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If you have watched any football 鈥� or soccer 鈥� over the past few years, you will know that the game has been consumed by controversies over its new refereeing technology. The video assistant referee (VAR) system was introduced to the English Premier League in 2019 to reduce refereeing errors and get more decisions right. Instead, it has created new kinds of uncertainty and undermined our understanding of fundamental rules like offside and handball. It has also infuriated fans, who can often be heard chanting 鈥渋t鈥檚 not football any more鈥� after a long-winded VAR check.

It is fair to say that football fans like to get irate, especially when refereeing decisions go against their team. But as I argue in my new book, I Can鈥檛 Stop Thinking About VAR, there鈥檚 more to this than meets the eye. As someone whose job involves developing new methods of measuring educational attainment, I have thought long and hard about the reasons why VAR has been so frustrating. I believe its problems relate to the challenge of pinning down objective reality, the difficulty of precise measurement and the human dislike of uncertainty.

What I have also come to realise, however, is that VAR exemplifies the limits of rationality in many walks of life far beyond the football field. As such, a brief exploration of the history of measurement more broadly聽鈥� from attempts to pin down the boiling point of water in the 18th century to the struggle to accurately assess the risks of new drug treatments today聽鈥� can shed light on what really underlies the troubles with VAR and how they might be solved.

One major problem with VAR is the assumption that more scrutiny is always a good thing because it will provide us with a more objective understanding of reality. A lot of the time, however, greater scrutiny just adds confusion and complication.

VAR reviews often involve one referee poring over a video replay and disagreeing with the on鈥慺ield referee who saw the incident in real time. We don鈥檛 always hear all the deliberations, but it is clear that the VAR official sometimes simply has a different interpretation of events than the on鈥慺ield official. In this case, the legitimacy of the on鈥慺ield referee has been undermined, but their decision hasn鈥檛 been replaced with a more objective one: the subjectivity has simply doubled. Far from removing arbitrary human judgement, VAR emphasises just how arbitrary it is.

Occasionally, the slow-motion replay allows the video referee to see things that the on鈥慺ield referee missed. But every so often, the things the on鈥慺ield referee failed to spot were also missed by all the players and fans as well, and if we change decisions based on previously unnoticed aspects of reality, then we are going to have a completely different game. In that sense, the fans chanting 鈥渋t鈥檚 not football any more鈥� have a point.

Take offside decisions, for example, which have always been some of the trickiest in football. A player is offside if, at the moment the ball is played to them, they are in the opponent鈥檚 half, ahead of the ball and ahead of the penultimate defender. This rule, then, requires a human official to look at at least three things at once: the player kicking the ball, the penultimate defender and the player receiving the ball. Of course, this is impossible, which is why the pre-VAR game saw so many errors.

VAR controversies

It seemed obvious that technology would fix this problem, because video replays allow us to look at multiple things at once. But VAR鈥檚 offside decisions are also wildly contentious, with fans and players outraged by marginal offsides for stray toenails and armpits. Clearly, you have to draw the line somewhere, but the problem is that VAR picks up offsides that would never have been spotted before. Although these marginal decisions might be correct according to the letter of the law, they aren鈥檛 in keeping with its original intention, which is to stop attackers camping out permanently in the opposition penalty box and having long balls pumped up to them. This means that, while VAR may be giving us a clearer picture of reality, it isn鈥檛 a reality we are happy with.

Another complaint is about the accuracy of offside decisions. After all, if you are going to claim that players鈥� toenails are offside, your measurement technology needs to have toenail-sized levels of precision. But it doesn鈥檛. VAR鈥檚 offside decisions depend on cameras with a frame rate of 50 frames per second: that is, one every 0.02 seconds. In that time, however, a defender and an attacker might each have moved as much as 20 centimetres.

Offside decisions have probably never had less error 鈥� and yet they have never been more controversial

So in one sense, the critics are right: some offside decisions are too close for VAR to judge accurately. But in another sense, those critics are wrong: measuring offside with VAR is clearly far more accurate than asking humans to measure it in real time using only their eyes. That leaves us in the strange situation where offside decisions have probably never had less error聽鈥� and yet they have never been more controversial.

It is a similar story with handball, the rule that outlaws players using their hands and arms to control or block the ball. Before VAR came along, the handball rule was just 20 words long: 鈥淗andling the ball involves a deliberate act of a player making contact with the ball with the hand or arm.鈥� Since VAR, it has undergone several revisions and is now 11 times as long. Referees must decide whether the hand or arm has moved towards the ball, whether the player in question has used their hand or arm to make their body unnaturally bigger, whether the handball has led to a goal or a goal-scoring opportunity, and numerous other elements.

In both cases, that of offside and handball, what we are seeing now in football has been witnessed throughout the history of measurement: improving measurement often first involves the quantification of error, and that can sometimes seem like a step back rather than a step forward. When you start scrutinising reality at an increasingly granular level, it often turns out to be weirder and more difficult to pin down than you might think.

