Jordan Ellenberg is a professor of mathematics at the University of Wisconsin, whose book How Not To Be Wrong – the Hidden Maths of Everyday Life makes only one, oblique reference to football anywhere in its 18 chapters. Aleksander Ceferin, a former lawyer from Slovenia, is the president of Uefa, the sport’s European governing body. They do not, on the face of it, have a great deal in common, but given Ceferin’s suggestion this past week that VAR is, by and large, “a mess”, he might like to know that Ellenberg has an interesting argument as to why that might be the case.

Ceferin, who was interviewed by the Daily Mirror, was talking about VAR in general, but ultra-tight offside decisions in particular. “If you have a long nose,” he said, “you can be in an offside position these days. Also the lines are drawn by the VARs. So it’s a bit subjective drawing of objective criteria.”

There was a rhetorical question in the pre-VAR age that wormed its way into almost every discussion on the subject. “If the technology is there and it works,” its proponents would say, “then why not use it?”

Which is where the maths professor from Wisconsin comes in, because Ellenberg has an answer. The question is rhetorical no longer. “There’s such a thing,” he argues, in a chapter devoted to closely fought elections, “as being too precise”.

It is, on the face of it, a somewhat unexpected view for a mathematician to take. There are sound reasons, after all, why we don’t just assume that pi is close enough to three that it makes no difference.

But in the 2000 US presidential election, for instance, a few hundred votes in Florida made all the difference nationally and put George W Bush into the White House. The final margin represented 0.01% of the total votes cast, but as Ellenberg points out, “the imprecision caused by ballots spoiled, ballots lost, ballots miscounted is much greater than the tiny difference in the final count”.

It would make more sense, Ellenberg argues, to decide the outcome on the flip of a coin. Some, he says, will recoil from the idea of choosing leaders by chance, and yet “close elections are already decided by chance”, be it “bad weather in the big city, a busted voting machine in an outlying town” or any one of dozens of potential random variables.

In an offside decision, there are often four moving objects, all heading in slightly, or completely, opposite directions

For tight elections, read marginal offsides. The point about ultra-precision is that it is all well and good when there is a single thing to measure. Hawk-Eye works well in tennis, for instance, but then, it is only the ball that is moving. The line is fixed, and so the ball is either in or out (and it is maybe no coincidence that whenever the “Why not use it?” question raised its head in the VAR debate , the “Technology works in tennis” line was rarely far behind). But what happens when there’s a lot more going on? Digital systems reduce every challenge and question to a long line of zeros and ones, which is fine for essentially quantitative problems. The more qualitative the data, however, the greater the issues that extreme precision is likely to present.

In an offside decision, there are often four moving objects, all heading in slightly, or sometimes completely, opposite directions: two attackers, one defender and the ball. It’s five if you include the referee’s assistant. Impose absolute precision on that and Ceferin’s “long nose” problem is all but inevitable. The problem is not that the technology is not working. It is that it is working too well.

This makes his proposed solution rather troubling. The answer, Ceferin says, is tolerance. “Our proposal will be that it is a tolerance of 10-20cm,” he said. “It’s OK if you don’t rule someone offside if it’s one centimetre. The meaning of offside is that I have to have some kind of advantage.”

Presumably this would mean that if the flag does not go up, a goal is scored and an attacker is shown to have been offside in the buildup by “no more than 10-20cm” the goal will stand. It is, in a sense, an attempt to turn the precision knob down from its current 11, to five or six. It hopes to blur the picture slightly, in the same way that it would if the VAR officials were forced to work with a 30-year-old black and white telly.

But they won’t be working with old tech. They will still be drawing lines one pixel wide on an ultra-high definition screen, and the level of “tolerance” will need to be a lot more precise – that word again – than simply “10-20cm”. If not, there will be constant debate over goals that are legal at one end of the scale but ruled out at the other. It will, in other words, still be possible to be “a nose” over the line. It will just be a slightly different line.

Spare a thought, too, for the officials who would still be wielding a flag on the sidelines. VAR already seems to have reduced the number of flagged offsides per match by 10%, from 4.1 per match in 2017-18 and 2018-19 to 3.7 per match so far in 2019-20. If there is an extra level of tolerance to be ruled on upstairs, why bother raising it at all?

And while Ceferin may not think that 10-20cm constitutes “an advantage”, the Premier League’s quickest attackers, and the defenders tasked with controlling them, might well beg to differ. Handling Raheem Sterling is a tough task for defenders as it is. Sterling +20cm could be all but unplayable.

The danger is that tinkering with VAR will exaggerate the current irritations, creating more interventions and more post-goal longueurs when no one can celebrate, while kicking off just as many arguments about whether the final decision was “right”.

When the Observer asked a fan of every Premier League team a series of questions about their season so far a fortnight ago, their antipathy towards VAR was almost unanimous. Just two expressed anything close to a positive opinion, and both cheerfully admitted that it was because – so far – it has worked in their team’s favour. The responses of the other 18 were either largely or wholly negative. Such, it seems, is the price to be paid for being too precise.