Buffalo Rumblings
Yes, Skarekrow’s back to bring math into football
Sure, I could have written about this back in December when, y’know... it happened. I wanted to hold off for when things were slimmer pickings. I also like these little oddities as both a look back on the fun moments and a hype piece for the upcoming season.
What the heck am I talking about? Check out this embedded tweet concerning Buffalo Bills quarterback Josh Allen.
As Benjamin Solak points out, it’s the fastest throw of 50-plus yards in the Next Gen stats era and he knows that based on how long it was in the air. Put differently, the shortest time in the air means it got to its target the fastest. The one thing Solak doesn’t tell us is the velocity of the throw. That’s something I kind of want to know.
Fans of the site know what’s coming next. I’ll make some estimates of the actual throw distance using the clip above to spot the throw point and catch point, then make a right triangle using those and the field. The Pythagorean Theorem will then give me the throw distance and from there we plug in some known (or good guess numbers) and toss them into calctool.org and their projectile motion calculator and learn all sorts of fun stuff about the throw.
First let’s get those measurements!
From the GIF you can see that I estimated the throw point to be about two yards from the sideline and the catch point to be about six. That gives us the first side of our triangle or “a” as four yards (the difference from the sideline). The second side is even easier as we have the yard markers. Allen’s hand is over the 28-yard line at the throw, and Keon Coleman’s chest is at the other 20 when he brings it in over his chest, which makes “b” a distance of 52 yards.
I’m sure you all remember that a squared + b squared = c squared. Or 4 + 2,704 = c squared. When you run the math, we get that the answer is basically that the distance of the throw is just over 52 yards. Yeah, not that exciting. If you want precise, it’s 52.0384 yards.
As a bonus, I calculated the time myself based on my frame rate and got 2.53 seconds but if I credit it with one less frame it drops to 2.46. Or in other words, I have no reason to distrust the more accurately timed number from Solak’s tweet.
Feel free to take a look at that projectile motion calculator and see that we have some data points already. To use the calculator you don’t need all of them. I only need:
When...
