The physics of a chuck it (dog fetch toy)

Over thanksgiving break, I was playing fetch with my dog. My dog is pretty fast so we use a chuck-it ball launcher to throw the ball extra far. While throwing the ball for him, I noticed that there had to be some physics involved with the item. For reference, a chuck-it looks like this when it is being thrown:

So why does a chuck-it increase the distance a ball can be thrown? The chuck-it is designed to be an extension of someone's arm. Thinking about torque, the chuck-it increases the radius of someone's arm. The equation for torque is Torque = Force * Radius. Assuming a person does not get a massive strength increase by using the chuck-it, we can assume the force they exert using the chuck-it is the same as the force they would exert on the ball alone. Thus, with the same force and a greater radius, the torque is much greater using the chuck-it. This increase in torque means that a greater force is acting on the ball. If a greater force is acting on the ball, the displacement is larger because displacement is proportional to force. Additionally, this explains why people with longer arms are able to throw the ball farther than people with short arms.