# Resolving the Parallax Error

Submitted by santy on November 28th, 2016 at 7:09 AM

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.

There's a very obvious angle in that video. I don't think it shows anything that hasn't already. The other thread with the picture that is looking down the line as opposed to looking down from above, at an angle, is much more convincing.

Either way, we need a camera built into the first down marker. They figured out how to get it in the pylon, why not the first down marker?

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How many buckeyes have joined this week to post their shit opinions on a Michigan board? Get a fucking life.

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the trolls have popped up to explain away their victory.  They know they were short and it was totally biased.  Note we didn't hear from them in 2013, also a last second victory for them.  Hmmmm.....  Guilt will get you, I guess.

I think I see Jim Delaney in the grassy knoll.

I still can't belive they went 3-9.  I did not see that coming.  At all.  Really thought they'd be good with how the media goes on and on about how they develop talent and preseason ranking.

I'm still pissed off

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The conspiracy theory level to which we're approaching is bordering on JFK assassination levels.

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I see holding that should have been called on #59, #85, and probably #88 as well.

A premise advanced by some is that on-field officials for the M-tOSU game were so incompetent if not corrupt that they influenced the game’s outcome in favor of tOSU. And, the premise continues, no better example of said incompetence/corruption came in the second overtime, when the officials “spotted” JT Barrett’s 4th-down, QB keeper. The “spot” gave tOSU a first down at the M 15 and paved the way for the winning touchdown.

Those supporting the above premise argue that the “spot” was overly generous. They admit Barrett’s effort got the ball close to the line, but by the naked eye alone anyone could see the ball was at least 6 inches or so short of the line to gain. The on-field officials, recognizing the importance of their decision, asked the replay official for a further review. The NCAA criterion for reversal appears to provide:

"Section 7, Article 1 (Criterion for Reversal):
To reverse an on-field ruling, the replay official must be convinced beyond all doubt by indisputable video evidence through one or more video replays provided to the monitor."

The video evidence failed to convince the replay official “beyond all doubt” that the on-field ruling was incorrect. Now for the above premise to stand, nine officials, the eight on-field and the replay official, would have to be found incompetent/corrupt.

All the good work done in santy’s post also tends to show that at the point of contact and forward progress, JT Barrett’s right arm, in which he cradled the football, was sufficiently close to the 15-yard line that the nose of the ball more than likely reached the line to gain: first down.

But the video evidence was admittedly ambiguous; the on-field official’s “spot” was admittedly a judgment call. Given such an ambiguous/subjective outcome, those supporting the incompetent/corrupt official premise might continue to selectively search for and consider information that confirms their beliefs, thus continuing the flogging of this poor, deceased equine.

I agree. While my homerism will always say that he was stopped short, it was hardly an egregious spot by the officials.  The fact that the game came down to a subjective call by an officiating crew who only threw two flags all day on OSU, though, is emblematic of the bigger problem with this game.

Anyone claiming a clear first down, or clearly stopped short is a homer.  You can't tell from the videos and its within an inch or two either way, well within the spotting error for any spot on the field and whatever was getting called on the field wasn't getting overturned.  The refs were bad in that game but not because of that spot.

Agreed. People are breaking down this video and asking for shots that don't exist and magnifying the pictures, and there's still nothing definitively conclusive. How can we expect the official(s) to get this right down to the millimeter?

I'm not convinced that homerism didn't play a small part in the spot, but I can't claim with any certainty that Barrett was indeed short. The egregious issues were the penalty calls/non-calls.

is not possible, based on videos and pictures out there.

Still seemed short based on the best info available.  But can't be certain.

Ball was not really visible to the line judge.  Obscured by Barrett's body.

More bothered about the no call PI on Michigan's 2nd OT possession.

Ive been reading a lot about this crew being OSU homers but a friend of mine said to me that the same exact crew worked the MSU/OSU game last year in Columbus as well.   Any rememberance if Sparty got screwed in that game?  Prob not a whole lot since they won but it would be interesting to see.

