Fixing offside and VAR using design

Plus data visualisation. And maths

Martin Smith
Nov 21 · 14 min read

If you follow football you may have noticed a little bit of controversy around the use of VAR (Video Assistant Referee) this season. One of the main reasons is offside decisions being decided by the slimmest of margins, based on the position of a player’s big toe or armpit, using a system that apparently isn’t accurate enough to make these kind of decisions.

There are two parts to the problem — how the decision is made, and then how it is communicated. The tools used for this involve drawing things on a screen, which brings it right into my backyard, as that’s pretty much my job.

Therefore, while s̶h̶o̶u̶t̶i̶n̶g̶ ̶a̶t̶ ̶t̶h̶e̶ ̶T̶V̶ ̶a̶n̶d̶ ̶c̶r̶y̶i̶n̶g̶ ̶a̶t̶ ̶t̶h̶e̶ ̶i̶n̶j̶u̶s̶t̶i̶c̶e̶ ̶o̶f̶ ̶i̶t̶ ̶a̶l̶l̶ idly watching the scores come in I decided to fix it. I shall do this by ALSO drawing lines on a screen, and some random maths.


What did I come up with?

Due to the distances the players and ball move during each of the 50 frames of video per second used to judge offsides, it is impossible to be sure EXACTLY where players or the ball are at any point. All we can really do is assign probabilities to a player’s position. A simple line is not a good way to judge or communicate this.

We can say that a player is probably within a certain area — and assign a rough probability to that.

So why don’t we use bands to show the areas we can be reasonably sure the players are in, then only give offside if those shapes don’t overlap? To make it clear what’s going on, we could show people what those shapes mean by telling them the probability and showing the threshold.

If you want to know how I came up with this, read on. Make a cuppa first though, it’s pretty lengthy…


How it works right now

  1. Each Premier League stadium has, in addition to all the cameras used for broadcast and goal line decisions, a camera to judge offside at either end of the pitch.
  2. The feeds from all these cameras are fed to a room at the FA where a team of technicians from Hawk-Eye and a referee (the actual VAR) use them to make decisions where the on pitch team hasn’t been able to, or have made a mistake.
  3. When there’s a possibility of offside, a Hawk-Eye operative selects 3 frames best representing the point at which the attacking player made first contact with the ball.
  4. In consultation with the Video Assistant Referee, the Hawk-Eye operative marks reference points on the player’s bodies to find the part furthest forward excluding arms
  5. This allows software to draw those thick red (attacker) and blue (defender) lines drawn exactly across the pitch to compare positions, as the position of the cameras and pitch is known and mapped.
  6. If any red shows goal side of the blue, it’s offside.

When you read up on it, and understand the way in which decisions are made, it starts to make sense. The thing is though, how does that take 3 minutes and 47 seconds? And how does something “binary and objective” LOOK so subjective to the fans, pundits and managers?

The problems

Margin of error

All the above is meant to be binary and objective, NOT clear and obvious. That is, the player is either onside or off, and it is a matter of fact not opinion.

But maybe it’s not quite as binary and objective as we’d like…

Disclaimer. I support Sheffield United. I may not be completely objective either…

Frame rate

Offside decisions are made using broadcast cameras — running at 50 frames per second. The decision on when the attacker first impacts the ball, however, is made using high speed, 120 fps cameras.

The thing is, players and the ball are all moving. Pretty fast. I’m not the first to spot this.

These cases all look at player speed, which is the most obvious place errors can creep in. But all sorts of things move. Players, the ball, players’ limbs as they run and kick. So let’s have a look at how far things can move between frames of those cameras.

The current fastest player in the Premiership is Marcus Rashford, who hits 22.5 mph flat out. This equates to 10 m/s. A typical leg velocity while kicking seems to be 20m/s, giving a ball velocity of 30 m/s. Typical speeds for a professional footballer average out at 8.6m/s.

But still, as twitter has noticed, if a player can move 10 metres every second, and a camera only takes 50 pictures in that time, Rashford runs 20 cm between frames. VAR is making decisions based on much smaller distances than that.

On the one hand, in most offside cases players aren’t running flat out; they’re accelerating from a jog, or spinning into a sprint. But the worst case scenario is a flat out Rashford moving in one direction while Enda Stevens, the second fastest player around, sprints the other way trying to catch him offside. At 50 fps they move 40 cm in opposite directions each frame.

And what about when the ball is kicked? Should be easier here, we’ve got those fancy 120 fps cameras, right? If the ball’s hit hard, it still moved 16 cm over a single high speed frame. Plus, we then match it to a normal speed frame during which it moved 40 cm again. And you’ve got to match up the point of impact with an object that’s also moving up to 30 m/s.

