How do you make something 10-times more lethal?
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BBC Sounds. Music, radio, podcasts. Hello and welcome to More or Less, your weekly guide to some increasingly idiosyncratic numbers. Thank you to everyone who emailed moreorless at bbc.co.uk because this particular programme is nothing but answers to the questions you sent in. Among them, what does the government mean when it commits to developing a ten times more lethal army?

Why was the much-missed sycamore gap tree said to be worth a strikingly exact £622,191? Are there really twice as many people teaching yoga as there are in the fishing industry? And is the number of workers per pensioner really falling from 4 to 3 to 2?

Actually, there is one question we took the liberty of asking on your behalf. When Donald Trump claimed the price of eggs had fallen by 400%, was he getting his numbers scrambled? Loyal listener Doug Kelly got in touch shortly after the launch of the UK's Strategic Defence Review to ask about the army's new target. The government's defence strategy commits it to developing a 10 times more lethal army.

Do we know how the relative lethality of an army is measured? Good question, Doug. We wouldn't want the truth to be the first fatality in a build-up of aggressive statistical rhetoric. To make sense of the claim, I spoke to Shashank Joshi, the defence editor at The Economist and a visiting senior fellow at the Department of War Studies at King's College London. What does it mean for an army to be ten times more lethal?

Well, last year, the Chief of General Staff, who's the professional head of the British Army, General Sir Roly Walker, said that the army would need to double its lethality by 2027 and triple it by 2030. So naturally, me and my fellow defence correspondents all asked, what does that mean?

And the answer we got basically was to say the idea is a British brigade, which is a formation of roughly 5,000 men, so a brigade combat team to be more precise, should be able to defeat a Russian formation that is about three times its size, which implies that currently it can defeat a unit about the same size.

So, ten times lethality would mean a British brigade could defeat an opposition unit ten times the size, which sounds like a lot. It also relies on being able to make a comparison between UK forces and those of the army it's fighting, which in this hopefully hypothetical case is Russia.

There's all sorts of problems with measuring this because right now British formations are severely understrength. We've given away lots of our artillery, in fact, pretty much all of our artillery to Ukraine. So we have vanishingly small amounts of it. Of course, on the other side, the Russian brigades are also moth-eaten, severely depleted. They're coming close to their millionth casualty killed or wounded in Ukraine. So we don't really know. But I suspect that there's weaknesses on all sides.

Is there a metric for lethality? Is somebody somewhere in the Ministry of Defence actually tracking a number and saying it's 1.1 or 1.4 or something?

The army will have a rough metric, which it will get by a combination of computer modelling and simulations, but also exercises in the field. And it will put up British units against opposition forces, against often American ones, for instance. And I remember being told, for example, about an exercise in California in 2020, where a company of British commandos demonstrated

perhaps a couple of hundred commandos, probably less than that, defeated a force of 1,500 American Marines by infiltrating their rear areas, by, you know, sort of hitting their logistics. And that was, again, seen as a way of enhanced lethality. And there will be a number or series of numbers that comes out of those exercises, such as the loss exchange ratio. How many of theirs did we kill for each one, losing one of ours? How easily, quickly did we defeat them?

that will come out of that that is quantifiable. But of course, in most cases, I suspect it will be classified. So lethality is potentially something that can be measured, although we may never know the result of that measurement.

And it does seem like increasing this number is possible. Imagine two equal forces, each with equal amounts of artillery, each with equal amounts of shells. But one force has drones over the target that can spot the enemy, can operate even where there's jamming so they can keep flying. And they have computer systems that can crunch very fast which gun should be firing at which target. That is the force that you would say is much more lethal than the equivalent force that doesn't have all those things.

Increasing lethality is definitely doable then, but increasing it by ten times? I think there's two problems with that. First of all, it just seems exaggerated, right? You can double your lethality, you can triple it by being incredibly good at finding targets, really good at hitting them, but ten times feels a little bit outlandish. And even the army itself, when it was talking about this last year, didn't.

didn't seem to see this as realistic. So I question that, and that's part one. I think the other part is the risk is you come to believe that an ever smaller force on your side can defeat an ever bigger force on the other side. And I think that's really dangerous. Let's say you defeat the first...

