Supermarket price wars

Summary

Podcast Summary: More or Less – "Supermarket Price Wars" (BBC Radio 4, Dec 9, 2011)

Episode Overview

In this episode of More or Less, host Tim Harford and his guests dig into the numbers and statistical claims behind news stories and everyday conundrums. Topics include the supermarket price wars and their claims to be the cheapest, the odds of finding multiple double-yolked eggs, and sensational figures about Italian government spending. The episode is marked by its analytical, occasionally playful tone, with a firm grounding in statistical common sense.

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Key Discussion Points & Insights

1. Do One in Three Children Really Not Own a Book?

• [00:54 - 02:39]
  • Statistical Claim: National Literacy Trust said one in three children don’t own a book, up from one in ten in 2005.
  • Analysis:
    • The majority surveyed were secondary students, not little children.
    • Owning a book correlates with better reading, but 25% of above-average readers still reported not owning a book.
    • Only 3% said there were no books at their homes.
    • Younger children are more likely to own books, suggesting this reflects teenagers’ attitudes.
  • Takeaway: The headline is misleading; the issue may be less grave than reports suggest.

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2. Supermarket Price Wars: Can Every Supermarket Be the Cheapest?

• [02:39 - 09:05]

  • Investigative Findings:

    • Panorama revealed “bigger pack, better value” is not always true; some “now £2” labels actually conceal price increases; comparing price per unit is often impossible.
    • Example: At Sainsbury’s, a prepacked bunch of five bananas (£1) cost more than five loose bananas (42p).
    • Similar discrepancies found with red onions at Asda.

  • How Do Multiple Supermarkets All Claim They're Cheapest?

    • Guest Anthony Rubins (BBC Online Business Team):

      • Supermarket price-matching/refund schemes (e.g., Tesco vouchers if basket is more expensive than Asda, vice versa, etc.).
      • Each scheme relies on discount baskets – shoppers tend to buy what’s on offer, making their basket appear cheaper than rivals.
      • Quote ([03:31]):

        “If you go into any decent-sized supermarket, there’s probably someone in there at the same time checking prices for another retailer or supplier.” — Anthony Rubin

      • The price guarantees apply only to the specific items you buy, not a standardized basket.

    • Behavioral Economic Insight (Pete Lunn, author):

      • Quote ([05:39]):

        “That basket of goods that you've bought will probably have some of the discounted items in. ... But if you'd gone to the competitor supermarket and gone for some of their discounts, the basket of goods you would have left that competitor supermarket with is probably cheaper...” — Pete Lunn

    • Standard Basket Comparison:

      • Trade publication “The Grocer” compares a basket of 33 staple goods.
      • Over recent months, Asda is generally cheapest (~3% less than others), not the 10% claimed in promotions.

    • Cheapest Shopping Strategy:

      • Buying each item at its respective cheapest supermarket would save £5.61 versus buying at just one, about 10% off the total.
      • Downside: Time-consuming and impractical.
      • Quote ([08:37]):

        “If you take the cheapest price at any of the supermarkets... you would have saved about 10%. On the downside, you’d have to give up your day job and spend your days wandering between supermarkets.” — Anthony Rubin

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3. Eurozone Numbers: Italian Politicians' Chauffeured Cars

• [09:05 - 17:24]

  • Claim: Italian politicians use 30,000 executive cars, costing taxpayers €2 billion/year.

  • Fact-Check (Wesley Stevenson):

    • Numbers range wildly; some sources claim over 600,000 cars, but Italian government review found 72,000 government vehicles.
    • After excluding vans, lorries, pool vehicles: 5,000 exclusive chauffeurs, 10,000 pooled chauffeur-driven cars – about 15,000 total.
    • UK comparison: ~1,100 chauffeur-driven cars for national/local government, far less than Italy.
    • The €2 billion figure is for the entire Italian government fleet (72,000+ vehicles), not just politicians’ cars.
    • Quote ([14:24]):

      “No, that's their entire fleet of cars, all 72,000 of them, including all the service vehicles... that costs 2 billion a year.” — Wesley Stevenson

  • Deeper Analysis (John Prideaux, The Economist):

    • Italy's government not extremely more profligate than others (ran a primary surplus for years), but spending is wasteful.
    • Italian economic structure incentivizes inefficiency (example: taxi license market keeps numbers low, prices high, jobs scarce).
    • Quote ([16:17]):

      “...the system favors insiders who do very nicely from these arrangements... and outsiders who are doing badly. That's a big problem for Italy and one that the government will have to tackle, but it will be very unpopular when it starts to do so.” — John Prideaux

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4. The Odds of Cracking Four (Six!) Double-Yolk Eggs in a Row