Tell your "friend" I said he can go fuck himself. No, I don't remember anything about that game, because I don't give one flying fuck about either of those teams. I saw Michigan get screwed by refs on Saturday and two of them live in the shithole known as Ohio. That's all I give a shit about.

If we found a way to tackle Samuel when he was busy running 5-10 yards backwards, we wouldn't even be having this conversation. You would've forced OSU into a ridiculously long FG attempt when their kicker has been erratic all day, or a Hail Mary against our secondary, which had shut Barrett down all day.

Neither of those scenarios would've likely ended well for OSU.

Very questionable call, indeed, but we put ourselves in that position.

When the overtime period begins, how is the ball located on the 25 yard line? Is the nose placed directly up against the 25? If so, then the idea that chains are not needed and the boundary of the white line is correct. However, looking at the original placement of the ball during the second overtime period, the ball appears to be placed with the 'horizontal center' of the football at the 'horizontal center' of the 25 yard line. These centers are placed in apostrophes since they are best estimates by the referees. Continuing with this, if the nose of the football is the location measured for the first down, then the nose of the football, in the original placement, must be the datum of the set of downs. I.e. the line to gain should be 10 yards from the NOSE of the football. Thus, using the original overtime spot, the ball should have to reach further than the boundary of the white line to be deemed a first down.

Also, the assumption that the green line is the correct "vertical" from this camera angle is suspect.

However, this does support the fact that it was very, very close and the call on the field could not be reversed.

The blue line was the most challenging to place.

From the Barron photo, the boundary side of 18-yard hash and the field side of the 16-yard hash almost align with each other. The actual gap between the two was estimated to be 1/8 the length of the 17-yard hash. I did what I could to preserve these observations when I drew the blue line. However, the overall result is not very sensitive to inaccuracies in the blue line. It just needs to be in the ballpark in terms of angle. At the most, it would affect the overall result by 1 pixel (0.5 inches).

The overall result is more sensitive to the green line, You are correct, I made it vertical on the assumption that there were no roll variations in the camera which could throw off the result by a couple of pixels (1 inch).

The result is also sensitive to how I drew the pink line, and that introduces an error margin of a pixel (0.5 inches).

...it looks like forward progress was about 3-4 inches short of the 15-yard line.

I used the same geometric approach as you did. However, the biggest problem is that there are visual obstructions to critical information. So some assumptions need to be made.  Your magnification of the pixelated view is much too inaccurate and should not be used.

It appears your assumptions slightly favor Ohio State/the refs.

If the call on the field was that he was short I would have a hard time with your analysis.

In my opinion, your conclusion should be that it was "too close to call and therefore the field ruling stands" NOT that he made it by a few inches.

What are the assumptions that are problematic?

The maginification of the pixelated view is to show the light spot that I think is the white stripe on the ball. If you only look at the pixelated shot, this won't make any sense at all! How on earth can one deermine that a couple of random pixels is that stripe?

But if you cycle through the frames from the GIF again and again, back and forth, you will notice that the light spot appears once Barret has twisted his body after contact with his tight end end, It appears, and it moves independent of his body and is at the spot where I would expect the ball to see.

Yes, there are a lot of obstructions, but there is just enough information to do some analysis

- He got the first down, barely. Seems to me both sides are distorting the "evidence" to whichever freeze frame benefits them most

- It was pass interference in 2OT, but a non-call is better than a phantom call IMO, unless it's egregious. Won't argue with anyone who has beef about that one

- There probably weren't any holding penalties called because UM sacked or pressured Barrett on just about every dropback. If OSU was holding, they weren't doing it very well. I don't recall Michigan being called for holding on offense either, frankly

- Not sure why anyone is complaining about the PI on Hill. He clearly got there early, and he admitted it with his body language afterward. It was just a bad play on his part, because Samuel more than likely wasn't going to catch it

Amazing game. I thought the better team lost, which has certainly happened in The Game before, and it won't be the last time.