Russian combined arms army, what casualties have you taken in the process? Is your brigade still functional? And then what happens when the Russians send in another army and another one and another one? At a certain point, do you have enough precision guided missiles, even with the best reconnaissance strike system in the world, to keep taking them out on the battlefield? So famously, you know, Stalin said, quantity has a quality all of its own.

So can we measure lethality on an individual basis? So for example, could we say that I am more lethal than Evan Davis? It's possible for him to be 10 times more lethal than you at the individual level.

But that's not really what determines combat outcomes often. It's about the formation as a whole. So it's logistics, it's air power, it's intelligence, it's engineering. And that can really transcend the lethality of any individual competent. Right. So it's really all about whether the more or less team can beat PM. I think we know the answer. Thanks to Shashank Joshi of The Economist.

Last week, we drew your attention to the new trend among world leaders to have a background in maths. We mentioned Pope Leo, the new Romanian president, and possibly more controversially, President Trump.

The US president's unique take on maths was on show again this week in a discussion of one of America's big issues, the price of eggs since an avian flu outbreak reduced supply. Grocery prices are down. Everything. Remember eggs, eggs. We weren't going to buy another egg for the next 20 years. They were so expensive, right? Remember? You guys all hit me about eggs. Eggs have come down 400%. Everybody has eggs now. They're having eggs for breakfast again.

Now in this world of footballers giving 1000%, it might take you a moment to realise what a 400% reduction actually means. So let's give a simple example. Imagine a carton of eggs costs $10. A 50% price drop would take us down to $5. A 90% drop would take us down to $1. A 99% drop would take us to $0.10. If we take it further, to 100%, eggs would cost $1.

Zero. Truly free range. But Trump has managed to go beyond zero. He said the price of eggs has fallen by 400%. That would mean a $10 carton of eggs would now cost negative $30. If you went into a store, you wouldn't have to pay anything at all for a carton of eggs. You would instead be paid $30 to take them away. No wonder eggs are back on the menu at breakfast time.

If you want to move away from Trumpian imaginary numbers, it is true that the price of eggs has fallen since Trump's return to power. But the actual fall is about 40%. The reason for the fall in price? Reduced demand, replenished stocks of hens, less bird flu about, and increased imports of eggs. Thank goodness for imports.

That is the actual sound of a particularly notorious piece of pointless vandalism, the chopping down of the Sycamore Gap tree, the glorious sycamore tree next to Hadrian's Wall in Northumberland National Park. Daniel Graham and Adam Carruthers were recently found guilty of that act of criminal damage following a trial at Newcastle Crown Court. So we can now talk about the case.

Loyal listener Glenn has written to us because he was fascinated by a detail of the case, the value of the tree. In the background of the legal proceedings, lawyers have been arguing over this, but the initial valuation presented by the police to the court was a strikingly exact £622,191.

This is a very unlikely yet extremely precise amount and I am puzzled as to how it was arrived at with such confident precision. Fear not, Glenn, we are here to help. In the course of the court case, it transpired that this valuation was done using a system called CAVAT, C-A-V-A-T, which stands for…

That's Chris Neelan, who would definitely know, because he invented and developed the CAVAT system, which is… A way of valuing trees that could be used to help councils or other major tree owners to put a value on their trees. There are various ways to put a monetary value on a tree. Its wood has a value as timber, for example. There are also…

There are also ways of working out a tree's value as if you had to pay for its services, for cleaning air or sequestering carbon. But Chris's system does something else. You're asking a question which is how much would it cost me to replace the tree if I want to do it immediately?

Re-plant a hundred-year-old tree? Sounds beyond my gardening skills, certainly. It is technically possible to move very large trees and historically that has been done. People like Capability Brown and the early landscapers would move large trees because the Duke of so-and-so wanted a tree at this particular place. But a CAVAT valuation is not based on the actual cost of getting another 150-year-old sycamore tree and

capability browning it into place on Hadrian's Wall. Instead, it calculates a rough value by scaling up the cost from the kind of trees of varying ages that you can buy from nurseries. There's a relationship between the price at which nurseries will sell you a tree and the cross-sectional area of the stem of the tree.