Shutter speed

Shutter speed — the amount of time the camera sensor spends recording each frame — is ½ the frame rate, due to something called the 180 degree rule. So in this case it’s 1/100 of a second. Seems fast, right? Well, everything is still moving in that time. Typically a sports photographer capturing stills will aim for at least 1/1000 s, and never drop below 1/500 for a sharp image.

So Rashford moved 10 cm while the shutter was open. A well struck ball moves 30 cm in that time. Ever wondered why stills from video aren’t that sharp?

Footballs aren’t really that shape. And VAR selected the SECOND frame here, not the first.

A smarter man than I would probably look at the numbers, calculate an exact margin for error, looking at how it changes depending on player and ball speed and direction.

Not me though. I’m going to take the path of wisdom, and simply make the undisprovable statement that there is a margin of error, and it’s impossible to be certain about the relative positions of everybody.

If I really wanted to (I really don’t) I could read some more of the internet, start banging on about uncertainty and how the impossibility of being sure about the exact position of John Lundstram’s big toe means it isn’t actually his at this point, but Schrodinger’s*. You’ll see in a bit the cunning, highly scientific way I actually calculated the margin to use.

But in summary, there is a degree of uncertainty, and we should be honest about this, show it and take it into account. Both in the VAR dungeon so they can make realistic decisions, and on TV and in the ground so the fans understand that decision.

* I know

Perspective

You know how this works, right? The further away things are, the smaller they get. Unless they are in fact small.

Far away = half as many pixels as near = half as accurate*

Far away. Not small.

* ish

Armpits

It’s bad enough when you can see the body part that’s furthest forward. But figuring out where a player’s blurry armpit is?

Baggy is SO last season Roberto

‘Binary and Objective’

So, are offside decisions taken using VAR binary? And are they objective?

Nope.

They are as objective as can be — the process is rigorous and involves a team of experts. But it is impossible to identify the exact point of impact between player and ball. The choice of frame is subjective, as is the measuring point.

But these decisions REALLY aren’t binary. They cover a range of probabilities. Even if everyone’s standing still and the ball is given a gentle tap, the ball could still move 10 cm per frame. If we’ve got Rashford vs Stephens, and Pogba is smashing the ball Rashford’s way from the half way line as hard as he can, you could easily have an uncertainty of a metre or more.

A solution

So, how could we fix this? Some people want to get rid of the entire thing, handily ignoring things like changing the rules half way through a season is generally not done, and the whole world is using it now.

But surely we can do better than live in the past and yearn for the good old days like they were some kind of sepia tinted dream. Seriously, go watch a top flight game from the 90's and tell me anything was better.

What we have here is a visualisation problem

What if we could show probabilities? Or margins of error? What if we were honest about the issues and worked with them?

Or is it an accuracy problem?

What if we reduced those margins as far as possible?

The thing is, there will always be margins of error. Lasers or radar still have uncertainty from wavelengths and frequency, and even the highest speed camera just reduces the margins.

Plus, does anybody really want that? There’s a lot of talk about VAR ruining football, and decisions based on the exact position of assorted body parts are part of it.

Why not embrace the uncertainty, and use it to go back to giving the attacker the benefit of the doubt?

So, this is the scene from Spurs vs Sheffield United. The ball is being played to John Lundstram on the far touchline. Eric Dier is the furthest defender back. The blurred end of Lundstram’s foot is goal side of Dier’s left knee. They’re both moving, but not too fast — let’s say 10m/s, about ⅓ max speed. Their legs are moving faster, because that’s how running works. This results in the blurring of what temporarily became the most famous foot based digit since David Beckham and his metatarsal.

BIG toe

The question is how much uncertainty? The answer, you’ll be delighted to know after wading through all of this is, I neither know nor care. Seriously people, I spent half a day googling stuff, what do I know? This stuff needs proper research and expertise!

So, let’s pick a number. How about that 20ish cm the player could move? As it happens, a football is about 22cm in diameter. Using a ball width feels right somehow.

So I’m not going to do that, I’m going to use John Lundstram’s foot, purely because there are feet ALL OVER a football pitch, which it makes it much easier to measure and mock things up in Photoshop. The average male foot in the UK is a size 10, which is 27.3cm. Say 30cm with boot. Close enough.

Told you the maths would go downhill.

So. Let’s look at Lundstram. Let’s assume the original end of toe marker was correct. Let’s draw in a shape either side of it representing that 30 cm margin of error - 15 cm either way.

Now onto Eric Dier and his knee.

What do these shapes represent then?

Simply put, the area in which the player’s toe/knee probably is when the ball is kicked.

It should really be a gradient, fading out to 0% certainty, but that won’t help us decide anything. A shape showing where there’s a (say) probability of over 50% the correct body part is situated — that’s useful. Change the threshold as you see fit, do the maths properly and use a better image and maybe you’ve got a useful tool.

So what happens if we overlay them?

