David Spiegelhalter, the chairman of the Winton Centre for Risk at Cambridge University, suggests that the risk posed to children by Covid-19 is “tiny”, with under-15s more likely to be struck by lightning than die of the virus. Young adults are slightly more at risk, but not by much. Seroprevalence surveys suggest that this age group are more likely than any other to have already come into contact with and recovered from the virus, which makes sense given the daily habits of young adults who are disproportionately likely to live in cities and to have work and social lives that bring them into contact with large numbers of people. Almost all young people experience Covid-19 as a mild illness, and often suffer no symptoms at all, meaning that the age-mortality graph for this disease looks less like a u-shape, and more like a hockey stick.

And here is the political problem. Many young people feel resentment towards the generation born between roughly 1945 and 1965, otherwise known as ‘boomers’, a word often spoken with derision by young adults, and sometimes with a snarl.

Boomers, according to the narrative popular among my peer group, had it easy. Boomer landlords sit atop the housing market and exploit their young tenants; boomer students enjoyed free tuition courtesy of the taxpayer while today’s students pay through the nose; boomer public sector workers are living the high life on gold plated pensions while their descendants suffer the effects of austerity; boomer voters gave us Brexit, against the wishes of the majority of the young; boomer job-seekers benefited from an economy that offered opportunities that today’s millennials, coming of age in the wake of the 2008 crash, can only dream of.

There are flaws in this narrative, of course, since the image of the complacent boomer doesn’t always fit with reality. A quarter of baby boomers don’t own their homes, the vast majority didn’t go to university, and almost a third can expect to enter old age with no financial security, since they have no private pension to call on. Plus younger members of the boomer cohort are likely to suffer terribly as a result of job losses, with a quarter of a million over-50s predicted to never work again.

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But the narrative is nevertheless attractive to a generation feeling the sting of downward social mobility. And now we have a new, even more enraging component to add to this tale of boomer entitlement: the fact that the lockdown has disproportionately protected the over 55s, who are at risk from a virus that is dangerous to them, but not to their children or grandchildren, while causing devastation to the economy. And it is not boomers who are predicted to foot the bill.

This framing relies upon abstraction. Even the young people most sceptical about the need for lockdown, and most resistant to its strictures, have no desire to put their older relatives in harm’s way because, as with all unpleasant political problems, it is difficult to support a policy when the costs must be borne by people you personally know and love.

But when the fear of death has lifted and this crisis ends, how will its story be told? We could well be suffering the consequences — economic and others — of these last six months for decades to come, and the precautionary principle that persuaded so many people that lockdown was a necessary evil will not have the same persuasive power once the panic induced by the pandemic recedes in the collective memory.

For a group of young people already comfortable with the vocabulary of ‘privilege’ and ‘oppression’, it might not take much to definitively add ‘boomers’ to the list of wrongdoers, alongside other reviled groups. And we might find that the generation who lost out most from lockdown will adopt a divisive myth about the crisis of 2020 that goes something like this: “Boris Johnson’s government destroyed our futures in order to protect Tory voting boomers.”

All it needs is a grain of truth. A longstanding Tory preference among older voters is as strong as ever, with the Conservatives currently leading Labour by 34 points among the over 65s. And children and young adults have endured some unique harms as a result of lockdown, with the closure of schools and the A Level fiasco doubtless leaving some permanent mark on students in this cohort. Meanwhile, surveys suggest that the mental health of the young has been particularly badly damaged by the experience of lockdown. And all this before the forecast global depression even arrives with its full and terrible force.

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The boomer narrative doesn’t require perfect accuracy in order to thrive. The fact, for instance, that the approach adopted by the British government was similar to that of most other Western countries, and a good deal less restrictive than some, will not necessarily counteract the mythological power of a story of old betraying young.

The inaccuracy, for instance, of the ‘lions led by donkeys’ account of the First World War has done little to undermine its potency. The phrase was already in use during the war, was quickly adopted in the years immediately following, and then further popularised in 1961 by Alan Clark’s The Donkeys, a book that excoriated the British leadership on the Western Front. The musical Oh What A Lovely War! and television series Blackadder embedded the image of heartless old generals sending brave young men to their deaths and, despite the best efforts of revisionist historians, this remains the popular view of the conflict. When a story is compelling enough, inconvenient details tend to be forgotten.

At the very beginning of lockdown, Max Hastings, a military historian who understands the power of popular narrative, wrote with impressive candour about the coming generational conflict. Echoing the sentiments of the most resentful twenty-somethings, Hastings described his own generation as collectively “monumentally selfish”:

“Despite our affluence relative to the young, the grey vote has fought tooth and nail against the BBC’s sensible termination of our free TV licences; deterred politicians from means-testing free travel passes; resisted fiscal curbs on our pension privileges, and the entirely just depletion of personal resources to fund care home costs.”