• [17:24 - 24:46]
  • Listener’s Story: Jennifer Clark opens four eggs for a batch of profiteroles—all are double-yolked.
  • Initial Stat ([18:48]): According to the British Egg Information Service, 1 in 1,000 eggs is a double-yolker.
    • Multiplying (1/1000)^4 = 1 in a trillion chance for four in a row.
  • Why This Calculation is Wrong:
    • Double-yolkers come from young hens; eggs in a box likely come from the same flock (same age).
    • Among young hens, double-yolkers may be as frequent as 1 in 100.
    • Adjusted probability: 1/1000 x (1/100)^3 = 1 in a billion—still rare, but far less unlikely.
    • If buying large eggs, odds become even more favorable.
  • Live Demonstration ([23:35 - 24:15])**:
    • Jennifer cracks eggs 5 and 6 in the studio. Both are also double-yolkers.
    • Quote ([23:50]):

      “It’s a double yolk! Excellent. That’s one in a... one in a quadrillion you just hit.” — Tim Harford

    • Discussion on the effect of statistical clustering and sample bias (eggs from the same flock).

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5. Probability Puzzles: Football Draw

• [25:22 - 26:14]
  • Scenario: What are the odds of Manchester United drawing Manchester City in the cup (with 64 teams)?
  • Correct Calculation:
    • Probability any specified team faces United: 1 in 63.
    • Probability as first and second teams out: 1 in (64 x 63) ≈ 1 in 4,000—though this is a less meaningful statistic.
    • Quote ([26:14]):

      “You are precisely correct. With 64 teams in the draw, the chance that any particular team will face Manchester United is 1 in 63. And therefore the chance that Manchester City face Manchester United is also 1 in 63. Not that likely, but not that unlikely.” — Tim Harford

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Notable Quotes & Memorable Moments

• Price Checking as a Lifestyle

  “You could spend all your spare time trying to shave pennies off the price of your supermarket shopping, but some people do this for a living.” — Anthony Rubin ([04:01])

• Supermarkets' Tricks

  “Because you’ll usually have bought a couple of deeply discounted products in there, your basket is always going to look cheaper.” — Tim Harford ([07:39])

• Egg-citement

  “If you find a large double-yolk egg, and the other large eggs are from the same flock, then the chance that the other large eggs are also double yolkers becomes a lot more likely.” — Tim Harford ([22:36])

• On Statistical Skepticism

  "This is not the kind of statistic we like here on more or less." — Tim Harford ([18:59])

• Probability Playfulness (Football Draw)

  "Not that likely, but not that unlikely... But why that might be an interesting number is beyond me, Andy." — Tim Harford ([26:14])

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Timestamps for Important Segments

• [00:54] — Breaking down “one in three children don’t own a book”
• [02:39] — Start of supermarket price war discussion
• [03:31] — How supermarkets check each other’s prices (Anthony Rubin)
• [05:32] — How supermarkets’ price guarantees work (Pete Lunn)
• [07:39] — Summary of “The Grocer” basket comparisons
• [08:37] — True savings from shopping at all supermarkets
• [09:05] — Italian politicians’ chauffeured cars claim analyzed
• [14:24] — Cost of Italian government fleet vs. chauffeured cars
• [16:17] — Italy’s structural economic problems
• [17:24] — The double-yolked egg conundrum
• [18:48] — Probabilities from British Egg Information Service
• [20:47] — Why probability is much higher if eggs are from same flock
• [23:35] — Live double-yolk demonstration (eggs 5 & 6!)
• [25:22] — The probability of the football draw scenario

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Tone and Style

The episode uses a lively, skeptical, and humorous tone, with Tim Harford fostering lively exchanges and always emphasizing critical thinking about numerical claims. Listeners are entertained while being equipped with the tools to better interpret news statistics—and have a bit of fun with eggs and cake along the way.

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Bonus: Profiterole Recipe (Listener Feature)

[27:52] Lindsay's Chocolate Profiteroles recipe read by Jen—complete with quantities and baking advice (“...double yolkers work just fine”). The episode encourages listeners to submit recipe ideas with a numerical twist, keeping things engaging and interactive.

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Perfect for listeners who want the real story behind statistical claims and a bit of fun with their numbers.

Transcript

[A]

You're listening to a More or Less podcast from the BBC. For more information about the program, please go to the website BBC.co.uk radio4 hello and welcome to More or Less, the programme that takes a closer look at the numbers in the news and in life. Today we'll explain how all supermarkets can claim to be cheaper than each other at the same time without being slapped down for false advertising. And once you've done your weekly shop and got busy in the kitchen, what are the odds of cracking four double yolked eggs? One after another, we continue to scrutinise the enormous numbers emerging from the Eurozone crisis. Do Italian taxpayers really pay 2 billion euros a year for their politicians to be chauffeured around? But first, the National Literacy Trust said this week that one in three children doesn't own a book. Listener Helen from Nottingham wasn't convinced.

