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Bills Mathia: Josh Allen Projectile (data) Vomit

The final part of a trilogy that started with the Pythagorean Theorem

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Have you been following along with my Buffalo Bills video content this whole time? Good for you! It’s about to pay off in the nerdiest way imaginable. Remember how we calculated distance of a Josh Allen throw using the Pythagorean Theorem? And then how we took that and added time to it so we could get average velocity? Well it turns out that if you have time, distance, and one more piece of information you can unlock the world of physics data using a projectile motion calculator!

Sound neat? Well I hope so. If you clicked on an article with this title, I assume you knew what you were in for.

Just think. If you watched that video in its entirety that’s over five minutes of your life you won’t get back. Not a problem if you wanted to know way more data about a Josh Allen throw than anyone else dared to take you. Hopefully that’s true and you enjoyed it. If not, thank you for expending some of your finite time on this planet with me anyway.

For the readers in the audience, we revisit the incredible Josh-Allen-to-Gabe-Davis throw from Preseason Week 3 vs. the Chicago Bears. To recap, I calculated a distance of 21.9 yards on the throw. It took almost exactly one second for an estimated 45 mph average velocity.

I took the first two elements of that (distance and time) and put them into a projectile-motion calculator courtesy of You can follow along or do your own calculations with this direct link. The calculator needed one more data point to spit out the rest.

After estimating the launch height and catch height, I plug the difference between the two into the calculator to give you the launch angle, maximum elevation of the pass, and the velocity of the ball off Allen’s fingertips.

You should check out the video to see the exact details, but the short version is that the ball came off his hand slightly faster than the 45 mph average velocity. The pass was about a 12º launch angle (great for maximizing speed, but not distance). And while it seemed like the pass was on a “frozen rope,” the reality is that it gained over five feet of elevation along it’s arc.

EDIT: Credit to Ben for reaching out and finding an error in the video. The maximum height should be measured from the Gabe Davis catch point, not the Josh Allen launch point. That means the above is incorrect. The pass gained a bit under three feet of elevation from Josh Allen’s fingertips.

That’s a lot of math for one pass, but oh so worth it.