Benefits vs minimum wage: Which pays more?

Summary

More or Less – Podcast Summary

Episode: Benefits vs Minimum Wage: Which pays more?

Date: June 24, 2026
Host: Tim Harford, BBC Radio 4

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Episode Overview

This episode investigates a widely-circulated claim by Conservative MP and former Chancellor Sir Jeremy Hunt that individuals on out-of-work benefits in the UK earn significantly more than those working full-time on the national living (minimum) wage. Presenter Tim Harford and reporter Nathan Gower clarify and analyze Hunt’s statistics, debunk misleading comparisons, and consult expert economists from the Institute for Fiscal Studies (IFS) to present a more accurate picture. The episode also explores, with signature wit and statistics, topics including wet bulb temperature warnings in the UK heatwave, the eye-wateringly complex mathematics behind the expanded World Cup, and the mathematical underpinnings of “Cymru Connection,” a game about social links among Welsh people.

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Key Sections & Discussion Points

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1. Jeremy Hunt’s Benefit vs Wage Claim

Main Points

• Claim: Jeremy Hunt stated: “If you're on the three main out of work benefits, you'll be earning between £31,000 and £46,000. If you're working full time on the national living wage, after tax, you get £22,000. It's just not possible to run a modern economy with those kinds of incentives.” (00:55)
• Nathan Gower investigates the methodology behind Hunt’s figures.

Analysis and Debunking

• Hunt’s Figures:

  • £31,000 out-of-work benefits in Newcastle, £46,000 in London.
  • These numbers assume maximum housing benefit, Universal Credit, and the top personal independence (disability) payments for single, severely disabled claimants.
  • “That difference between the two figures is because you get more housing benefit in London than in Newcastle.” – Nathan (02:12)

• Crucial Flaw: Double Adjustment

  • Hunt’s £46,000 is the pre-tax salary equivalent of the highest possible benefit receipt, not the actual amount received.
  • “But then he’s comparing this inflated, pre-tax figure to the minimum wage take-home AFTER tax. It’s a double adjustment.” – Tim Harford (03:40)
  • “Charitable and wrong... Jeremy Hunt does precisely the opposite. He compares it not to a pre tax salary, but to an after tax salary.” – Nathan (03:23)
  • Actual bank account figures in London (per year):
    • Benefits claimant: ~£37,000
    • Minimum wage worker (full time): ~£22,000

• Typical Cases Are Much Lower

  • Expert: Edwin Latimer, Institute for Fiscal Studies, says Hunt’s example requires severe disability, qualifying for higher levels of personal independence payments and health-related Universal Credit.
  • Edwin: “Around 800,000 people are in that group… about 8% of the out of work population.” (05:05)
  • Average benefit receipt for single, non-parents out-of-work: ~£15,000/year.
  • “Both the examples that Hunt sites get significantly more than that and are in the top 10% of single people receiving benefits.” – Edwin (05:57)

• Benefits Cap

  • Many claimants are subject to a cap: £15,000 outside London, £17,000 inside.
  • Disabled claimants (as in Hunt’s example) are exempt.
  • “So if they didn’t receive these disability related benefits, there'd be a hard cap on how much they can receive.” – Tim (06:45)

Memorable Quotes

• Tim: “Wait a minute, that is brazen… It’s a double adjustment.” (03:40)
• Nathan: “Nathan, the first part of the more or less dance is over… Now, while I always enjoy the sugar rush of a good debunk, is there something a bit more meaningful to say?” (06:55)

Timestamps

• Claim introduction: [00:55]
• Breakdown of Hunt’s figures: [01:45]–[03:18]
• Explanation of double adjustment: [03:18]–[04:00]
• Typical cases & benefits cap: [04:36]–[06:54]

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2. What Are Real Incentives?

