What Does It Take to Make a Pitching Machine That Replicates a Major League Pitcher?

Trajekt Sports controls 11 out of 12 degrees of freedom with its pitching robot.

Trajekt Sports makes a pitching machine like no other. Think of a robot that can replicate the pitches a batter would face from the most skillful pitchers in Major League Baseball (MLB).

A pitched baseball can have 12 degrees of freedom. Our machine replicates 11 of those 12, says Joshua Pope, CEO and cofounder of Trajekt Sports, of his robot, Arc. “Our nearest competitor has five degrees of freedom.”

Pope’s education is in biomedical engineering (University of Waterloo, an hour from Toronto). It was there that he and his cofounder took a class in sports engineering, which provided the basic math that enabled them to build the pitching robot, and learn how to impart gyro spin on the ball, control the ball’s orientation, and change the release position…. And also compare the robot’s pitch to those of real pitchers from MLB data.

At the University of Waterloo, Pope and Trajekt cofounder Rowan Ferrabee did an independent research project on building a baseball pitching machine to replicate human pitches. The two have a patent from the project’s process of collecting data of someone throwing a pitch and building a machine to replicate that pitch information.

“I like to call it closed-loop training,” says Pope.

The three wheel machines in common use can only be set for a desired speed and spin, and the pitches come from a static location. You can’t measure how the pitch comes out or give the batter feedback on how they perform against that pitcher.

“We’re closing the loop of training so that batters can see a specific pitcher; they can measure certain characteristics of their performance.

Trajekt partners with Rapsodo for its ball-tracking technology. Rapsodo is used by all 30 MLB teams to collect training data. A camera with a pitch tracking unit and a batter tracking unit are combined into a single device.

“We integrate each one of our machines with the Rapsodo device, which sits between the pitching machine and the batter. It records the speed, spin, release position, movement of the pitch. It measures the exit velocity of the ball, the bat and the launch angle, the hard-hit average. That’s what we try to replicate.

“Now the batter can get feedback on their performance. We validate that the pitch came out of our pitching robot exactly like the opposing pitcher. And you can also measure your progress, how you’re performing over time.

“Our machine is the next frontier of training smart,” says Pope.

What’s next for Trajekt?

What we want to do in the next three years is make this technology more ubiquitous, have fans be able to engage with their favorite pitchers. This may be with a machine outside the stadium where a fan can pay to play, see their favorite picture on the screen. They could hit the same ball that Aaron Judge hit for his 62nd home run—that exact pitch, and give that fan an appreciation of how talented these athletes really are. That’s what we’re moving into, making a fan engagement tool and not just an MLB tool used by professional athletes. Right now we’re geared towards precision and accuracy and closed-loop training. That’s great for the MLB players. But for the fan who just wants to appreciate the game, it’d be cool if the technology was a little bit more readily available.

Ted Williams once said hitting a baseball is the hardest thing to do in all of sports. How on Earth would a fan be able to hit a major league pitch?

It’s an extremely difficult thing to do. A good batter fails 70 percent of the time. But if they knew what kind of pitch it was going to be and where, a fastball to the bottom left in the zone, for example, they’d probably hit it 10 times out of 10. So one of the ways to make a pitch hittable by the fan is to say, ‘Hey, look, we’re not going to give you really Clayton Kershaw’s curveball, you’re never going to hit it; we’ll give you 70 percent of his speed and spin.’ We can dial it back with our app. The other thing to tell the fan is where the pitch is going. Those two things will make our fan engagement robot more enjoyable. But it is cool to ramp it up to 100 percent to give them an appreciation for the sport.

How precise is the pitching robot?

For some pitch types, we have more control at the plate. Oftentimes our pitches can be more accurate than MLB pitchers in where they place the ball. But for a subset of pitches, there could be an MLB pitcher who’s more accurate than our machine. The precision on the machine is unprecedented for a pitching machine.

What are the 12 degrees of freedom you mentioned?

The 12 degrees of freedom are broken down into four each with three degrees of freedom each along XYZ directions. You’ve got the position of the ball. Where’s the ball released from? What if you’re tall? What if you’re a tall lefty? There is the velocity vector, the speed and the angle that the ball is thrown. You have the angular velocity of the ball. That’s the 3D spin axis. You have the same orientation relative to that status. There are four components: position, speed, spin, orientation, and each along X-, Y= and Z-axes to make up the 12 degrees of freedom. We can replicate 11 of them. The only one we can’t is release extension. We don’t move the machine forward and back. We move the machine left right up and down to the correct slot. We use a formula and interpolation models to simulate the ball released at [distances] other than 55 feet. If you really release at 57 feet, we do an interpolation. If you are a supertall pitcher and you release it a bit farther, like 54 feet, and you’re jumping off the mat, we do an extrapolation. We have figured out what the launch conditions needed to be to get the exact same trajectory.

How can a pitching machine really give the same experience as a real pitcher?

