We all know how the debut of quarterback Nathan Peterman went by now. And if you don’t it’s probably better that way (psssst...turn back now). Turnover after turnover marred his first start to the point where he was pulled after only half a game and written off by many fans before even that long.
Just in case anyone felt like coverage on this was lacking, let’s
overanalyze his first interception. Seeing the ball ricochet off Patrick DiMarco’s hands, it’s easy to assume DiMarco should have caught it. But how easy of a catch was it really? We turn to math and science...grooooooaaaaaan...to find out.
Some fun data to set us off
Here’s the play in question for reference purposes.
Now that we’re all just a little more sad than we were a minute ago, let’s discuss fault for a second before moving on to the math and science part of the show. Typically, to blame the quarterback you need to make the case that the ball was uncatchable. Accuracy is often the easiest argument. While the ball wasn’t placed perfectly (more on that later), it wasn’t so far off as to be uncatchable. However, Peterman rifles it in pretty good. Is there such a thing as “too fast” in the NFL? Let’s examine a second gif to get that conversation percolating.
Please note that due to camera angles and other factors, calculations will be in the “pretty darn good” category instead of “exact.” This view of the play shows the ball exiting Nathan Peterman’s hand and being marked at the Buffalo 48-yard line. The second line as the ball reaches Patrick DiMarco’s hands is at the Los Angeles 44.
Between these two points the ball traveled 8 yards (24 feet) in 413 milliseconds. I put this data into an equation to find feet per hour. (If you’d like to check my math I did this: 24ft/.413s = x/3600s). The result turns out to be 209,200ft/hr. We divide that by the number of feet in a mile (5,280) and we have our first fun fact of the article.
Nathan Peterman threw the ball at 39mph. Not his fastest by any means, but pretty darn fast.
Human reaction time and the concept of “too fast”
There is indeed a risk of “too fast” on an NFL pass. Rather than being based strictly on speed, however, we need to turn to reaction time to a visual stimulus. This is essentially a measure of the delay between seeing something and taking appropriate action. Put another way, when a receiver sees the ball coming his way there is a short delay before the hands and arms start moving. Additionally, time is needed to make the correct movement (move the arms). A 39mph pass in and of itself is not a problem. The problem then becomes this. If the pass took just under half a second to travel between players, is that enough time to react and respond appropriately?
Human reaction time to a visual stimulus is a little over a quarter second (a quarter second = 250 milliseconds). There’s deviation dependent on which study you refer to, but we’ll use the 250-millisecond mark for the purpose of our discussion.
If you really feel like diving in, there are a few items linked below with brief summary here. In the studies/pieces linked, participants were asked to respond with a simple physical action when a visual stimulus was noted. Typically pressing a button with one finger. Response time is recorded from the moment the stimulus appears until the button press acknowledges it.
This paper from Jose Shelton and Gideon Praveen Kumar had limited participants but concluded response times to be around a third of a second (331 milliseconds).
This study from Annie W.Y. Ng and Alan H.S. Chan had better participant numbers. For Patrick DiMarco’s age group it concluded a similar response time of approximately one-third of a second.
The website Human Benchmark has a similar test and arguably provides the best data. With over 65 million participants and the inclusion of data regarding screen and device latency, it represents the most comprehensive look for a similar test. Their data suggests around 280 milliseconds.
If everyone agrees that testing with a simple physical reaction has response times greater than a quarter second, why are we running with the 250-millisecond estimate? First off, none of the studies examined professional athletes. There’s some reason to think they may have an advantage (better diet and overall health for example). Also, wherever there’s some doubt, I’ve erred on the side of caution.
Are these controlled tests fair parallels to the DiMarco situation?
The worry is that either Patrick DiMarco or the test subjects could have differences that lead to a significant advantage that make it difficult to use the 250 millisecond estimate. Luckily, Patrick DiMarco’s situation is not too dissimilar from the studies above in many key areas.
Practicing a given task can lead to better response times, and Patrick DiMarco has definitely practiced football tasks. Similar to DiMarco, participants in trials such as these often are given practice runs. Their times are also generally not recorded off of a single trial, meaning multiple attempts accounts for additional practice. The overall low complexity of the requested action in the test setting should also be considered.