Expressions of this kind of anti-boomer sentiment will only grow louder without some kind of government intervention. The proposal to end the triple lock on state pensions in order to pay for this crisis may go some way towards repairing the generational rift. As Scott Corfe, the research director of The Social Market Foundation, said in response to this proposal, “[t]here is a clear case for intergenerational reciprocation when it comes to meeting the fiscal costs of the crisis in the years ahead.”

It might also become necessary to increase taxes on assets, or even introduce a means test for pensions — a controversial proposal in the UK, although long established in Australia — in order to settle the lockdown bill. And we should expect those moves to be resisted “tooth and nail”, just as Max Hastings describes. This isn’t an easy problem for the Government to solve, and the age profile of Tory voters disincentives action.

But the effects of this crisis demand some kind of action, if we are to avoid a toxic narrative of exploitation which casts millennials as vulnerable lions, and boomers as entitled donkeys. Covid-19 could have had a classic u-shaped mortality curve, or it could even — like the 1918 flu — have been most dangerous to working age adults. Instead, by a stroke of dumb luck, the young turned out to be peculiarly resistant to this virus. And now, without some effort to remedy the generational inequality feeding the anti-boomer narrative, that flap of the butterfly’s wing could have ugly political consequences.

Exams are a blunt instrument. They assess performance on the day, not ability. But when they were cancelled, they left a gaping hole in an education system that depends on the grades they spit out. If only we had an oracle that could see into the mind of each student and judge them: a statistical model, objective, fair, and well-fed on data from every student in the country. So that’s what Ofqual built.

Then, around 40% of the A level grades awarded by the algorithm fell below the teacher predictions for the student in that subject. Cue teenage demonstrations and widespread political recrimination. But, contrary to what students may have expected, those teacher predictions were never the starting point for the awarded grades. In many cases, they didn’t even form part of the calculation.

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Instead, the system was designed to give an overall distribution of grades that looked similar to previous years, with similar numbers of A*, A, and all the other grades for each subject — though they did allow more A and A* grades than usual. Ofqual even went so far as to check that the proportion of grades handed out to different subpopulations (by gender, ethnicity and deprivation, for example) would look similar to recent years. If your definition of fairness is that boys, or claimants of Free School Meals, won’t do demonstrably worse than last year, you should be happy.

Ofqual’s Direct Centre Performance model is based on the record of each centre (school or college) in the subject being assessed. Whatever the range and distribution of grades achieved by previous students over the last three years, that is the range of grades allocated to the class who would have taken A-levels in 2020. There was some adjustment, if your class has shown better (or worse) performance than its predecessors in GCSEs or other previous assessments, or if other changes would leave the national distribution of grades looking too different from previous years.

Meanwhile, each teacher was asked to rank each class from highest to lowest in expected achievement. That ranking, not predicted grades, was used to slot each student into the predetermined range of grades from A* to U. The exception to this was small groups, less than 15 in most cases, where Ofqual did resort to teachers’ predicted grades. That is why less popular subjects and smaller schools have seen less marking-down from expected grades.

Any one individual’s achievements so far, or their potential in the view of teachers who know them, had less influence on their eventual results than the attainments of others who attended the same school in past years. It’s closer to buying car insurance than taking an exam for which you have worked for nearly two years. Just enter postcode, make and model and we will predict your likelihood of making a claim, and hence your premium.

This wasn’t inevitable. “Any statistical algorithm embeds a range of judgments and choices; it is not simply a technically obvious and neutral procedure,” wrote the Royal Statistical Society (RSS) in a scathing statement published on 6 August. “Calibrating this year’s estimated grades to previous years’ exam results is one such choice. How to take account of evidence of individual students’ prior attainment is another. How to take account of uncertainty is another.”

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I asked Professor Guy Nason, Chair in Statistics at Imperial College, London, and fellow of the RSS, what Ofqual could have done differently. He was surprised that the UK had not attempted any kind of socially-distanced, in-person assessments, as some other European countries had done. But, given that some kind of statistical grade allocation was needed, Guy pointed out some specific pitfalls that could have been avoided, if a wider range of experts had been involved at an earlier stage.

“Overall, I think they ignored, or in some cases, underestimated uncertainty in many steps of their process. For example, the teacher-provided rankings for students within a subject were treated as if they were correct, when, in all likelihood, they are subject to considerable uncertainty. So, for example, tied rankings were not permitted, which might have resulted in students being assigned different grades even though their Centre thought that they were indistinguishable.” He also thought it was unfair to assess students by a completely different method if they happened to be part of a small class.

Nason had serious concerns about how Ofqual tested the predictive ability of their algorithm. “You’ve got to run a fair test, one that runs under the same conditions as the real deal.”

