Washington National’s pitcher Stephen Strasburg and Baltimore Raven’s quarterback Joe Flacco are two of the most prolific athletes in the Mid-Atlantic; each is well-known for his incredible arm strength. Flacco just completed a remarkable run leading the Ravens to a Super Bowl victory (we’ll leave the “elite” debate to another day), while Strasburg is preparing to follow up his successful, yet abridged, 2012 season. Both are known for their big arms, but have you ever wondered whose is bigger? How far could Strasburg throw a football? How fast could Flacco throw a baseball? With some simple statistics, a few assumptions, and some basic physics, we can compare the two gunslingers.

To compare these two we will use two physics concepts: change in energy and power output.

**1) ****Change in energy** is simply the change in energy of the ball from its rest position to the moment it leaves the athlete’s hand, as all of the energy the ball gains is caused by the athlete.

**2) ****Power** is simply the change in energy divided by the time it takes to undergo this change. If the energy changes faster, it means it took more power, but as we will actually see later the power is actually not all that useful in this comparison.

So the initial stats we will use are Strasburg’s 101 mile per hour fastball, and an account of Flacco throwing a pass 81 yards in a college competition. The mass of the baseball and football also matter, and those are 5 ounces and .4 kilograms respectively. Finally, I will make two pretty safe assumptions regarding the throws themselves to make the math possible. First, I will assume that Strasburg’s 101 MPH pitch loses minimal velocity on the way to where it was clocked, and therefore that 101MPH is the speed right out of his hand, which is very close to being true. Secondly, I will assume that Flacco makes his throw at exactly 45 degrees, which is reasonable because a 45 degree launch maximizes distance, and since this is Flacco’s longest throw, it would be logical to assume it was launched at or very close to 45 degrees. Now it is time to apply some kinematics equations to figure out the change in energy.

I’ll save you most of the math, but essentially the change in energy boils down to being the mass of the ball x (initial velocity)^{2} x (.5). Strasburg’s change in energy is very easy to figure out since we are given his velocity. His change in energy works out to be **144.43 joules**. Flacco’s numbers take a bit more work to figure out since we only have the total horizontal distance, not the velocity. However, using some algebra and basic physics equations, and the fact that we assume the launch angle to be 45 degrees, we can find the initial velocity. Then we find his change in energy to be **145.15 joules**.

Now that we have the change in energy numbers we need to divide these by the time this takes to find the power. To do this, I simply watched videos of their releases and timed them many times, taking the mean of my measurements. To make life easier, I slowed down the videos to 25% speed in order to improve my ability to accurately time, and then I just divided my numbers by 4 to correct for the slowed video. Keep in mind that the change in energy only occurs from the moment the ball begins moving forward to when it leaves the athlete’s hands because that is the only time when the movement is in the direction of the velocity that is created, so I’m not timing all of Strasburg’s wind-up, rather only from when his arm is all the way back to when he throws it. Now after dividing energy by these times, I find that Strasburg’s power is **418.64 watts** while Flacco’s power output is **492.03 watts**.

Now it is time to analyze these results. While Flacco has a clear advantage in power output, it is actually misleading. While power makes sense to compare some things, it simply takes more time to throw a baseball because in general a pitcher brings a baseball further back than a quarterback brings a football. So in reality, the change in energy is more reliable to compare the cross sport athletes (power would be great to compare pitchers to pitchers or quarterbacks to quarterbacks). So when we look at the change in energy, we see that the athletes are nearly identical, **144.43 j **(Strasburg) to **145.15 j** (Flacco).

Since energy is the best way to compare the two, the ultimate conclusion is that Flacco and Strasburg are nearly identical in terms of how much of a “cannon” they have.

Just for fun I decided to reverse the calculations to see, presuming the necessary skill, how Flacco and Strasburg would fare in the other’s domain. It turns out that they are nearly the same. Flacco would be capable of hurling a **101.2 MPH** fastball, while Strasburg would be launching a football **80.6 yards**. So the ultimate gunslinger competition comes to an interesting draw, with Joe Flacco and Stephen Strasburg essentially equal in this competition.

Have any other physics/math sports questions? Let me know at mlr78@georgetown.edu and your question could be answered next.

*Max Roberts*

*Georgetown University Class of 2016*

Follow Max on Twitter: @Maxroberts611

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