Analysis of Moving from Benefits to Work

• Proper comparison: How much does someone actually gain—net cash—by moving from benefits into work?
• Typical scenario: Single renter in Newcastle, on moderate disability benefits.
  • Out of work, receives ~£16,000
  • If they move to full-time minimum wage: Receives £28,000 (£6,000 of which is from personal independence payments, permissible while working)
  • Without PIP, still better off in work: “They would be getting 22,000 or nearly £23,000 in earnings, and that would leave them better off than the £16,000 that they were getting out of work.” – Edwin (08:26)
• Conclusion: “They would still be better off in work than out of work. The gap would be smaller.” – Edwin (08:41)

Jeremy Hunt’s Response

• His office acknowledged the mistake: “Jeremy is grateful... he inadvertently used the net rather than gross salary for the national living wage.” (08:51)
• Tim: “I'm glad to hear he is correcting the record.” (09:00)

Timestamps

• Incentive discussion: [07:13]–[08:49]

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3. Wet Bulb Temperature and Heat Risk

Key Statistical Concepts

• Wet bulb temperature = a measure of the combined effect of heat and humidity on the human body’s ability to cool itself by sweating.
• Dr. Chloe Brimicombe explains:
  • “It's telling you how effectively you can cool yourself through sweating.” (10:36)
  • Critical survival threshold: 35°C
  • “A dangerous wet bulb temperature threshold is about 35°C. But for vulnerable people, this could be 30 to 32°C.” (12:48)
  • UK heatwave ~25°C wet bulb, which is “not a critical threshold for wet bulb temperatures.”

Public Misconception Addressed

• Social media claim: UK at 25°C “critical” wet bulb – not accurate for general population.

Timestamps

• Wet bulb temperature explainer: [09:36]–[13:58]

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4. Why Is the World Cup So Complicated?

Mathematics of Tournament Structure

• New format: 48 teams (was 32), not a power of two; 12 groups.
• “You need to have powers of two to keep things simple in the knockout stages.” – Oliver Johnson, University of Bristol (16:16)
• “To fill up the round of 32, you pick the 8 best third-placed teams from 12 groups.” (16:43)
• 495 combinations for possible third-place teams—hence, the massive, unwieldy table for scheduling, so repeat matches are avoided.
• “I think you do have to have some sort of system like this to deal with it.” – Oliver (18:48)

Timestamps

• Tournament math begins at: [15:53]
• The 495 combinations problem: [18:17]–[18:56]

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5. Cymru Connection: Probability and Social Networks in Wales

Game Premise

• Regular feature on Ellis James’ podcast: Try to find a mutual connection with a random Welsh caller in 60 seconds.
• “Success rate is about 48% on the radio.” – Ellis James (20:28)
• Mathematician Dr. Cat Phillips explains:
  • Using mean known names from study (~611): random overlap between two lists out of 2.25m Welsh people should be ~15%, three times less than the game’s 48% success.
  • “Ellis is in the massive tail category.”—i.e., a top social connector (23:39)
  • Real-world social networks cluster, meaning mutual friends (overlapping “clumps” of acquaintances) are more likely, especially in closely-knit, smaller communities.

Example Game Segment

• Live attempt at finding a connection. Initially fails, but outside studio they identify a common acquaintance—Steve Balsamo, a Welsh musician (26:16).

Mathematical Insight

• The higher-than-expected hit rate is explained by social clustering—friendship groups, families, professions, and geographic concentration dramatically boost the odds.
• “It’s easier if you’re in the right kind of cluster and much harder if you’re in the wrong kind of cluster.” – Cat Phillips (25:03)

Timestamps

• Social network maths: [21:06]–[24:54]
• Sample Cymru Connection round: [25:08]–[26:32]

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Notable Quotes

• Tim Harford:

  • “Wait a minute, that is brazen... It’s a double adjustment.” [03:40]
  • “The first part of the more or less dance is over… we usually unpack an eyebrow raising claim, only to find that it's stuffed full of unjustified comparisons.” [06:55]

• Nathan Gower:

  • “Charitable and wrong.” [03:22]

• Edwin Latimer (IFS):

  • “That puts them in the as severe as possible group you can be in within the benefit system for disability… about 8% of the out of work population.” [05:05]

• Dr. Chloe Brimicombe:

  • “A critical threshold for wet bulb temperatures is about 35 degrees Celsius. However, for vulnerable people... as low as 30 to 32.” [12:48]