DiMarco is expecting the ball, and should have an advantage. Similarly, participants in response time studies are told “you will see [visual stimulus].” Similar to the practice point above, participants are told what to expect and are given the opportunity to see it before going “live” with their numbers. If anything, Patrick DiMarco is at a relative disadvantage from the simple trials. If you look at the play again, Nathan Peterman has left the pocket. Even if this is a designed rollout, the receiver needs to first locate the quarterback effectively which raises the difficulty. Comparing this to the simple trials it would be like asking participants to first locate the screen before testing.
Furthermore, there are three receivers on the same side of the offense all running similar routes at different levels. Until they see the trajectory they can’t know if the ball is coming to them or one of the other options. It’s critical that this is evaluated in the air, as each receiver can cause problems for the next if they were to...ahem...tip a ball that wasn’t meant for them. The best case scenario is that the play is designed to go to DiMarco, but this merely puts him on the same level of expectation as study participants rather than providing an advantage.
There’s actually good cause to think Patrick DiMarco is at a disadvantage, as his task is also muddied by the fact that he’s running, needs to be worried about getting hit, has multiple responsibilities to mentally juggle and has distractors such as crowd noise and sunlight (look at the shadows). To err on the side of caution, we’ll simply leave it at the fact that he does not have an advantage, which suggests our 250-millisecond estimate should be safe.
With the safe guess of 250 milliseconds established, our next step is to identify when DiMarco should start his response. Compared to the gif used to determine velocity, we’ll back the timeline up by one frame to the point where the ball can first be seen to be released. This span was selected as DiMarco cannot fully expect a pass to come his way from the windup, as the ball could be thrown away or Peterman can pump fake. The time from Peterman’s hand to DiMarco’s hands is 463 milliseconds. We subtract the reaction time as this represents time before the physical action can occur. DiMarco is left with just over a fifth of a second (213 milliseconds) to raise both hands and make the catch.
What good is average reaction time when talking about one specific person?
It’s not ideal to draw conclusions about one person based on an average. In fact, most of the above is really best left to the theoretical world and works more to establish a concept of “too fast” for NFL throws. As an example, a conclusion we can say is that most people would have no realistic chance of catching a 39mph ball from 4 yards away. That’s neat, but it doesn’t help us here.
Luckily we have a Plan B. This plan consists of seeing when DiMarco shows any sign of reacting to the ball coming his way. From there we can use the frame by frame to determine times just like we’ve been doing. For this exercise, I look to the first frame in which we see a deliberate motion to catch. This simulates our simple physical movement akin to pushing a button in the studies above. Naturally, there’s a gif.
There are two important stoppages. The first is to point out where it’s tempting to think DiMarco is making a move to catch the ball as he’s turning his body toward the quarterback. This is squaring to the play in case the ball is coming but nothing more. First note that his arms continue pumping for a couple more frames, until the second freeze. Also, note Nick O’Leary is going through the same process of squaring to the play behind him. The second pause represents the first frame he’s making a motion like he anticipates the ball. Specifically, his arms stop swinging like they’re running and start to come up.
From Nathan Peterman’s hand to when Patrick DiMarco acts like he expects the ball, it’s 230 milliseconds. It turns out our quarter second estimate was pretty good. From there, DiMarco is then left with the remainder of 233 milliseconds to make the catch.
Whose fault was it then?
Both players. Patrick DiMarco gets his hands up and around the ball so you do have to assume he had a shot at it. Nathan Peterman should have taken some heat off of it and given his receiver a much better chance. When looking at the play in totality, I tend to place a little more blame on Peterman. With DiMarco wide open, the velocity wasn’t remotely necessary. Putting the ball ahead of him and slower carried no risk. The ball pops DiMarco in the facemask as well. For this route that puts the ball a little high and behind where it should be, further adding to the catch difficulty.
There is a flaw in my argument when shifting blame away from DiMarco. None of the conversations so far addresses whether 230-250 milliseconds is enough time to get your hands up to make a catch. There aren’t good enough studies on this either, so we’ll have to be more creative.
The Patrick DiMarco Experience!
Below is a gif with a few different visual stimuli. Before each one is a blank slide that will last two or three seconds. On the blank slides pump your arms like you’re running. If you can stand up and run in place, even better. As soon as you see anything, try to raise your hands as fast as you can and catch an imaginary football in front of your face. Each stimulus will last for 480 milliseconds before disappearing (slightly longer than what DiMarco had).
How’d you do? Now remember that he had some things that made it tougher for him. Impossible catch? Nah. Tough catch? Very much so.