- It was pass interference in 2OT, but a non-call is better than a phantom call IMO, unless it's egregious.

I would agree if they had done that both ways. The problem is that it was PI when one team had the ball and not when the other team did.

Can someone more technically advanced post a photo of the 1st down placement of the ball (which was inside the 25yd line, probably placed by the ref that is a lifelong OSU fan). Thus, to get 10yds from the 1st down spot, OSU needed to get about 4 inches past the back of 15yd line. There is no way OSU made it 10yds from where they were given the ball on 1st down.

The key assumption in this analysis is the following:

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.

To me saying the "ball is lined up vertically over Barrett's left pinky" is very, very generous. Any and all side views show the ball is behind his left hand. To me it looks like it probably four to six inches (haha to all the jokes to come) behind his left pinky. Once you take that into account he is still inches short.

To clarify, I am not saying that the ball is directly above the hand. I am not saying that when you look at it top down, the ball would be covering the hand. I mean that from the viewing angle of Barron's photo, the ball is 'above the hand, and so you can use the hand as a reference to place the ball. That is what the blue line is for. I totally get that the ball is behind the hand from a field position perspective.

Edit: I mean to say that the ball, Barrett's hand, and Barron's camera are all on the same vertical plane. The first blue line parallel to the intersection between this vertical plane and the field. The second blue line *is* the intersection between this plane and the field.

Lewis' feet are only useful for timestamping Barron's photo.

If the camera were in the same vertical plane as Lewis' foot, Barrett's hand, and the ball, Lewis would be obstructing the view.  Based on the picture, Barron must be between the hash and the boundary.  More to the point, Barron must be between Lewis and the Boundary.

This convinces me even more that your blue line is wrong.  Let me see if I can follow what you've written:

The first blue line parallel to the intersection between this vertical plane and the field.

...is not a sentence (lacks a verb).  I can't follow it.

The second blue line *is* the intersection between this plane and the field.

Not possible.  Think of it this way, if we say that the football field is an xy-coordinate system, and the x-coordinates are the yard line on the field, we need to find the y-coordinate of the football.  I believe that you intend that the blue line is parallel to the y-axis with the same y-coordinate as the football.  Since Lewis's foot is on the field, the intersection line between any plane containing his foot and the playing field must pass through his foot. Similarly, since Barrett's hand is on the field (or close enough in the far field approximation), the blue line should also pass through his hand.

Re-drawing the blue line as I suggest would move the green line (the z-axis) slightly left.

Why use those horribly angled shots when there is this?

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I actually saw the picture before I typed my OP. I tried to look for clues to timestamp the instant it was taken but it is too zoomed in. I tried looking at the angles of the other players' legs and stuff. I can't conclusively say that that the picture was taken at the moment of forward progress and so it becomes meaningless in that regard. It doesn't prove that at another instant, he wasn't closer to the first down.

I can't blame them for not overturning it after they messed up the first time. But that's the thing; they gave him more than enough the first time.

As much as I admire the hard work that was done on this, how can we be sure that this is totally lined up right? Only a degree or two  from the 15 yard line can change this from a first down to a non-first down, and you can't really tell from here.

Last time I remember such detailed analysis.  I guess the effect on Michigan fans all over the wworld is no different.

to beleive the ball did not advance, is the position of #88 body at the time of impact. His feet and backside, in which Barrett runs into, stopping his forward progress is outside the 15 yard line.

I hate to say it but there seems to be as much if not more reason to believe he made it to the line. Looks like a first down. At the very least there is no way a ref could overturn the call given the angles that we've all looked at. Tough pill to swallow. Game of inches.

My ire toward this game has shifted from "he was short" (still think he was) to "OSU got basically every call that could have gone either way".