They overlap. What does this mean? It means, according to me, an unbiased Sheffield United fan, that it is impossible to say to a reasonable degree of probability that Lundstram is offside, therefore we beat Spurs.

So what would an actual offside look like? Let’s move the defence up a couple of feet.

Clear daylight between the shapes. And positions I think most people would say is actually offside. I’d expect the assistant ref to spot that in this case, but it would be hard if the players were moving at high speed. So VAR is still in fact helping, while being probably right.

How close can they get while still having daylight? How about this?

Using the randomly allocated margins I picked out of thin air, this is as close as you can get and get an offside.

To my enormous relief after all this, it passes — for me at least — the ‘feels about right’ test. You can say it looks offside. You’d also say it’s close. No clear advantage has been gained.

There is a slight issue though. I’m a blade. I’m still going to be looking at that last screenshot VERY closely, because those boxes again make it look like a binary, on or off decision.

Bugger.

They still don’t communicate the varying levels of probability. Back to the gradients? But we still need a way to make a decision, so we need a line SOMEWHERE. Also I mocked one up and it looked awful. And don’t forget I’m biased. You shouldn’t be listening to me if I’m upset about this decision.

Even on a still image that can be shown on in the stadium we can still surface a bit more information. We are working with probability*, right? Why not show it?

* I know, I know, I’m throwing around words like probability as if I know what I’m doing and I understand p-values and things. I DO point out at the end I should talk to experts at some point.

So where should the threshold be?

I mentioned 50% earlier. Thinking about it, that’s a bad idea. If it’s 50% then a pixel still means the difference between probably on and probably off side.

So I’d suggest 67%. A 2 in 3 chance the players is offside. Something to stop people like me crying over a single percentage, because even if there is just a single pixel making Lunnie’s toe offside, either side of the line he’s still probably offside.

I’m not going to shut up, but you can morally tell me to stop whining about it.

In fact, if we’re going to do that, we probably need a visual indication of the threshold:

You can now see a visualisation of the probability, but also the threshold it must pass to be offside.

How does that look in real life then?

I KNEW we won really

GOOOOOOOOAAAAAAAAAALLLLLLLLL!!!!


What now?

The odds are I go do some proper work. I know there’s a ticket I’ve been dodging all week, and apparently I left some post-its on a wall somewhere.

But let’s say this randomly gets spotted by the FA and they want to use this? Basically, what would this look like as a proper project, not a rambling blog post? Or what do I do in my day job?

If you only came here for the football bit you can leave now.

  1. Discovery
    Research. Watching the VAR team do their job, talking to them about it. Talking to fans, sitting in pubs and watching their reactions. Interviewing players and coaches — how has the current system impacted their tactics? What would happen if we changed it? Look at other sports using similar things. Understanding the technical aspects properly, and finding people to do actual maths. Discovery is all about understanding a system’s users and the problem to be solved.
  2. Alpha
    Coming up with and trying out different solutions. I quite like mine, but there are many, and designers don’t have a monopoly on ideas. We like to work with everyone involved, and give them a chance to come up with ideas too. Then we try out the tricky bits to make sure they can be done.
  3. Beta
    Putting it together and trying it out in the real world. The FA has already done this with VAR — remember hearing about it being tried out in matches behind closed doors? That’s effectively a closed beta, where you invite a few people to try out your early version, so you can understand the issues and improve it. Then they tried it out in a cup competition or two. A public beta, where everyone can get involved and feed back. All the way through we’re continuing to research and test — watching and talking to the VAR team, fans, players and coaches, and improving wherever we can.
  4. Live
    Once everyone is happy, it goes live. In this example, the new offside system is used in the Premier league. We keep researching and observing though — as we’ve seen this season, new issues will occur, we’ll learn much more from the volume of matches, and we can start to work on an improved version for next season…

(For the non-geeks still here, these phases come from the gov.uk service manual.)

Who am I?

I’m a designer and researcher at Hive IT, and I mostly design websites. Quite a lot of my work involves data visualisation — using graphics to communicate complex data simply in an easy to understand way. I’m also a Sheffield United fan, the latest team to be bitten on the arse by a VAR offside decision. So I know a bit about football, and a bit about putting things on a screen so people can understand them. You have probably come to understand the extent of my mathematical skills by now…

Want to know more?

Get in touch! We do do cool digital stuff, and we exist to make good things happen. Our mission is to use the right tools & technology to make positive changes to the world we live in. And VAR. We’re awesome. Hire us!

References

Hive IT

We are a digital agency making a positive difference to our world using the right tools and technology

Martin Smith

Written by

Designer, researcher, finder & solver of problems @HiveIT_uk. @theRSAorg fellow, @CodeFirstGirls instructor, @legup_social mentor.

Hive IT

Hive IT

We are a digital agency making a positive difference to our world using the right tools and technology

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