• Dr. Cat Phillips:

  • “Most people don’t know as many [acquaintances as Ellis]. And then you have this massive tail of outliers.” [23:26]
  • “Clustering is... how many of your connections also know each other?” [24:22]

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Takeaways

• Politicians’ use of selective or misleading figures in the benefits-vs-wages debate can give a warped public impression.
• For the vast majority of claimants (those not in the most severe disability group), benefits are not higher than minimum wage work—and the incentive to work is preserved.
• Wet bulb temperature, while currently topical in the UK, is not at life-threatening levels yet.
• Complex event formats (like the World Cup group stage) require intricate mathematical planning when not using powers of two.
• Social network mathematics—and real-world clustering—means “everyone in Wales knows everyone else” is not just a joke, but mathematically explainable.

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For further questions or clarifications on today’s numbers, contact the More or Less team at [e-mail].

Transcript

[A]

Hello and welcome to More Or Less. We're the programme that clears up more statistical goal mouth scrambles than Cape Verde's goalkeeper. And I, aiming for a clean sheet as always, am Tim Harford. It's hot and damp and that means we can start talking about wet bulbs. But what is a wet bulb temperature? And could we hit critical levels? As a viral social media post has claimed, the World cup continues its majestic progress. But why are the permutations for the knockout round so extraordinarily complicated? And with the help of Ellis James, we explore why everyone in Wales seems to have a friend in common with everyone else. But first, at the start of June, Conservative MP and former Chancellor of the Exchequer Sir Jeremy Hunt was a guest on Radio 4's Start the Week, where they were discussing solutions to the UK's economic problems. In the discussion, he made a striking claim. You know, I think that we've gone very badly wrong when it comes to the welfare state. If you're on the three main out of work benefits, you'll be earning between 31 and 46,000 pounds. If you're working full time on the national living wage, after tax, you get 22,000 pounds. It's just not possible to run a modern economy with those kinds of incentives. We received a lot of emails about this, so Keen Bean and more or less reporter Nathan Gower stuck his hand up. Hello, Nathan.

[B]

Hi, Tim. So I got in touch with Jeremy Hunt and his office, offered to sit down, discuss it over a flat white.

[A]

That is a deep cut, Nathan.

[B]

One for the aficionados, Tim? No, I emailed them and they sent me a detailed breakdown of how they came up with these figures.

[A]

Well, that sounds very helpful.

[B]

It certainly was. Quick definition here. The national living wage Jeremy Hunt talks about is the official name for what we generally call the minimum wage for those 21 and over. But now for the benefits. These figures that he cites are for two hypothetical individuals who are both claiming three benefits housing benefit, universal credit and personal independence payments. Now, we'll come back to these benefits later, but let's start with the numbers attached to them. So one of these individuals lives in Newcastle, they're the £31,000 example. The other lives in London, they're the £46,000 one. That difference between the two figures is because you get more housing benefit in London than in Newcastle.

[A]

Ok, makes sense.

[B]

Let's focus on London for now. Jeremy Hunt's claim is that if you live in London and are on these three benefits, you'll be earning £46,000. But when I read his office's breakdown of the figure. It was clear that the figure is deceptive. Someone on those benefits would not receive £46,000 a year. They'd only get about 37.

[A]

So why did he say £46,000?

[B]

That's how much an employed person would need to earn before tax in order to have a take home income of 37,000. What the benefits claimant is getting.

[A]

That's strange, but it is hard trying to compare benefits and employed income because one subject's a tax and one isn't. So you got to make an adjustment somewhere. So maybe that's what he was doing. He's adjusting the benefits income so you can more fairly compare it to a pre tax salary.

[B]

Tim, that is you all over. Charitable to a fault.

[A]

Thank you, Nathan.

[B]

Charitable and wrong. As he says in the original clip, Jeremy Hunt does precisely the opposite. He compares it not to a pre tax salary, but to an after tax salary. That 22,000 pounds he talks about is how much you take home on the minimum wage of after tax.

[A]

Wait a minute, that is brazen. So he's adjusted the benefits income upwards, so it's like a pre tax salary, but then he's adjusted the minimum wage figure downwards, so it's a post tax income. It's a double adjustment.

