The Intersection of Physics, Football & Technology


  • Reading Time  Min Read
  • Publish Date December 11, 2015

First of all, I am a Clemson fan. Let me get that out of the way. I’m happy with the outcome of last Saturday’s ACC championship, but I want to try and stay objective here.

I’ve been thinking a lot about the offsides call that pretty much sealed the fate of the game. When you look at the available camera angles, it doesn’t appear that the player is offsides. But this is because we are limited by the camera perspectives. If the official had a camera mounted to his hat, we would have a much better view of the play.

unc-clemson-angle-one-unedited unc-clemson-angle-two-unedited

But what we do have is some basic geometry and physics that we can use to analyze the call.

According to the high camera angle, it looks like the player’s left hand was very close to the line, when you take into account that the line is considered a plane (much like the goal-line). This means that if any part of the player crosses the line before the ball is kicked, the player is offsides.

unc-clemson-angle-one unc-clemson-angle-two

Based on the camera perspective, and fairly unscientific pixel measurements, I’m posing a few thoughts:

  1. It’s quickly apparent that the 35 yard line is not straight, and it bends back towards the middle of the field. So we’re applying science to a very imperfect medium here.
  2. The camera capturing the video appears to be at midfield and mounted on the upper deck of the stadium. It’s much more difficult to gauge distance from that far away and at that angle.
  3. Assuming that the camera is level, we can create a second line that is parallel to the 35 yard line by translating it up to the appropriate height. I drew in this line at what appears to be a similar height to the official on the far sideline.

Using these drawings and a little math, it appears that the player’s left hand is within 8 inches of the plane and above the line at the time it’s captured in the screenshot.

Distance between hashes in picture = 30.5px = 36″
36″/30.5px = 1.18″/px
Distance between drawn line and player's hand = 3.61px x (1.18″/px) = 4.2″

The player in question looks to be on or around the 12 yard hash mark from the sideline, or 36 feet away from the official. An 8 inch measurement at 36 feet is the equivalent of a measurement of 1/4″ at arm’s length (28 inches).

36' = 36' x 12″/1' = 432″
4.2″/432″ = 0.01 ratio
28″ x 0.01 = 0.28″ at arm's length

Remember that while this is happening, the official is also trying to gauge the timing of someone kicking the ball in the middle of the field 80 feet away.

Now let’s look at the timing of the player in motion. Ryan Switzer (#3), the speedster for UNC, runs a 4.52 second 40 yard dash. Hunter Crafford (#30) doesn’t have a listed 40 yard dash that I can find, but we’ll give him a 4.64 since that was my 40 time from high school (#humblebrag), and I think he’s at least as fast as me. Based on research, the first 10 yards of a 40 are between 1.5 and 1.7 seconds for a fast player, so if we go in the middle at 1.6 seconds for the first 10 yards of a sprint, that gives us 360 inches per 1.6 seconds, or 225 inches/second.

10 yds = 360″
360″/1.6 sec = 225″/sec

That means that the 4 inch difference from the line would be covered by the player in 0.019 seconds or approximately 1/50 of a second.

4.2″/(225″/sec) = 4.2 x sec/225 = 0.019 sec

To add another wrinkle, the player’s hand is swinging forward in the video. It looks like the player’s hand does 2.5 swings per second through that segment of the clip (one swing being forward and backward). If each swing of the arm travels 4 feet, that is 10′/sec or an additional 120″/sec of velocity. A combined velocity of the player’s hand and body is 345 inches/second when swinging forward.

2.5 swings/sec x 48″/swing = 120″/sec
225″/sec + 120″/sec = 345″/sec

A young human eye (these officials are not young) takes 350 milliseconds to shift focus. This means that to look at the ball and then the player takes 0.35 seconds. This is 20 times as long as it would take the player to cross the 35 yard line and be offsides. Another way of looking at it is this: if the official is watching the ball and then shifts focus to see if anyone is offsides (the very moment the ball is kicked) the player could have moved 78″, over 2 full yards.

0.35 sec x 225″/sec = 78″
78″/(36″/yd) = 2.17 yds

This leads me to believe that to be perceived as onsides you must be at least 1 yard back from the line when moving as fast as the players are moving.

So, what if the play had been reviewed by the replay official?

Well, first of all, the camera angle is very poor for reviewing this type of play. Secondly, the video that is available to the replay official is the same resolution and frame rate as the feed seen on TV. In the case of ESPN, that is 720p30 (1280×720 at 30fps, sometimes at 60fps, but that video doesn’t appear to exist online). This is pretty awful quality for clarity especially when digitally zoomed, and a fairly terrible frame rate to observe motion. At 30fps, this means that the player’s hand could move over 11 inches per frame.

345″/sec x sec/30 frames = 11.5″/frame (player's hand)

So that means if given twice the frame rate, we could see the player’s hand move forward 5.75″ and back 5.75″, and it would appear to not have moved in the frames that we have available. This means that in an uncaptured frame, his hand could have possibly been across the plane and offsides. Let’s say that we did have twice the frames at 60fps. If each pixel in the video is equivalent to 1.16″ that means we’re looking for 1 or 2 pixels in the video, and we’re going to need a much higher resolution to better analyze. For example, the video quality is so bad, the ball is a blur and invisible as it starts to move. If the video resolution were 4K (4096 x 2160 resolution) then each pixel would represent approximately 1/3 of an inch. Much better, as it would provide 9 times as many pixels.

1.18″/px  / (4096 pixels / 1280 pixels) = 0.36″/px

(4096*2160) / (1280*720) = 9.4 more pixels

The replay official could have overturned the call, but without a much higher quality video, and at a much better angle, and a faster frame rate, it would be very hard to find "indisputable video evidence." After my analysis, the video review should be "play stands as called on the field" because the video evidence just isn’t there.

Now back to the on-field official.

He’s tasked with making sure the players are onside by watching the ball and ensuring nobody crosses the invisible plane above the yard line. In order to make a good call on the play, he needs to be able to shift focus in less than 0.019 seconds, which just isn’t physically possible. And don’t forget that the official is trying to gauge a 4″ gap between a hand and an invisible line from 36′ away as he shifts his focus. This simply is impossible for any human.

If we really want to do video replay in a sane manner, that doesn’t make officials completely second guess everything they do, we should mount a 4K camera at 60fps on the official’s hat, and let the official choose when they would like to review their personal footage and correct a call. This allows the officials to admit that they’re human and more or less have super human eyesight whenever they feel it’s needed.

On the other hand, do we really want to make 4 hour long games even longer with more replays? What if there was a better way?

Next year, the new Bluetooth Low Energy (BLE) specification is set to increase the range from 150′ to over 500′. By putting sensors on the gloves and cleats of football players, we could use trilateration to determine a player’s position on the field with a high level of certainty. Combine that with other sensors on the chains and in the football, and you can now automate a whole host of penalties from having to be called by officials in the game. BLE chips are becoming more power efficient as well, enabling them to become smaller and lighter to the point where they are are just a few millimeters thick.

I would love to create the IoST (Internet of Sports Things). So if anyone from the NCAA or NFL is reading this, let us know. We know a thing or two about beacons.

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