[B]

I heard the national literacy research that says that now one in three children don't own a book. And in 2005 it was one in 10 children. Well, this seems quite shocking, but I wondered what actually is going on. Does it matter if you don't own a book? How significant is that for your reading?

[A]

If you also heard the news this week that a third of children don't own books, you might have pictured little children who have no opportunity to get into reading because. Because they have no books at home. But on closer reading, this report isn't talking about little children. The research mainly surveyed children of secondary school age. And what about the reading skills of children who don't own books? The report's findings show that if you have books, you are more likely to be good at reading. But of the children who are identified as reading above the level expected for their age, still, 25% said they didn't own books. And while a third of children said they didn't personally own a book, only 3% of children said they lived in houses with no books. What's more, although the survey suggests things are getting worse, it's actually the younger children who are more likely to own books. So perhaps this report is really saying something more about teenagers attitudes to books. Another statistical story in the news this week has been the supermarket price wars. An investigation by BBC's Panorama program has revealed that not all bargains are quite what they seem. Among their findings were that bigger pack, better value is not always true, that a label that boasts now £2 neglected to mention that this actually represented a price rise and that it can be impossible to compare costs when pre packed fruit and veg is Priced per unit, while loose produce is priced per kilo.

[C]

At Sainsbury's, five bananas in a packet were £1. Buying five loose cost 42 pence. So they turned out to be almost a pound more expensive per kilo simply

[B]

for being pre packed.

[A]

It was the same with red onions

[C]

in Asda, just 86 pence per kilo for the loose ones on rollback. But £2.85 per kilo in a net,

[A]

well that'll be a surprise to some and perhaps not a surprise to everybody. But you know, I think there's something a bit more fundamental going on here amongst these price wars. The supermarkets are fiercely proud of their low prices. In fact, sometimes it seems that they're all claiming to be offering the lowest prices. But how can that be true? Anthony Rubens here from the BBC's online business team. Anthony, is that a supermarket barcode scanner in your pocket or are you just pleased to see me?

[D]

Neither, Tim. It's a smartphone, but you can use it as a price checking device and I can use it to check the barcode on, on this packet of chocolate biscuits that I brought in to endear myself with the more or less. Tea?

[A]

Yeah, they look delicious. Okay, so you're just photographing the barcode and what does it tell you?

[D]

Well, it tells me that I could have bought it for £1 in one supermarket or I could have got it at two for £2.50 in two other supermarkets.

[A]

Oh gosh, that's all very thrifty. Do you get out much, Anthony?

[D]

Of course not. I have small children. But you're right, you could spend all your spare time trying to shave pennies off the price of your supermarket shopping. But some people do this for a living. I've been told that if you go into any decent sized supermarket, there's probably somebody in there at the same time checking prices for another retailer or supplier.

[A]

I guess that makes sense. All the supermarkets love to make this big fuss about how low their prices are. So they need to keep an eye on their competitors, figure out what sort of marketing tricks they're using and where the discounts are. They're spying on each other.

[D]

Well that's true, but it's more than just that. Three of the big four supermarkets offer deals designed to keep you loyal, which require up to the minute information about the other supermarkets prices. So Tesco will give you vouchers for money off your next shop if your shopping is more expensive than it would have been at Asda. Asda will give you vouchers if your shopping is not 10% cheaper than Tesco, Morrisons or Waitrose, but with both, you have to enter details online. After you've shopped, Sainsbury's automatically gives you vouchers at the till if any branded goods you've bought would have been cheaper at Tesco or Asda.

[A]

So effectively they're all refunding the difference.

[D]

Exactly. I once got a voucher for four pence from Tesco and every little helps.

[A]

Ok, so this is really interesting, I think, and I'm sure loyal listeners will have spotted the puzzle. How is it that Tesco can offer to refund your money if Tesco isn't cheaper than Asda, while Asda also offer to refund your money if they're not a good 10% cheaper than Tesco and Sainsbury's say they're cheaper too. How can they all be claiming to be cheaper and offering cash compensation if they're fibbing?

[D]

Good question, and here's a hint at the answer from Pete Lunn, a behavioural economist and author of Basic Instincts.