That, of course, is just the start of the process. There's ten steps, but essentially it's four stages. And first is working out how big the tree is. You then put in various factors that are to do with the surroundings in which the tree now finds itself. Apply a discount if the tree isn't in great condition or is near the end of its life. And all of this you plug into a handy spreadsheet. It's actually a pretty simple process.

Chris has handed over the running of the CAVAT system to a group of tree experts, but he knows how it works and did a back of an envelope CAVAT analysis in the normal way for the Sycamore Gap Sycamore, based on very rough assumptions about its size and health. So, how close was it to 622,191 pounds? Drum roll please. I end up with something like 175,000 as the end result.

This figure is obviously very ballpark. We don't know the exact size of the tree or any of the details of the assessment, but if they're using the CAVAT system in the ordinary way, the number comes out at around this figure, certainly not three or four times higher. So whoever did the valuation clearly didn't do it in the ordinary way. The sycamore gap tree is of course

completely unique. I'm wondering how much your methodology allows the capture of the value of such a unique tree. The methodology is designed to value thousands of trees across largely urban boroughs. And it's designed to do that well. When you get extremes, like a tree in a forest or this tree, which is in a fairly remote area, but super visible,

It may be that we're not doing justice to that particular tree because the methodology isn't specifically designed for it. In short, Cavat is designed to value a nice sycamore tree lining an avenue in Leamington Spa or adorning a park in Darlington. It was never designed to value one of the most iconic trees in the world. So at that point...

you might bend the methodology and explain why you're doing it to allow for the unique attributes of the tree. Whether or not the methodology was bent in a justifiable way is yet to be determined. By the end of the court case, the valuation had already been revised down to £450,000 and it seems the judge may make a determination on the value during sentencing. Thanks to Chris Neelan.

Loyal listener Tim wrote in querying a stat he heard on TikTok. So what would you say then, Zoe, to people who say, well, we're full, we're full, we can't take any more people?

So if you look back to the 80s, we had about four working age people for every one pensioner. And at the current time, we have three working age people for every one pensioner. And that's dropping towards two quite quickly. And what that means is there's fewer people who are working and therefore paying tax, who are providing the services that we all rely on, and more people who have greater needs.

Tim wanted to know whether this was true and what this means for the economy and us. It is no secret that the UK population is getting older. This comes with some economic challenges, but that's obviously not the same as saying it is a bad thing. So, ageing is a real huge societal success. And as Professor Andrew Scott, the economist, said recently, no one fist bumps the air when they hear ageing society, yet it is one of humanity's greatest achievements.

That's David Sinclair from the Longevity Centre UK, an independent think tank that gives advice about how to navigate and benefit from an ageing society. The main thing we economists are concerned about, and what that TikTok clip was discussing, is something called the dependency ratio, specifically the old age dependency ratio. The basic premise is that if you have a higher number of workers to retirees, you have more tax coming in and a healthier economy.

Once that proportion falls, it all gets a bit iffy, economically speaking. It sounds quite a technical thing, but it's really quite simple. What it does is tells us how many people over 65 there are for every 100 people of working age. Very simple indeed. At the moment, as the video says, the UK has around three workers for every pensioner. But there's a catch.

It depends who does the counting. The OECD defines working age as 20 to 64, which would give the UK a ratio of 36%.

one pensioner for every three workers. But it's a pretty blunt tool. Many under 20s are still in education. The state pension is 66. We don't have a default retirement age anymore. And lots of people work into the 70s. So actually, the old age dependency ratio doesn't really help us any more understand who counts as dependent or working. Yes, because there are plenty of people of working age who aren't working, and quite a few people over the age of 64 who are working.

So it's the dependency thing that is really the misnomer, isn't it? And this is the problem. It's a pretty blunt tool. It's used mainly by economists and mostly is because we tend to pay more in taxes during our working years and draw more on public services like pensions and health care when we're either young or when we're old. So, you know, if there are fewer working age people, there's more financial pressure on the system.