[C]

J'.

[A]

Accuse. So Nathan, if you only did this tax adjustment once, which is the correct number of times, what would you get?

[B]

Let's look at how much you'd actually get in your bank account. So sticking with the London example, for the benefits claimant, they'd get about £37,000, while someone full time on minimum wage after tax would take home about 22,000 pounds, as Jeremy Hunt correctly said. Everything that we've said about the London example holds for the Newcastle one as well. Remember, a single person in Newcastle would get about £25,500 compared to the 22,000 on minimum wage.

[A]

So doing it right means that the differences shrink a lot. But the figures for the benefits are still higher than the figures for the minimum wage.

[B]

But that brings me on to the second big problem. The examples of benefit claimants that Jeremy Hunt has chosen are not typical of people who are out of work.

[A]

How so?

[B]

Well, they're not just out of work, they're also disabled. In fact, to receive the payments that Jeremy Hunt describes, they would have to be recognised as severely disabled. Edwin Latimer is a senior research economist at the Institute for Fiscal Studies, focusing on benefits policy and the low paid labour market.

[C]

So the example that Hunt gives each claimant has a very severe level of disability as assessed by the benefit system. So they have the higher levels of PIP for both daily living and for mobility. And they also have the health element of universal credit. So that puts them in the as severe as possible group you can be in within the benefit system for disability. And around 800,000 people are in that group. So and that's about 8% of the out of work population. So it's a relatively small group and it's a severe group. Although it is worth noting that that group has grown significantly since the pandemic. So before the pandemic was about 400,000 people in that group and it's doubled since the pandemic.

[B]

And because they're not your typical out of work claimant, the amounts they receive aren't typical either.

[C]

The examples that Hunt cites are both single people without kids. So thinking about that group of single people out of work without children, the average benefit recipient gets around £15,000 a year. And so both the examples that Hunt sites get significantly more than that and are in the top 10% of single people receiving benefits.

[B]

There's one other massive thing to mention here. Because these hypothetical claimants are on the top level of health benefits, they're exempt from the benefits cap. This is a policy brought in by the then Chancellor George Osborne in 2013 to limit how much money a household could receive in benefits. For a single adult with no kids outside London, it's capped at about 15,000 pounds. Inside London it's about 17,000.

[A]

So if they didn't receive these disability related benefits, there'd be a hard cap on how much they can receive and they'd get nowhere near near the figures that Jeremy Hunt's using.

[B]

Correct.

[A]

Okay, Nathan, the first part of the more or less dance is over. We've done what we usually unpack, an eyebrow raising claim, only to find that it's stuffed full of unjustified comparisons. Now, while I always enjoy the sugar rush of a good debunk, is there something a bit more meaningful to say?

[B]

I am all about the high fibre content, Tim. If we want to have a proper analysis of incentives when it comes to working versus being on benefits, we have to look at what happens to someone's actual income, the amount they get in their bank account as they move from benefits into work. Now you could try and do that for Jeremy Hant's examples, but these are people who have been assessed as having severe disabilities, so there's a good chance that many of them wouldn't be able to make that transition. Though hopefully some would. Instead, I asked Edwin to run the numbers for perhaps a more typical scenario. Someone who's still disabled, but less so. Okay, so take a single renter in Newcastle. They're out of work, and get a more moderate level of disability benefit as well as support for their rental costs. Their income from benefits would be about £16,000, but if they start working full time on the minimum wage, that income would rise to £28,000, £12,000 more. I should say that figure is based on them keeping the £6,000 that they were getting in personal independence payments. So that's a disability benefit, but it's not an out of work benefit. You can get it while you're working, but even without it, they're still better off. Edwin Latimer, again.

[C]

So they would be getting 22,000 or nearly £23,000 in earnings, and that would leave them better off than the £16,000 that they were getting out of work. So they would still be better off in work than out of work. The gap would be smaller.

[A]

Thank you, Nathan. And thank you to Edwin Latimer from the Institute for Fiscal Studies. Nathan, what did Jeremy Hunt have to say about all this?