[E]

I mean, if we accept that consumers are drawn towards discounts, then what happens? You go to a particular supermarket, you end up with a basket of goods and that basket of goods that you've bought will probably have some of the discounted items in. So it's probably the case that that particular basket of goods is cheaper than it would be in the competitor supermarket. But if you'd gone to the competitor supermarket and gone for some of their discounts, the basket of goods you would have left that competitor supermarket with is probably cheaper than it would have been in your first supermarket.

[A]

I love behavioral economists. Bless him. So did he just say that people buy more stuff when prices are low and less stuff when prices are high?

[D]

He did.

[A]

That's what I thought. But, you know, actually, Pete Lund's onto something here, isn't he? I mean, imagine I go to Asda and I find that butter and bread rolls and apples are on sale, so

[D]

I buy them while meanwhile I'm shopping at Tesco and see there's a deal on margarine, French bread and pears. So I buy them and I log

[A]

into the price guarantee site at Asda and it says, yup, we've checked, the stuff you bought is more than 10% cheaper than it would be at Tesco.

[D]

Meanwhile, the Tesco price check system is telling me that the stuff I bought is cheaper than it would have been if I'd bought it at Asda.

[A]

And both of these statements are true, but they don't really get Us closer to saying which supermarket is cheaper. Any ideas?

[D]

Well, the Grocer magazine publishes a weekly basket of 33 goods, including the prices at all the major supermarkets and 33 goods, because 33 is the average number of items in a shopper's basket, apparently. Now, these goods are chosen with some structure. There's always one alcoholic item, for instance, and a certain number of dry goods. And it has to be stuff you can buy at all the big supermarkets, but within that structure, it's basically random each week.

[A]

You're telling me it's random? What have you got there? Devil's food cake mix. What is that stuff?

[D]

Okay, Tim, so the selections aren't exactly straight out of your organic farmers market in Islington, but they're a good cross section and they're always changing. If you look back over the last six months at the Grocer Magazine's basket of goods and average the prices, you'll find that Asda is generally the cheapest, although not by as much as 10%. Actually an average of about 3%, followed by Tesco, then Morrisons and then Sainsbury's.

[A]

But these money back offers, they're a bit of a swizz, aren't they? I mean, they're supposed to make you feel you needn't bother checking prices, but in fact, because you'll usually have bought a couple of deeply discounted products in there, your basket is always going to look cheaper.

[D]

Maybe, but do you want to hear how to really get cheaper prices at the supermarket?

[A]

Oh, go on then.

[D]

Well, what really interested me was whether you could actually save a decent amount of money by systematically shopping around. Okay, so I fired up the more or less spreadsheet with the grocer 33 basket of goods.

[A]

Okay, you got a computer there, and

[D]

I've got on each of the lines, I've got the prices for each of these 33 goods at the five supermarkets. Asda and Tesco and Sainsbury's and Morrisons. And Waitrose is also listed on here.

[A]

So on your bargain hunting, you'd even have to go to Waitrose, which a lot of people think of as a more expensive shop.

[D]

Yes, it turns out that in this week's basket of goods, one of the items, it's a type of pizza, is cheaper at Waitrose than it was at any of the other four supermarkets. Go on.

[A]

So what did you find?

[D]

Well, if you take the cheapest price at any of the supermarkets, then in the end it turns out to come out £5.61 cheaper than it would do at any of the five individual supermarkets. In this case, it turns out that Asda would have been the cheapest of the five at £57.32 for this particular basket of goods. So you would have saved about 10%. On the downside, you'd have to give up your day job and spend your days wandering between supermarkets. But maybe you could get a part time job as a price checker and.

[A]

Well, thank you, Anthony Rubin. And there are some less than loyal listeners who seem to think that's exactly where I should end up. Here's Ben Falatt, who emailed more or lessbc.co.uk, after last week's programme. You tried to squeeze the world's population into your studio. You asked later editions to come on, breathe in and squeeze. Surely breathing in increases the size of the torso and one should be asked to breathe out to reduce one's girth. Well, thank you, Ben. The truth is, if you were surrounded on all sides by the flesh pot that is the Moneybox production team, you certainly wouldn't want them to breathe in your direction. Now time for another invasion of our new weekly feature, Eurostats. After last week's debunking of the number of Porsches owned in Greece, we move our automotive number watch to Italy to look at this claim made in the Telegraph. Earlier this year, the newspaper reported that Italian politicians are chauffeured around in expensive

[E]

Alfa Romeos, Maseratis and Audis with tinted windows. There are a staggering 30,000 of these executive cars and they cost the Italian taxpayer an estimated 2 billion euros a year.

[A]

Staggering indeed. But is it true? Our very own nosy Parker, Wesley Stevenson, has taken a look.