Consider the thermometer. When scientists first started to develop instruments for measuring temperature, they were frustrated by how hard it was to define boiling water. As Hasok Chang discusses in his book Inventing Temperature, in the 18th century, scientist Jean-Andr茅 Deluc produced a detailed categorisation of the different stages of boiling water: common boiling, sifflement (hissing), soubresaut (bumping), explosion, fast evaporation only and bouillonement (bubbling). 鈥淒eluc had started his inquiry on boiling by wanting to know the temperature of true boiling,鈥� wrote Chang. 鈥淏y the time he was done, he no longer knew what true boiling was.鈥� What had seemed like a simple and well-understood aspect of reality became clouded in confusion, in the same way that VAR set out to make handball decisions more accurate and ended up with no one knowing what handball was any more.

We have forgotten this in the world of the physical sciences, because the confusion over soubresaut and sifflement are long behind us. We now have measurements for temperature, time, distance and mass that are many times more precise than most of us require when setting an alarm or weighing flour, say. Outside of the physical sciences, however, the errors and compromises involved in measurement sometimes make you wonder if the game is worth the candle 鈥� and that鈥檚 true not just of football but lots of other areas too.

Watch mini humanoid robots showing off their football skills

These soccer-playing robots can respond faster than ones trained in a standard way because they improved their skills via an artificial intelligence-based technique called deep reinforcement learning

GDP is a metric that the whole world relies on to decide if national economies are succeeding or failing. But when you dig into it, it is a bit of a mess. In his book The Hidden Half, Michael Blastland shows that measurements of quarterly GDP growth are often subject to several revisions in subsequent years. In the first quarter of 2012, statisticians said that the UK economy had shrunk by 0.2 per cent, for instance. Five years later, that had been revised upwards to growth of 0.7 per cent. That鈥檚 the difference between likely recession and exceptional growth.

Exams are another example: employers and universities depend on the ability of these tests to measure human achievement, yet we know that exams are beset by error and uncertainty. And there are many other fields that are trying to create new measurements for nebulous concepts. Health economists use a metric called quality-adjusted life years to estimate the benefits of a new drug. Risk managers have developed the 鈥渕icromort鈥�, a unit of risk that represents a 1-in-a-million chance of death.

Many of these new measurements are like VAR鈥檚 offside calls. They provide answers to important questions, and they are better than one human making a snap judgement. But they have frustrating weaknesses and limitations. In some ways, they are the victims of the stunning success of measurement in the physical sciences, because they can鈥檛 provide the same degree of certainty we have come to take for granted there.

When new drugs are being trialled, people want guarantees they are safe, not probability distributions of different side effects. When students sit exams, they want to be sure they will get the grade they truly deserve, not confidence intervals that overlap the grade boundaries. When politicians write snappy tweets about how increases in GDP prove the wisdom of their policies, they don鈥檛 want to add asterisks saying 鈥渟ubject to rolling revisions and redefinitions over the next decade鈥�.

How to fix the problems with VAR

Could we improve these new metrics and reduce their measurement error down to the levels seen in the physical sciences? For the measurement of offside, the solution is simple, if not easy: more cameras, better cameras, constant tracking of players and the ball, and balls with sensors in. Semi-automated offside systems have been trialled in big tournaments and one is due to be introduced to the Premier League soon.

Handballs and other fouls are a trickier problem. In my book, I propose creating a metric similar to the micromort and quality-adjusted life years: the Foul Probability Index. Here鈥檚 a brief summary of how it would work: first, you would get a large group of players, managers, fans and officials to judge a series of short video clips of football incidents. You would use the results of their judgements to determine the percentage chance that each incident is a foul. You would then have a distribution of incidents and could decide where on the distribution the cutoff for a foul lies. The resulting data would be used to train an artificial intelligence, and in a live match, you would send a video clip of an incident to the AI and ask it whether or not a foul was committed.

Although you would need AI to apply such an index during a live match, the index would be constructed using human intelligence 鈥� ideally, the aggregated judgements of thousands of humans drawn from every part of the amateur and professional game. I also propose making these decisions using a psychometric technique called comparative judgement. In this context, this would mean each judge would look at two clips of possible fouls and say which is more likely to be a foul. This is better than deciding based on a single video clip in isolation, a more common but more error-prone technique known as absolute judgement.

However, it isn鈥檛 clear that fans would welcome such an approach. One striking aspect of the debate about VAR is that it has made people realise that accuracy isn鈥檛 the only virtue. Speed and simplicity matter too, and are threatened by complicated and lengthy VAR checks that ruin spontaneous and joyful goal celebrations.

Making a decision on VAR

One school of thought says we need to stop focusing on trying to optimise the accuracy of decisions and instead focus on optimising the experience of the game as a whole. Sweden鈥檚 top-flight football league has refused to introduce VAR. Perhaps others will follow.

The alternative view is that data is already taking over football, as it is taking over everything else. New metrics are invading the game: the expected goals metric 鈥� which tells you how likely it is that a shot on goal leads to an actual goal聽 鈥� is used extensively by team analysts, and is popular with fans too. Given that, some kind of data-based upgrade of VAR seems inevitable.

I don鈥檛 think VAR as we know it will be around for much longer. But will it be abandoned as a dead end while we revert to old-fashioned human refereeing, or is it a stepping stone to something better?

The answer will have significance beyond the game of football. A world in which we have a new and improved VAR is probably one where we have powerful AI-enhanced abilities to measure all kinds of nebulous concepts, and where we have made our peace with the trade-offs they require. That will have implications for all the new measures of the seemingly immeasurable that are increasingly defining our world.

Daisy Christodoulou is author of I Can鈥檛 Stop Thinking About VAR