[B]

His office told us Jeremy is grateful

[D]

to more or less for pointing out that in a relatively quick fire exchange, he inadvertently used the net rather than gross salary for the national living wage.

[A]

I'm glad to hear he is correcting the record.

[B]

Oh, he did have one more thing to say.

[A]

Hi, can I get a flat white, please? Not now, Jeremy. You don't need me to tell you that it is hot out there. Very hot. Temperatures have been in the high 30s in a central part of southern England and eastern Wales. But online, lots of people are talking about a different kind of temperature, still measured in Celsius, but called something a little bit strange.

[E]

Wet bulb temperatures on Tuesday, Wednesday and Thursday could exceed 25 degrees Celsius. Widely. This is the critical threshold for vulnerable populations, elderly infants or individuals with chronic illnesses.

[A]

So what is a wet bulb temperature? And are we really on the brink of a critical threshold for vulnerable people? To find out, I spoke to Dr. Chloe Brimicombe, a climate scientist and postdoctoral researcher at the University of Oxford.

[F]

When we take a temperature reading, we use a thermometer and this would be what we cool dry bulb temperature. Now, the difference of wet bulb temperature is it's basically the same thermometer, but we wrap it in a damp muslin cloth, similar to ones that you might use to sort of burp a baby. So it's basically a thermometer wrapped in this damp cloth. And it's an indication of how much moisture the air can hold, but also our ability to lose heat through sweating.

[A]

Think of that wet bulb thermometer as a proxy for a human being dripping with sweat and evaporating away heat. It is basically telling you how effectively you can cool yourself through sweating. In usual circumstances, even if the normal

[F]

temperature is high, when the relative humidity so the amount of moisture in the air is lower, the wet bulb temperature is lower because it can pass that energy into the surrounding air.

[A]

There are two things that could cause that wet bulb temperature to creep up. The first is a rise in the normal temperature, the dry bulb temperature. But the other is a rise in humidity. Humidity is important because if it gets too high, it's harder for us to lose heat through the evaporation of sweat. At an extreme situation of 100% humidity, you can't lose any heat this way.

[F]

So if the amount of moisture in the air reaches 100%, then the dry bulb temperature and the wet bulb temperature would be the same because you would no longer be able to lose any heat. You would no longer be able to cool down that thermometer through the moisture from the muslin cloth.

[A]

And that also would be an indicator that sweating is going to do you no good either.

[F]

Yes, you would not be able to cool your body down anymore through sweating.

[A]

So this combination of high temperatures and high humidity makes it harder to lose heat to evaporation, and that would be measured by a high wet bulb temperature. If the wet bulb temperature gets high enough, well, that can be fatal because there's no natural way to cool yourself down. Unless you find somewhere with air conditioning or you're able to immerse yourself in cool water, you'd simply die. But what level of wet bulb temperature is dangerous? We've seen a tweet getting quite a lot of attention this week saying that wet bulb temperatures are hitting 25 degrees in the UK this week and that that is dangerous for vulnerable people. So, first of all, are Wet bulb temperatures 25 degrees or are they likely to get there?

[F]

This week, the temperature of wet bulb is likely to be around 25 degrees Celsius in the UK this week. So already for Monday, there are observations of 22 degrees Celsius in the wet bulb temperature for the UK, so we are likely to reach that. However, that is not a critical threshold for wet bulb temperatures. So a dangerous wet bulb temperature threshold is about 35 degrees Celsius. However, there's a range depending on the type of person. So Those that are most vulnerable to heat. So these would be people that we've heard of, like the elderly or those who are children under the age of five. This could be as low as sort of 30 to 32 degrees Celsius. But the one that people quote is 35 degrees Celsius. And this is not being seen in Europe. It's not likely to be seen. We're reaching that threshold in parts of the world like Pakistan and India. And this is where, you know, temperatures in the sort of hottest season regularly reach 50 degrees Celsius or above.

