is the event that forever named the left field foul pole in Fenway.

Back on task. To go a bit deeper on the required trajectories in Fenway requires a physical model of the flight of the ball. I used the model from Alan Nathan’s 3D Trajectory Calculator, although not the calculator itself. Using this methodology, the trajectory of balls with exit velocities between 90 and 120 mph as well as launch angles between 10 and 50 degrees were examined for right-handed batters.

The plot below shows the limiting curve for three different spray angles, -10˚, -20˚, and -30˚. In Statcast coordinates, -30˚ is closer to the left field line while -10˚ is closer to center field. Note that balls hit with a -30˚ spray angle wind up very close to the Fisk Pole when they clear to wall due to the fading of the ball toward the line caused by sidespin.

As you might expect, the minimum exit speed for a Monsta Shawt grows as the spray angle moves toward center field. In addition, the maximum launch angle and optimal launch angle both drop as the spray angle moves toward center field because the distance to the wall increases. The funny behavior is with the low launch angle–the line drive-type homer.

Look at the 20˚ launch angle. The ball hit toward center field needs an EV of about 111 mph, the one hit to left-center demands about 108 mph, but the one hit down the left field line requires more–not less–EV, about 113mph. This is the Green Monster Effect–it discriminates against line drive homers down the line.

So the physics agrees with the data and even “common sense.” There are fewer line drive homers down the line than more toward center field due to the wall. In addition, there are more high flyball homers down the line than toward center field as well.

Let’s compare this to the case of a more traditional outfield. In a nod to one of the oldest and most enduring rivalry in professional sports, let’s pick Yankee Stadium. Here is the same plot for the Bronx.

Just like Fenway, the minimum exit speed for a home run increases as the spray angle moves toward center field. Also, the maximum launch angle and optimal launch angle both decrease as the spray angle moves toward center field. Again, there is something funny with the low launch angle–line drive homers.

Again, look at the 20˚ launch angle. The ball hit toward center field needs an EV of about 107 mph, the one hit to left-center demands about 104 mph, but the one hit down the left field line requires more–not less–EV, about 105 mph. Why is there this strange behavior for line drive down the line? You know the answer: the distance down the line is dramatically smaller in most parks.

To get a clearer sense of the Green Monster Effect, let’s compare balls hit down the line between the two ballparks using the graph below. Fenway is, of course, green while Yankee Stadium is what else? Blue.

The two curves are remarkable similar for LA’s above 35˚. However, the optimal launch angle is clearly higher in Boston, 34˚ compared to 32˚. The dramatic difference in in the line drives. At an LA of 20˚, Fenway insists upon a minimum EV of 113 mph while Yankee Stadium requires a paltry 105 mph. This again demonstrates the Green Monster discriminating against line drive dingers.

So, the Green Monsta does create its own unique brand of baseball even though is it less than 6.8˚ tall. I probably don’t need to remind you, but physics does a pretty good job of explaining the “real world” behavior of a baseball.