As the birth rate is stagnating and we're tending to live longer, this pressure will keep growing. Other countries are already in trouble. Japan shows what this can look like. Their old age dependency ratio is already 55%. So that would be roughly...

one pensioner for every two people of working age? Yes, and it will go to one to one by 2050. So a huge shift. And governments need to worry because in the UK, around a quarter of public spending already goes on health and pensions. But in Japan, with a high ratio, you see government debt of over 200% of GDP. So there is some worry. It's tempting to imagine the UK state pension system as a kind of gigantic piggy bank.

People save into it all their lives and then withdraw money from it when they retire.

I am sorry to report that the giant piggy bank exists only in our dreams. Instead, the UK is paying pensions as it goes along, with the state pensions currently being paid out, being funded through the national insurance contributions currently being paid in, and other taxes if necessary. If you have fewer people paying national insurance and other taxes, you have less money to put towards the state pension. Hmm.

Time for some creative solutions. I want to throw a few possible solutions at you and just get your response as to

to what extent these would in fact solve our ageing population problem. So number one is encourage everyone to have lots and lots of children. So having lots of children isn't going to solve the challenges we have that come from ageing. This is partly because it takes 20, 25 years potentially for children themselves not to become dependent. But also there is a risk it becomes a bit of a Ponzi scheme that you have more children in order to just cope with more older people.

Having lots more children doesn't necessarily solve the problem because your dependency ratio potentially gets worse for 20 or so years, not better. The other problem with the increasing birth rate strategy is that the countries that have tried it haven't had significant results.

The second possible solution is immigration. So higher net migration can play a role in slowing aging, but it can't stop it. The ONS projections show that under high migration, the population ages half as quickly compared to a zero migration scenario. But even then, aging continues. Migration can buy you time, but it's not the ultimate solution.

Okay, so solution number three then is to empower people to work for longer. So we're all likely to need to start working a little bit longer. It's worth saying we're actually now working less than we did in the past in lots of different ways. We've seen a big growth in the amount of part-time working. Actually, the proportion of men working at 65 was actually higher in the 1960s than it is today.

Okay, I've suggested various solutions. The fourth one I wanted to suggest is

was purely financial. We changed the structure of pensions. I think we do need to look at making the state pension age a little bit later. If you use the OECD tool, at the moment we see about one pensioner for every three workers. And if we want to keep that the same going forward, we're likely to need to see our state pension age to be closer to 71%.

Alas, there is no simple answer to the economic challenge posed by an ageing population. More immigration of working-age people would help, until they also grow old. Having more children makes things worse for 20 years, before you eventually see a benefit. Or we could try higher taxes, lower pensions, and pensions that start later. None of this sounds like a winning political slogan.

Loyal listener Sarah wrote in to moreorless at bbc.co.uk to question a statistic she's seen swimming around on social media. The UK fishing industry is worth an estimated £1.1 billion. It directly employs 6,800 people, around the same as the employee headcount at Harrods

and just half the number of yoga instructors working in the UK. This claim seems to come from various sources, including an article in the New Statesman.

But why are people comparing yoga teachers to fisherfolk, or as the government calls them, fishers? Is it something to do with pike? Or is it a statistical red herring? Our sea correspondent Lizzie McNeill has been trawling through the data. Hi Tim. Well, this all centres around the ongoing argument between the EU and the UK over fishing rights, one of the slipperiest areas of the EU-UK relationship. How so? Arr, tell you a tale from the depths of the sea…

Let's just stick to UK coastal waters, actually. Fine. So a long, long time ago, before midnight, 31st of January 2020, the UK was part of the European Union. As such, it had been under the EU's Common Fisheries Policy, which gave all European fleets equal access to EU water.

Many people in the UK fishing industry were not happy with this agreement, as they argued the UK has a relatively large fishing zone compared to other European countries. Ireland. Ireland. So UK fishers have long felt their industry is being damaged by European vessels, and European vessels want to maintain their right to fish UK waters.

It's a long-standing political debate and often makes the news. Who can forget the Icelandic cod wars of the 70s and the Great Scallop War? You're making that up? No, it really is.

it really happened in 2012 off the coast of Le Havre. The French called it La Guerre de la Coquille. I hope we won. Tim, as you know in fishing, when two sides go to war, a point is all that you can score. Anyway, after Brexit we had a five-year deal which runs out in 2026 and the British government has just renegotiated a new agreement. Right.