[A]

The UK is not going to hit the wet bulb temperatures that test the very limits of human survival. That only happens in countries with very high temperatures and high humidity. But that's only one metric on which to judge the health impacts of a heat wave. As we saw in last week's program, heat waves do increase excess deaths as vulnerable people struggle to adapt to the changing temperature. It is still extremely hot out there and loyal listeners should take care. Thanks to Dr. Chloe Brimacombe. It's World cup season and here in the more or less house we've got our big World cup wall chart to tell us which teams will be playing who when next. Let's get it out on the table. It's a bit more complicated this time around. There are 48 teams instead of 32. So let's see who England will be playing if they come first in their group. It says here England could be playing the third place of either group. E, H, I, J. Okay, that's a little bit more complicated than previous years where each group winner would just play the second place of the next door group. Fortunately, I have a wall chart here which gives me all 495 third place combinations to tell me who England might play. Let me just get that out. Oh, my goodness. It is very complicated. Perhaps the head of mathematics at the University of Bristol and friend of the show, Oliver Johnson, can help me clear up this mess. Hello, Oliver.

[G]

Hello.

[A]

So is there a mathematical reason why some numbers of teams make things more complicated for a tournament and others do not?

[G]

Well, on a very basic level, it comes down to whether things are a power of two or not. Because once you get into the knockout stages, if you're going to end up with two teams in the final, you need to have four teams in the semi final, eight teams in the quarterfinals and so on.

[A]

Yes.

[G]

And so the challenge with that is if you start off with a number of teams, that's a nice power of two. The last time we had a World cup there were 32 teams. It all worked very nicely.

[A]

Yes.

[G]

Now we have 48 teams. 48 is not a power of two. And so things get more complicated.

[A]

Yeah. So we're trying to get to 32 teams from 48. We're trying to eliminate a third of the teams. Why is it so hard?

[G]

So the idea is that there are 12 groups. The two top teams go through, so that makes 24. And so then we need to fill eight more places in the draw. And so the way that we'll do that is we need to find the eight best teams of the 12 third place teams.

[A]

Those spots are decided on points. If the points are the same, they're decided on goal difference. And if the goal difference is the

[G]

same, well, there's a whole series of tiebreakers that are lined up. So they'll then look at goals scored. If they still can't split teams, they will go to the number of yellow cards and red cards, then they'll go to FIFA rankings.

[A]

So I now understand how the third place teams are picked, but our troubles are really only just starting because then we've got to decide who those third place teams play. But why can't we just draw pairs out of a hat if it's so hard?

[G]

Well, we could do, but the danger with that is you might end up with fixtures happening that have already happened. So, for example, Scotland play Brazil in the final game. It could be the case that you draw them out of the hat and then Scotland play Brazil three days later in the last 32, and that wouldn't seem very interesting. So we want to mix things up as much as possible. So the way that this draw is designed is that games that have happened once can't happen again until at least they get to the quarter final stage. So it's meant to keep it more interesting.

[A]

Right. But since we don't know which team is going to rank highest on the basis of goal difference and all of the things that they use, since we don't know which of the third place teams are going to rank highest, you have to have a lot of different combinations in order to separate them out from other teams they might be playing.

[G]

Yes. And so this is why FIFA have this very, very complicated table. If you go to their website, they have a table which has 495 ROSEN corresponding to each of the possible sets of teams that might come through, assigning where everybody will end up and where everybody will play in the next round after that. It's a magnificent thing.

[A]

And is there a better way to have done this, because it's a table with 495 entries, seems unwieldy. Have they missed some simple trick that would have sorted everything out?

[G]

I'm not sure that they have, to be honest. If you want to have 12 groups, unfortunately, I think you do have to have some sort of system like this to deal with it.

[A]

Thanks to Oliver Johnson. He's the author of Number Crunch. As we promised last week, the unexpected Welsh theme of this series is continuing. We've looked at Wales literacy levels and its surface area, but today we return to its quintessence, the Welsh people and the deep and abiding sense of social connection that knits the nation together.

[D]

Where are you from originally?

[B]

Tumble.

[D]

Tumble.

[F]

Okay.

[D]

What school do you go to?

[A]

Mytharova.

[D]

Okay. How old are you?

[E]

42.

[A]

Caricelleri. I was only there in year seven, then we moved. Here he is in his little college.

