Tag Archives: Maths

Covid, Health, Maths, Politics

Boris Johnson’s massive maths mistake over Covid deaths is an embarrassment

This post is adapted from my Indy Voice article of the same title originally published on 02/03/23

Yesterday many of us woke up to read headlines about Matt Hancock having ignored scientific advice about protecting care homes in the early stages of the pandemic (though a spokesperson for the former health secretary has since said that the reports are “flat wrong”, and that the interpretation of the messages’ contents is categorically untrue).

The story arose from a cache of over 100,000 WhatsApp messages that had been leaked to the Daily Telegraph.

Buried in WhatsApp conversations between then-prime minister Boris Johnson, his scientific advisers and Dominic Cummings, is an exchange which is arguably even more worrying than this headline-grabbing story.

On 26 August 2020, Johnson asked the group:

“What is the mortality rate of Covid? I have just read somewhere that it has fallen to 0.04 per cent from 0.1 per cent.”

He goes on to calculate that with this “mortality rate” if everyone in the UK were to be infected this would lead to only 33,000 deaths. He suggests that since the UK had already suffered 41,000 deaths at that point, this might be why the death rate is coming down – because “Covid is starting to run out of potential victims”.

In fact, death rates were still coming down as a result of the earlier fall in the number of cases brought about by lockdown. Already though, by the time this conversation took place cases were rising again in the early stages of what would become a catastrophic second wave.

Based on his faulty maths, Johnson questioned “How can we possibly justify the continuing paralysis to control a disease that has a death rate of one in 2,000?”. He was suggesting that anti-Covid mitigations could be relaxed at perhaps the worst possible time. His whole argument was based on two fundamental misunderstandings.

His first mistake was a mathematical one. Johnson had seen the figure 0.04 in the Financial Times and interpreted it as a percentage. In fact it was a fraction – the number of people who were dying of Covid-19 divided by the number of people testing positive. This is known as the case fatality ratio (CFR).

At 0.04 (or 4 in 100), the CFR calculated by the Financial Times was 100 times larger than Johnson had suggested – it was actually four per cent, not 0.04 per cent as he believed.

The chief scientific adviser Patrick Vallance patiently explained this to Johnson: “It seems that the FT figure is 0.04 (ie four per cent, not 0.04 per cent)”. Johnson replied “Eh? So what is 0.04 if it is not a percentage?” at which point Dominic Cummings had to jump in and break it down into even simpler terms. Even then the messages show no acknowledgement from Johnson that he had understood.

The other mistake that Johnson made in his calculation was to confuse the case fatality ratio with the infection fatality ratio (IFR). The IFR is the number of people who die from Covid-19 as a proportion of those who get infected.

Though they may sound similar, there is a big difference between the CFR and the IFR. In the CFR we divide the number of Covid deaths by the number of people who test positive. However, in the IFR we divide by the number of infected people.

Early on in the pandemic, when testing was not readily available, the number of people who tested positive was much lower than the number of people who were actually infected with the disease. Because of this, the CFR overestimated the IFR.

By mixing up percentages and proportions, Johnson’s calculation actually underestimated what the figure should have been by a factor of 100. If he had had the CFR correct he would have come to a very different conclusion – that over 3 million people in the UK would die.

In reality, to do this calculation you need the IFR, not the CFR. With a 1 per cent IFR (closer to the true figure), the correct version of Johnson’s simplistic calculation would suggest that 660,000 people might have died in the UK if everyone became infected – 20 times more than Johnson’s mistaken numbers suggested.

It is almost unimaginable that the leader of the United Kingdom could allow his thinking to be informed by calculations which contained such rudimentary errors. Mistaking the CFR and the IFR would perhaps have been understandable in the early stages of the pandemic, but this conversation took place long after the first wave had subsided.

To have made this mistake over six months into the UK’s pandemic response is indicative of a leader who has failed to fully engage with even the most basic science required to make important decisions surrounding the pandemic. It perhaps explains Johnson’s reluctance to institute stronger mitigations in the autumn of 2020 as were called for by his own scientific advisors.

