Resolving the Parallax Error

Submitted by santy on

EDIT: TLDR - From what I can estimate the tip of the ball crossed the plane of the first down (as I define it) by about two inches. The margin of error indicates there is a possibility it might not have, but that's unlikely :(

 

THE SPOT has been debated to death. Both OSU and us have provided camera angles that "prove the result", without really doing so because of the following resons: When a still camera image is analyzed, it begs the question "was that taken at the instant of forward progress by Barrett?". When a moving image is analyzed, the issue of parallax error is not resolved fully enough, even for #ThePerfectAngle. It is pretty important to do so simply because it is such a close call.

The most important variable to resolve is Time. Now both wolverines and buckeyes have all seen this GIF and drawn various conclusions and posted screenshots that vindicate their arguements and show their gross negligence of parallax error. 

 

Let's a closer look at this. I've taken the liberty of running through the GIF frame by frame and have isolated the instant where Barrett has made the most forward progress. This would be Frame 53 shown below:

Okay, so now we've got Time out of the way. This image has been posted by many buckeye fans because they can just draw a line along the 15-yard line and say that the tip of the ball is clearly past that line demonstrating that education system in ohio has yet to incorporate the concept of a parallax error in the school syllabus. 

The most important step in this is to determine exactly where along the width of the field the ball is at this instant. If we can do that, we can resolve the parallax. Fortunately we have a few clues. Here is Barron's picture from Ace's game recap:

It's a really useful shot because of when it was taken. The positioning of Jourdan Lewis' feet correspond to Frame 51/52 of the GIF above, which places this at almost the instant of most forward progress. The first thing this shot tells us is that the front tip of the ball is lined up vertically over Barrett's left pinky finger from this angle. [EDIT: I mean to say that the ball, Barrett's hand, and Barron's camera are all on the same vertical plane. The blue lines below are parallel to the intersection between this vertical plane and the field.] 

The relative positioning of the hash marks in the bottom right corner actually give us a pretty good estimate of this angle shown by the light blue line. It also tels us that the ball is slightly past Wormley's right arm.

If we assume that Barron was sufficiently far away, we can slide that blue line down to the outside of Barrett's left hand we know where along the 15 yard line the ball would have had to be in order to cross the first down.

Here is where things start to get a little tricky. Where exactly is the plane for the first down located relative to the 15-yard line? If we assume that it is at the border of the 15-yard line facing midfield and assume that the TV camera that recorded the GIF is not rolled to either left or right, we can resolve the prallex error. First we draw the position of the presumed boundary for the first down (shown in pink):

The intersection of the pink and blue lines indicate the position of the ball projected down onto the field, if it had crossed the plane for a first down. Again, if there were no roll variations in the camera that recorded the GIF, we can simply draw a vertical line (in light green) from this intersection to mark the boundary of the first down with the parallax error resolved:

I've drew the green line with a gap around the area where the ball should be. I've run through the GIF frame by frame several times, and there is a light spot only a couple of pixles big to the left of Wormley's forearm and I believe that is the white stripe of the football. You'll notice on Barron's picture that the stripe is facing up so it makes sense that it should be barely visible from this angle. You can also see that it is literally a pixel past our hypothesized first down line. Given the dimensions of a typical football, that would make the tip 2-3 pixels past the green line. 

 

It really depends on where exactly you define the plane of the first down to be. Is it the edge of the 15-yard line as I drew it? Is it on the opposite edge? Is it right down the middle? FWIW, the width of the line is 9-10 pixels on the GIF.

 

P.S. With regards to the tweet below,

 

 

 

The frame in this video that corresponds to Frame 53 in the GIF above (I used the positioning of Gedeon's legs to figure this out) has OSU's #73 obstructing the view so it's not very conclusive, also the ball was under Wormley's arm and part of it was past his arm as clearly seen in Barron's photo.

Comments

Wazoo

November 28th, 2016 at 12:28 PM ^

Fascinating analysis, but is there anyone else who thinks the first blue line is drawn at the incorrect angle?  It seems off a bit to me: lower on the y axis, if you will, than it should be. 

Red is Blue

November 28th, 2016 at 1:40 PM ^

Yes, I agree the angle of the blue line seems off.  You can see the inside of the 14 yd line hash mark outside of Lewis' left shoe.  Where sock meets ankle of  the outside Lewis' right shoe lines up just inside Wormley's cleat at the same height.  Both of these give you a flatter blue line.  This doesn't matter a lot because JT's hand is so close to the line to gain, but it would seem that the ball didn't make it as far as suggested.

I think there are a lot of assumptions baked in about camera's not being rolled, images being far enough away that the lines are indeed parallel, and the graininess of the pictures blow up this much that you can't be definitiive and intellectually honest.

gggrove

November 28th, 2016 at 11:36 PM ^

Obvious first down.  The ball obviously breaks the plane of the 15 yard line, replay or not.  I do not understand the controversy surrounding this call. Plus, tackle Samuel on this next play and the game goes on.

The missed PI non-call on UM was an obvious officiating gaffe.  UC on Harbaugh was not and it cost 7 points that came back to bite us. 

 

zachary_carson

November 30th, 2016 at 8:07 PM ^

That would be treating the 15 yard line like the goal line.  However, the peg of a marker is probably only 1/4 the width of a field marker.  Therefore, what if the chains were at the front of the 15?  Then he isn't close.  But if they are at the base, he is over.  The ball has to cross the marker.

UMgradMSUdad

November 29th, 2016 at 12:02 AM ^

I was going to start a new thread, but damn that Brian, who the hell does he think he is?

Anyway, on the Sirius/xm College Sports Nation channel, they played the audio of Buckeye Announcers calling the game, and the announcers sounded surprised at how generous the spot was. Now, i'm quoting from memory 7 hours and a few beers ago, but I'm pretty sure what was said after Barret's run was, "Wow! They're going to give it to him!"

zachary_carson

November 30th, 2016 at 8:03 PM ^

My only issue with the spot of the ball isn't whether or not he "got" the first down.  It was the officials confidently spotting the ball and without thought, signaling for a first down.  In all my years of football (and close marker calls), I have never seen them not bring out the chains for something that close.  The fact that people use the, "the tip of the ball touched the line, therefore it's a first down" makes zero sense.  That would be treating the 15 yard line like the goal line.  However, the peg of a marker is probably only 1/4 the width of a field marker.  Therefore, what if the chains were at the front of the 15?  Then he isn't close.  But if they are at the base, he is over.  The refs man.  If they overturn that call, the Ohioan refs would return home to burning houses.  They made a business decision.

umich1

May 1st, 2020 at 1:07 PM ^

3 years later.... I think the white in the final frozen pixelated frame is JT’s mouthpiece and not the stripe of the ball.  If you watch the GIF closely, that white pixel and the stripe of the ball are separate as JT falls backward.  Going back to Barron’s photo, the nose of the ball looks to be a few inches behind the mouthpiece.