[D]

What happened after year 7? Where did you go then?

[A]

I moved to school of Preselli Griffith,

[D]

Ivan, the drummer who was in Publicum. Come on, mate.

[B]

Griffith.

[A]

Ivan I do know. Yay. Right, don't you ever, ever, ever, ever

[D]

send me down a meister of a cul de sac again. Year 7 is not good enough. Ellis.

[G]

Tone.

[E]

Tone.

[G]

Sorry, Tone.

[A]

That is comedian Ellis James on his five Live podcast. Ellis and John playing their recurring game Cymru Connection, in which Ellis attempts to find a mutual connection with a random Welsh caller to the show, all within a 60 second time limit. It's great fun, but it also raises some interesting questions about probability. We invited Ellis into the studio along with Dr. Cat Phillips and an innovation research associate at the University of Warwick and a digital maths communicator. And she's Welsh. First of all, what is Ellis's success rate?

[D]

It's about 48% on the radio.

[A]

About 48%?

[D]

Yes, I think it's 48%.

[A]

It's so 50 50. We'll call it 50 50.

[D]

Yeah, it's higher in real life. So occasionally I will talk to someone and I'll ask them where they're from and they'll say bristwith. And I won't get it in the 60 seconds, which is deeply frustrating and I feel like I've let Wales down. A thing I used to say was, yeah, but if we were on holiday and I was on a sun lounger and I had, you know, sort of limitless time, I would definitely get. Yeah, I would definitely get a connection. Because also I'm famously on the show, not very good into time pressure. I tend to crumble so cat.

[E]

Yes.

[A]

Wales is a small country. It's not that small. How is it possible that Ellis is able to do this? Can we think about it mathematically?

[E]

So we're going to go off like complete back to basics random chance here. So you can play the game of just people in Wales or. I think the stat that we pulled out was if you look at just the people who identify as Welsh in the ONS, you get about 2.25 million people that self identify in the UK. So if you start with sort of a random sample within that, let's say of those 2.2 million people, Ellis knows a subset. Any of those people are a win condition. If we pick a random person in Wales and Alice knows them, then we're done. So what we can say with the caller is they know a different subset of people in Wales. But what you're looking for is the odds of if the caller was to list out everyone they know, the odds of at least one of those people being the same.

[A]

And we're oversimplifying here because we're assuming that all of the friends that Ellis has and all of the friends that the callers have are themselves Welsh.

[E]

Yes.

[A]

What is the chance then that there is such a person that the lists overlap?

[E]

If I start looking. So we go with our 2.25 million people. Trying to find statistics for how many people know is quite hard. So there's been a few different studies done, and in 2013, a paper came out by McCormick et al that looked at a few different methods of measuring acquaintances, but the number that came out was the mean number of people that people know is 611 in the US based on this study.

[A]

Okay, so if you just had Ellis knows 600 people, 611, and the corner knows 611 and there's 2.25 million people, what then is the chance that there's overlap?

[E]

So just given those numbers, completely random uniform distribution, you're looking at 15%.

[A]

So 15%, 1 5.

[E]

Yes.

[D]

So I should be getting 15%.

[A]

15% should be your ceiling. It should be impossible for you to do better. Obviously, that's not describing the situation. So what's different? Is it just that Ellis knows a lot of people?

[D]

I get it, Rand.

[E]

So, yeah, there is a really interesting thing that came out with this study was that even though the mean was 611, the median number was lower by quite a lot. 480 odd.

[F]

Right.

[E]

But what that was meaning if you plotted the number of people that people knew, most people don't Know as many. And then you have this massive tale of outliers. So there's something like the top 10% of people know over 1500.

[A]

So you're saying Ellis is in the massive tail category.

[D]

Use the word elite.

[E]

I'm saying nothing. So if I pick the number 1500, because that was sort of the cutoff point for the lower end of the elite. Sorry, Ellis. That puts you at 33% elite wannabe

[A]

is what I'm hearing. But he's doing better than that. 33%. And again, 33% should be the maximum that Ellis can possibly achieve. And he's getting nearly 50% under time pressure. So either then Ellis knows thousands of people or there's something else going on.