The normal way to test a predictive algorithm is to see how good it is at predicting the past. That is, you run the program for the previous year and see how well its predictions match what happened in real life. Ofqual did that for 2019, but because teachers in previous years were not asked to rank students, Ofqual could not use 2019’s teacher-generated rank orders for a test run.

Instead, it used the rank order that emerged from the 2019 exam results. Which is like showing you can predict the results of a horse race by including data about the order in which the horses crossed the finish line in that same race. “If a test uses aspects of the same data that it is trying to predict, then it results in a false sense of security,” says Nason.

Even by including some of the data they were trying to predict, Ofqual found their accuracy in predicting exact grades ranged from two thirds for History to one in four for Italian. For most non-language subjects, over nine in 10 students would be within one grade of the true result, but 3% of Maths students (for example) missing a fair result by two grades or more adds up to a lot of teenagers. Over 10% of Further Maths students, ironically the only ones who can understand the tortuous workings of the algorithm that betrayed them, would be over a grade away from a fair result.

“Their algorithm’s predictability is, especially for some subjects, not that good anyway, but if you then realise that they are over-optimistic and cannot be trusted, then one has to really question whether the algorithm is fit for purpose,” says Guy.

This isn’t just hindsight talking. The RSS offered to nominate two distinguished experts to the Ofqual technical advisory group in March. Guy was one of them. But Ofqual wanted to impose a Non-Disclosure Agreement that would bar them from public comment on the model for five years, in direct contradiction of the Society’s commitment to transparency and public trust.

Ofqual also ignored the House of Commons Education Select Committee’s call to publish details of their methods before releasing the results. They might have been spared some of the post-hoc dissection of their work, before public outcry and political pain caused Monday’s abandonment of the algorithm.

Because the grading algorithm has been withdrawn for political, not statistical reasons.

Its workings seem to have hit harder the very students who already felt the cards were stacked against them, and the communities to whom this government promised “levelling up”. Students in state schools and FE colleges, especially, and more deprived students, saw their awarded grades fall well short of their teacher-predicted grades.

It’s no surprise that small teaching groups, and less popular A-levels like Law, Ancient Greek and Music, are more common at private schools, which insulated those students from being marked down. Nor that previous results in selective and private schools would have been higher, bequeathing a higher range of grades to this year’s cohort.

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But the picture is messier than that. Historically, teachers in large state schools, and of more deprived students, have been more likely to over-predict. There may be good reasons for this. Teachers may consciously give a student the benefit of the doubt, figuring that it at least gives them a shot at a good university place. If they fall short, they can haggle later. If they exceed more honest expectations, it might be too late for them to raise their sights.

And in a high-attaining school where students routinely get A and A* exam results, there is not much headroom for over-optimism, unlike schools whose students walk away with the full range from A* to U.

Whatever the causes, that over-prediction means that every year state school students are more likely to find their exam results lower than their predicted grades. Universities are often flexible, recognising that it’s easier to get good grades in a good school, and that students who fought harder for OK results often do better at university than the ones who got good results in easier circumstances.

It’s bitter to be disappointed with your exam results. Perhaps, like me in those Stats exams, you turned over the paper and finally acknowledged, too late, how poorly your work matched the standards expected for the subject. But even if you were unlucky on the day with what was on the paper, or with your own state of mind, you still had your chance to do the best you could.

To find that a faceless system has allocated you to a lower grade, simply because your school hasn’t previously achieved much in this subject, looks like the epitome of systematic unfairness. Why did you bother to put in all that work, only to be pre-judged on the assumption that you’re homogenous with your older schoolmates?

That’s the embarrassing truth about algorithms. They are prejudice engines. Whenever an algorithm turns data from the past into a model, and projects that model into the future to be used for prediction, it is working on a number of assumptions. One of the more basic assumptions is that the future will look like the past and the present, in significant ways.

You may think you can beat the odds stacked against you by your low-attaining school, and your lack of extra-curricular extras, and your having to do homework perched on your bed in a shared bedroom, but the algorithm thinks otherwise. Isn’t it strange that we are repelled by prejudice in other contexts, but accept it when it’s automated?

Until now. Now school students shouting “Fuck The Algorithm” have forced a Government U-turn. Some of them seem to think the whole business was an elaborate ploy to punish the poor, instead of a clumsy attempt at automated fairness on a population scale. But some of them must be wondering what other algorithms are ignoring their human agency and excluding them from options in life because of what others did before them: Car insurance? Job adverts? Dating apps? Mortgage offers?

Some disgruntled Further Maths students will no doubt go on to write better algorithms, but that won’t solve the problem. As the RSS wrote to the Office of Statistical Regulation, “‘Fairness’ is not a statistical concept. Different and reasonable people will have different judgments about what is ‘fair’, both in general and about this particular issue.”