One of the main goals at Trajekt is to give batters the exact same neurological stimulus, the exact same impression on your eyes they would see during the game. During the game, you see the pitchers wind up, you see the mechanics, you see the ball released from the hand, the pronation of the hand. You have 400 milliseconds after the release before it goes over home plate for a look at the split, the spin and the blur on the ball. If the ball is not oriented in the correct location, the seams relative to the spin axis. Your eyes are going to look a certain way for a slider. Batters will see a red dot if there’s a lot of gyro spin. If it’s spinning about one of the seams, they will know it’s a slider because they see this red dot. Fastballs are a bit more red because they show four seams, whereas two seams will give it more of a white tint. The batter is mapping the visual stimulus to a known path. If he can tell early whether it’s going to be a slider from his training, he has this ability to see that red dot and know it’s a slider; he can predict based on where that ball leaves—the speed of it and its blur—where the ball is going to end up. That lets him make better decisions about swinging in a split second.

Nowadays, pitchers are inventing all new pitches. Can the robot pitcher keep up?

Our machine isn’t just like replicating the trajectory; it’s also replicating the whole wind-up and the optical stimulus of the ball. If a pitcher invents a new pitch, it’s no problem for us. We take a snapshot at the release and dial in speed, spin orientation … any possible speed, spin or rotation in the world—even something that a human can’t really produce. Our machine can do it because we got down to the physics of how balls fly.

Knowing the initial conditions of the ball when it is released and the geometry of the ball, do you use physics to determine its trajectory or machine learning?

We started by using pure physics. One of the things that makes the trajectory difficult to determine is the seams that make asymmetric airflow around the ball. You can model drag and lift with a single coefficient, but it becomes nonlinear depending on the orientation of the ball and the spin axis. You can have effects that are non-Magnus, contributing to movement and flight. The best-in-class physics models don’t have enough precision to calculate the true trajectories even if you know the initial conditions during release. You might be able to estimate the final position within something like four inches. We use something called transfer learning, where we start with a physics-based model. We collect empirical data and we tune the parameters with the ground truth data.

We want to get to a point where, given the initial conditions, we know instantaneously the entire path, where the end position will be. We want to be able to pinpoint it. That’s a research project on our R&D roadmap.

Right now, we estimate where we think it will go. We aim at the center and we take the user through four sample pitches. They’ll throw four pitches in training. We’ll measure where they actually went. We make an accuracy ellipse that will do two things. One, it’ll tell us if our model was correct in guessing that [the pitches] went to the center. You might get some spread around the center, and we tell the user the true variants of that pitch. No pitching machine is going to be perfect, just like no human throwers gonna be able to go down the middle every time. Our machine has about a two- to eight-inch variance around the desired location. This allows us to tell you by pitch type, by pitch characteristics, the speed span, the release conditions, what is the inherent variance with that given pitch? We provide that graphically to the user in our web app. You can see with 60 percent confidence, 85 percent confidence and 95 percent confidence where that pitch will go in the zone.

We use a projection model to determine a miss to the strike zone. We use the Rapsodo data to tell us where [the pitch] actually went. Then we amalgamate those two and let the user choose any location in the zone from there.

What’s your safety record?

We have nine MLB teams using us. They’ve thrown 95,000 pitches this year alone. Seven of those machines were at MLB stadiums, behind the dugout used by players before the game to practice against opponents. We haven’t hit a single batter.

How did you arrive at using Onshape for your design application?

We started in 2019, four years ago, during the peak of the pandemic, and we had to make a decision on which mechanical modeling tool we wanted to use. The obvious pick for us was Onshape because it was cloud based. We didn’t need to be on-site. We were working out of an incubator. We had three engineers at the time—myself, my cofounder and a mechanical engineer. Onshape enabled us to iterate on various subsystems independently and then roll up those designs into a single machine. It wasn’t built to replicate human pitchers. We had to design this mega machine. First, we needed to be able to control three-dimensional spin. We needed gyro spin. How do we do that? Okay, here’s a mechanical system that enables us to do that. Now we know we need to control the orientation of the ball. That’s what we call, like the ball orientation submodule. We outsourced that to an engineer. With Onshape, we could work on various subsystems independently and roll them up into a single system. I found that to be really helpful.

Trying to replicate a human pitcher would have been a multimillion-dollar R&D project. But breaking it down into subsystems with requirements for each of them made the problem solvable.

Onshape allowed us to think about it in terms of subsystems and assemble on the subsystem level. We could say to an engineer, ‘Your job is to build a benchtop model of the ball inserter. The ball inserter takes a hundred balls like a gumball machine and drops the balls to where it is set to the desired orientation. That could be discrete module that works independently of the rest of the machine. The machine has a flywheel that propels balls forward and imparts gyro spin speed spin. Another engineer could work on the flywheel subsystem, which is three wheels that propel the ball. Another engineer could work on the gantry system that moves the physical device left, right, up and down.

After we roll up all these subsystems into a larger system, we can measure things like the weight. That’s important for the gantry, which has to move that weight around.

What can you say about your pricing?

We don’t disclose pricing. But I can say it’s in the six-figure range per year and we do three-year leases for our system with the MLB teams.

Where is Trajekt Sports based?

Trajekt is located in Mississauga, Ontario.