Analyzing Josh Allen’s NFL-record throw

Photo by Mike Mulholland/Getty Images

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.

There are 70 throws of 50+ air yards in the NGS database. This throw was in the air for 2.47 seconds. That is the fastest 50+ yard throw we've

seen. https://t.co/7ab5H3Mcvj

— Benjamin Solak (@BenjaminSolak) December 15, 2024

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To the projectile motion calculator!

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:

• The time from Benjamin’s tweet (2.47 seconds);
• the distance traveled (52.0384 yards);
• and use an initial height of 1’ (estimating Josh Allen’s head is about a foot higher than Coleman’s chest).

When we plug those items in, it allows us to see all sorts of fun facts. Remember that on an arc, the velocity is not the same thing as on a car or on the ground moving only horizontally.

• I, and I mean IF, we only care about the horizontal velocity (straight line on the ground like a car) the average speed of the throw was 42.95 mph. Doesn’t sound impressive, but remember the thing I said;
• the initial velocity out of Josh’s hand was 50.75 mph;
• the top speed was 50.93 mph right as the ball was coming into Coleman’s hands (Allen’s speed plus a tiny boost from gravity);
• the lowest velocity was at the top of the arc and just over 43 mph (see why we don’t use the horizontal speed now?);
• the maximum height was just over 25’ in the air;
• the launch angle was just shy of 32º.

How much does time matter?

Let’s do a hypothetical and say the throw took a quarter second longer to achieve the same distance. That’s not a huge jump in time. But for some of the fun facts...

• The average horizontal velocity (which we don’t care about too much) drops to 39.13 mph, a loss of nearly 4mph;
• the initial velocity drops by about 1.7 mph;
• the angle of launch increases by 6º;
• the maximum height increases by 5’;
• the lowest velocity drops about 4 mph at the apex.

What’s your point Skare?

Nothing crazy, but when we start visualizing the trajectory of a ball as an arc rather than merely as a function of the horizontal difference, we can see that seemingly minor shifts like travel time can mean fairly significant differences in what that actual arc looks like.

If you’d like to see a comparison, thanks to the miracles of AI, here’s a graphic that I’m assured is to scale to compare the two arcs. The reddish brown is Josh Allen’s actual throw and the blue dashes are my hypothetical “same throw but imagine it took an extra quarter second to arrive.”

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