You don’t need Maths, or Further Maths, or even a 2:2 in Maths and Statistics, to question what assumptions are being designed into mathematical models that will affect your chances in life. Anyone can argue for their idea of what fairness means. Algorithms, and what we let them decide, are too important to be left to statisticians.

I spent the sixth form in what was then a self-consciously radical comprehensive school in Milton Keynes. Stantonbury’s purported aim was to treat us like adults and to encourage us to believe we were part of an educational collective. The school was built, the teachers declaimed, on three Cs: Christian names, our own clothes, and carpets in every classroom. Once a month, on what was called Day 10, lessons were off and we did other activities, which we were supposed to initiate ourselves. Lower down the school, students – and we were all students not pupils – had hours each week of ‘Shared Time’, which was a strange hodgepodge of activities, with quite strong political undertones.

On my first day, I found my way to what a list on the wall said was my form class, only to be told that I wasn’t supposed to be there, because there was someone well established at the school who shared my name, and it was her class not mine. No-one, it seemed, knew I was starting, even though I had visited a few days before to meet the head of sixth form. By the afternoon, the form teacher had reluctantly accepted that she might have to accept me.

But then I discovered that one of the economics classes had been timetabled at the same time as subjects we had been informed, in the morning, that we could take alongside economics – because the economics teacher only wished to teach three lessons a week rather than the four offered for every other subject. What was supposed to be 12 teaching sessions a week was down to 10.

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That day was, I think, the first time in my life that I acquired a palpable sense of what competence means. There was knowledge about how to organise practical things – at my old school in Nottingham, for instance – and there was an absence of it – embodied by Stantonbury. What I learned over the next two years was just what consequences could follow from this distinction that now loomed in my mind.

My friend’s geography class was entered for one exam board but taught another board’s very different syllabus. She worked harder than anyone I knew. She was the only person in the class who passed and her grade cost her a place at her first and reserve choice universities.

One history teacher regularly turned up seriously late, and then, when he finally arrived, set about dictating to us from a textbook we had all been given at the start of the year.

When the economics teacher left during the first term of the upper sixth, we had not started macro-economics, which was half the syllabus. The school could not find anyone inside the school willing to replace her, even though there was a teacher who could, and said the class wasn’t big enough to make it worth appointing a new teacher. Eventually, after weeks of being left largely to our own devices, they sent someone to our classes who we called our babysitter. By this time my friend Joe and I had bought a macro-economics textbook and were teaching ourselves.

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Attempts to complain about these problems were met with at best indifference and at worst resentment. We were supposed to consider ourselves fortunate that we attended Stantonbury. To expect the school to be competent about timetabling, exam boards, or even teaching us at all when there was Shared Time to worry about, was implicitly deemed unreasonable and reactionary.

Yet Stantonbury’s idealism was not all hollow. My English teachers were brilliant. The two Pauls were the school’s ideals in action, and there were others like them. Without courting a cult of personality, they gave passionately of themselves in imparting their knowledge, and cultivated in us a desire and ability to think for ourselves. They taught us about the set novels, then expected us to go away and read the rest of the major work by those authors so we could come back with thoughts to discuss as their equals. Their classes were the most intellectually exhilarating educational experience I ever had.

When I left in the summer of 1985, I was more angered by the results carnage around me than grateful for what I had learned. I could in retrospect say that concentrating on what had gone wrong for others paradoxically represented an idealism that Stantonbury had, if not inculcated, probably sharpened. But it seemed more a simple matter of daily observation.

I knew my comprehensive school in Nottingham, for all its faults and with no ideological pretension about what it was doing, gave more to more children across the class spectrum than Stantonbury did or could. I also knew that where I lived many parents, for well-intentioned reasons, did not want to see how bad the worst of Stantonbury actually was. They wanted to believe, and I did not want my success to be another rationalisation for them, averting their eyes.

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During the 1990s, Stantonbury turned away from its radicalism, although for a long time there was still no uniform and I presume the carpets remained in place. In large part, I thought the changes were the inevitable consequence of realities from which the school had run. I hoped it would let fewer people down.

Some part of me now looks back with sadness. I was better equipped for university education than the great majority of the students I now teach, because I had both been taught to think for myself and been forced to take responsibility for spending a lot of time learning by myself. A few years ago, I asked one of my first years – who I knew was struggling in ways I have come to recognise as common – whether “school felt a million miles away”. “No,” he instantly responded, “much farther than that.”

Yet I also cannot see the contrast as a vindication of the Stantonbury way. My student’s time at university eventually turned out well. Stantonbury, by contrast, would not have served him in the slightest. I have come to realise and accept that I am indebted both to the school’s ideals and the failures that dwarfed them. But I was fortunate; many of my schoolmates were not. And educational ideals should not yield such haphazard outcomes.