So, Lizzie, where do the yoga teachers come into all of this? They really don't, at least not in the political negotiations. They've just been used as an example about why people think it's a bit nonsensical to risk other trade agreements just to protect one arguably small industry. Do I sense a bit of mockery of the ancient practice of yoga here? Perhaps. The point is, nobody has been demanding that we take back control of yoga or demanding a national yoga policy. But somehow fishing is political dynamite.

Okay, so how big is the UK fishing industry? Well, we export roughly 1.7 billion pounds of fish each year and import around 3.5 billion pounds worth. Interestingly, we export 80% of what we catch and we import roughly 70% of what we eat. So we spend more on the fish we buy than we earn from the catch we sell.

Government data said there were 10,356 fishers employed in the UK in 2022. 46% of them were in England, 40% in Scotland, 8% in Northern Ireland and 6% in Wales. However, these people aren't all full-time workers.

Data from the Marine Management Organisation, a governmental office, say there are just over 6,532 effective full-time employees. Which is similar to the claim that our listener Sarah heard. Yeah, but yoga teachers were much more difficult to pin down. Well, that's because they're so flexible and strong.

Anyway, we contacted the author of the New Statesman article for her sources. She sent us one report from a marketing company, IbisWorld, and another from Hiscox, which is an Anglo-Bermudan insurance provider.

Hiscock stated that there are more than 15,000 yoga teachers currently operating, and IbisWorld say there are 20,000, but they also included Pilates teachers in that count. There's definitely an overlap in the Venn diagram of yoga teachers and Pilates instructors, but they're not the same. As a Pilates princess, I agree. Not the same at all. And Tai Chi masters?

They need not concern us at the moment. I spoke to the British Wheel of Yoga, which is one of the original yoga bodies in the UK. They told me that industry reports on this topic tend to be estimates, as many yoga teachers hold multiple jobs, meaning they're not fully captured in census data. They

They also said that there is no reliable breakdown of how many yoga teachers work part-time, though it's likely the majority do, given the relatively modest pay in our profession. Any number we get is likely going to tell us more about the qualifications people have than whether or not their whole livelihood is supported by yoga.

Right, so it's a flawed comparison, but it is perhaps not surprising that there are more yoga teachers than fishers amongst the general population. You're right. Hard to catch cod and wheelchair. Both industries do have hotspots. Plymouth has the highest number of fishers in any British town with around 870, which is similar to the amount of yoga teachers teaching in Brighton. Classic Brighton.

I guess if you're from a small coastal town that relies on fishing, then any fishing deal is a big deal. Yeah. So basically, the claim is really just questioning why such a relatively small industry is causing so much international tension when it's really just a regional employment issue. Yes. And as anyone who knows where their towel is will be aware, the really key industry is telephone sanitizers. Thank you, Lizzie.

That's all we have time for this week. My side hustle, Cautionary Tales with Tim Harford, is available on BBC Sounds. And if you want to try some puzzling probability problems, head to bbc.co.uk, search for More or Less, and follow the links to the Open University. Please keep your questions and your comments coming in to moreorless at bbc.co.uk. We will be back next week. Until then, goodbye.

More or Less was presented by me, Tim Harford. The producer was Tom Coles, with Nick Barrett and Lizzie McNeill. The production coordinator was Brenda Brown. The programme was recorded and mixed by Neil Churchill. And our editor is Richard Varden. This is Dr Chris. And Dr Zand here. And we are dropping in to let you know about our new BBC Radio 4 podcast.

In WhatsApp Docs, we are going to be diving into the messy, complicated world of health and well-being because it can be confusing, can't it, Zant? That's right, Chris. The massive information out there can be contradictory, it can be overwhelming, and Chris and I get confused too. That's right. We get seduced by the marketing, the hype, the trends, so we want to be your guides through it. And I think it's fair to say, Zant, we are going to be getting personal. We're

We're absolutely going to be getting personal, Chris. What I want to do is bring in my own health dilemmas in the hope that we can help you with yours. Listen and subscribe to What's Up Docs on BBC Sounds.