Even less forgivable is his mathematical mistake, which is indicative of his failure to engage in scientific thinking more generally. At a time when other country’s leaders were going on national television and defining important epidemiological concepts the masses, we endured a prime minister who was making basic mathematical errors the likes of which most 11-year-olds would not succumb to.

When it came to scientific literacy – such a crucial currency in the response to the pandemic – this incident suggests we suffered under the worst possible leader at the worst possible time.

Immigration, Maths, Politics, Uncategorized

Suella Braverman’s numbers on small boats are all wrong

This post is adapted from my Indy Voices article of the same title originally published on 13/03/23

Upon unveiling new plans to deter people from crossing the Channel in small boats, Suella Braverman claimed that 100 million people could already be on their way to seek asylum in the UK.

In her speech to the commons, the home secretary claimed: “There are 100 million people around the world who could qualify for protection under our current laws. Let’s be clear. They are coming here.”

An article she wrote the following day repeated the claim and went further suggesting that there were “likely billions more” eager to come to the UK if possible.

In reality, just 85,000 people have arrived in the UK in small boats across the Channel since 2018 – just 17,000 a year on average.

Even the relatively high 45,000 people who arrived in the UK last year to seek asylum by crossing the channel on small boats pales into comparison – at just 0.045 per cent of Braverman’s touted 100 million figure. In total, around 90,000 people applied for asylum in the UK in 2022.

To set the record straight on the numbers, of the 100 million people that the United Nations High Commissioner for Refugees estimates are displaced around the world, only around a quarter have actually left their home country.

Estimates vary, but around three-quarters of displaced people who do leave their own country remain in a neighbouring country. Surveys consistently demonstrate that the majority of refugees would like to return to their homes as soon as it is safe for them to do so.

Historically, we have relatively fewer asylum seekers applying to the UK, compared to our population size, than many of the EU nations. In 2021, there were around nine asylum applications per 10,000 people in the UK.

Across the rest of the EU, this figure was 14 applications per 10,000 residents, placing the UK below the average in 16th place. In 2022 the UK received 75,000 asylum applications. Germany received almost 250,000.

Despite these facts, the home secretary sees it to her advantage to overinflate the potential scale of the number of people arriving in the UK. She believes that the potential threat posed by this hypothetical deluge justifies legislation which, many believe, is in contravention of international law.

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The huge numbers being bandied about are hard for us to get a handle on. Many people struggle to visualise the difference between thousands, millions and billions. Even if they know that a billion is a thousand times more than a million and a million is a thousand times more than a thousand, when numbers get really large they can go beyond the scale of things we are able to relate to. Everything just seems big.

One way to comprehend the difference is to think about time – a phenomenon which we experience both on very short and very long scales. A hundred thousand seconds is a little over a day. You can go 24 hours without eating no problem.

A million seconds is about 11.5 days. Not eating for that long would push most people to the limits of their willpower. A billion seconds is about 35 years. Fasting for half a lifetime is patently impossible. The scale of the problem changes significantly as the numbers ramp up.

Here’s another way of thinking about it. If I give you £1,000 a day it will take just 100 days for you to amass £100,000. In three years you’ll become a millionaire. To become a billionaire, however, will take 2740 years.

When we compare the 100 million displaced people in the world to the fewer than 100,000 people who claimed asylum in the UK last year, at less than 0.1 per cent the number of asylum seekers doesn’t seem so large.

When we start to place the figures in context, it seems possible that by overplaying the scale of the situation to the public – by bandying around figures of hundreds of millions or even billions – Braverman’s tactic runs the risk of backfiring, making the scale of current asylum applications look eminently manageable.

Even the 45,000 people who came to Britain to claim asylum via boats across the channel represent only around 0.07 per cent of the current population of the UK.

Even when placed in context though, we must be careful not to focus too heavily on the numbers which have grabbed the headlines. We must remember, at its heart, that this story is not about numbers. It is about people. Often desperate people fleeing the traumas of their past and hoping to build a better life for themselves.

By denying them the protections afforded under international law; by breaking the European convention on human rights, the UN convention on refugees and the universal declaration of human rights – all of which the UK was a founding member of – we are betraying the legacy that our country fought so hard to secure.