[E]

Yes, which there is definitely something else going on.

[A]

So this was assuming that she's accusing you of something.

[D]

I'm dumping.

[E]

It's rigged.

[A]

I mean, the thing that would make it easier is some kind of clustering.

[E]

Yeah. So obviously the initial calculation was, like, if everyone is uniformly random, you're just picking people out of a bag. But when you actually look at social interactions and social dynamics, you have this network spread of different connections. So. So the clustering thing is how many of your connections also know each other?

[A]

Yes.

[E]

For example, families tend to all know each other. Not uniformly, but if you have a household of people, they all know each other. So instead of Alice needing to find a specific person in that house, he can just find someone in that house.

[A]

Does that make it always easier then to find a connection, or is it easier if you're in the right kind of cluster and much harder if you're in the wrong kind of cluster?

[E]

It's the second one. It's exactly.

[A]

I'm excited. I want to play this.

[D]

I want to see enormous pressure. Now, I've talked the talk.

[A]

We're all full of confidence. Okay, let's get ready to play Cymru Connection.

[D]

Age in school?

[E]

29. And Gower College.

[D]

Gower College in Swansea. Oh, which part of Swansea did you grow up in?

[E]

Mumbles.

[D]

Mumbles. I suppose you don't know what Catherine is.

[E]

Eaty Jonesy, unfortunately.

[D]

Die Hollywood. Her dad.

[C]

No.

[D]

Neither do I. What university did you go to?

[E]

Cardiff.

[D]

Cardiff. And you studied maths at Cardiff?

[E]

Maths at Cardiff.

[D]

Oh, I went to Cardiff University. Okay, let me think about this. Where did you live in Cardiff?

[E]

Catayes and then Heath.

[D]

Catayes and then the Heath. Okay, you don't know. No, that's not true. When you worked in Cardiff, where were you working?

[E]

I didn't work in Cardiff?

[D]

You didn't work in Cardiff. Okay, so you just worked in Warwick and Bath? And Bath. My sister went to Bath University. My friend Gareth studied maths at Bath. That's interesting.

[E]

Okay, bath maths. Uni, 2019-2020.

[D]

Oh, he was before that, Gower College. So where did you go to secondary school?

[E]

Bishopstone.

[D]

Bishopston.

[A]

Time's up.

[D]

Do we. Do you know of any connections? No, I'm definitely gonna get one. Bishop stun. So which pot swans you to grow up? The mumble.

[E]

Yeah.

[A]

Even then, Ellis would not let it lie.

[D]

What does your mother do for a living?

[E]

She was a lawyer in Neath.

[D]

A lawyer in Neath. Now I know a lot of criminals in Neith.

[A]

Alright, that's it. That's it. But then, at last, once they'd left the studio and were chatting in the corridor, they finally found a connection. 1 Mr. Steve Balsamo, lead singer of the now defunct Welsh country rock band the Stories. Our thanks to Dr. Cat Phillips, known as Kat Does Maths Online. And to Ellis James, co host of the Ellis and John podcast. And if you enjoyed Cymru Connection, they play it every week on the podcast, which is available now on BBC Sunday Sounds. That's all we have time for, but please keep your questions and comments coming in to more or lessbc.co.uk we'll be back next time, and until then, goodbye. More or Less was presented by me, Tim Harford. The producer was Tom Coles with Nathan Gower, Josh McMinn and Lizzie McNeil. The production coordinator was Brenda Brown. The programme was recorded and mixed by James Beard and our editor is Richard Varden. So, Alice Loxton. I'm here for the history.

[E]

Well, Ben Henderson. I like the formality and that's perfect

[F]

because we have a lot of history to share.

[E]

Why did tea become such a British obsession? How did English turn into the language we speak today? And yes, why do women's clothes, clothes still not have pockets?

[A]

Well, in our new podcast, Here for the History, we're investigating how stories from the past shape everyday life today.

[F]

Basically, the things we've all noticed but

[E]

never stopped to question.

[A]

Listen on BBC Sounds or watch on YouTube, just search for here for the History.