[C]

Thanks, Tim. I mean, if you are going to make obscure Thunderbirds references here, remember, if I'm nosy Parker, that must make you Lady Penelope.

[A]

My blue blood shows, Wes.

[C]

Yeah, and the puppet strings that the producer keeps yanking.

[A]

Enough. What have you found out, Wes?

[C]

Well, initially when I looked at this, I found an even more staggering figure that actually there were 629,120 of these cars, which was a figure put out by the Taxpayers association of Italy, I suppose their equivalent of the taxpayers alliance.

[A]

Over 600,000 cars. That's completely astonishing.

[C]

Yeah, but it's not true either. Rumours of these figures have been swirling in the Italian press for a while and this is what prompted a review by the country's Ministry of Public Administration. Now, this review found that there were 72,000 vehicles operated by central, regional and local governments.

[A]

Okay, so that's More than the Telegraph said.

[C]

Yes, but what you've got to do is strip away to the detail and you'll see that of these the majority are service vehicles. So pool cars, vans and lorries used for things like maintenance and deliveries and things like that. So when you strip these out, you're left with 5,000 chauffeur driven cars for exclusive use of politicians and executives and another 10,000 other cars which have chauffeurs but work on a pool basis, I suppose.

[A]

So 15,000 chauffeured cars, not 30,000. So the Telegraph was wrong.

[C]

Yeah, but to be fair on them, they were only repeating what the Minister of Public Administration in Italy was saying when this article was originally written. He did that classic politician thing of give people a high number, so when the number comes in it looks a lot lower.

[A]

OK. Now all these cars, 15,000 cars, are they all Maseratis, Audis and Alfa Romeos?

[C]

Well, the research doesn't state the make and models, but the implication is, is that they're pretty plush cars from the the Telegraph article. But what we do know are the engine sizes and only 20% are actually a 1.6 litre engine or above. So it's not really the case that they're all high powered luxury cars. Although I think the reason that this idea may dominate is that in central government 67% do have engines of above 1.9 litres. So most of the high profile cars are probably high end Audis, Maseratis and Alfas. But despite all the bad publicity, it hasn't stopped the Ministry of Defence who've just ordered 19 high end Maseratis.

[A]

OK, so 15,000, it's clearly a smaller number than 30,000, but it still does sound very big. How does it compare with the uk?

[C]

Yes, it's a difficult comparison to make because the numbers would actually take a long time to collate. But I've done my best. And if we start with central government, they have 195 ministerial cars with drivers. That's down from around 261 last year. But of course the Italian survey also includes regional and local government. So I asked the Scottish government, the Northern Ireland assembly and the Welsh government how big their fleets were and between them they have around 48 cars. I also asked the the Mayor's office in London and they haven't got any cars at all. But where we hit some difficulty is local government. Now there are 430 local authorities in the UK and we couldn't ask all of them. So what I decided to do was ask the biggest Birmingham now, they say they've only got two chauffeur driven vehicles, one for the leader and one for the mayor. So if you assume there are two for every council in the uk, is that reasonable?

[A]

I mean, Birmingham's the biggest. Surely most will have fewer than two.

[C]

Well, we don't know. And you may be right. County councils, for example, don't have mayors for a start. So you might assume that they only have one car instead of two. But we're just guessing. Maybe Birmingham's a bit thrifty as well. But just for the sake of producing a number, say there are two per local authority. That would make 860 local authority cars and just over 1,100 nationally, which is way off 15,000 that they have in Italy.

[A]

And does this huge Italian fleet of chauffeured limousines really cost 2 billion euros?

[C]

No, that's their entire fleet of cars, all 72,000 of them, including all the service vehicles and things like that, that costs 2 billion a year. But the Italian government clearly feels it's too much, because earlier this year the government vowed to cut it by €300,000 a year.

[A]

Profligate spending on cars sounds a bit like Greece. But are two countries and their predicaments similar? I've been talking about this with John Prideaux of the Economist.

[E]

The answer to that is yes and no. Really? In some ways, Italy hasn't been profligate over the last few years when particularly compared with a like the uk. If you look at the government finances, Italy actually ran a primary surplus. That's before debt payments are taken into account, from 1992, right up until the financial crisis hit. And Britain, meanwhile, ran rather large deficits. That said, Italy's government does spend an awful lot and spends it quite wastefully. And in that it does have rather a lot in common with Greece.

[A]

Now, do you think that if the Italian government cut back a bit on cars and so on, that would basically nail this problem?

[E]

I think fundamentally the frippery is like lots of government ministers. Having cars, while irritating to Italians, are not the root cause, but it's really they're symptomatic of a country that's lived beyond its means really for rather too long. Italy hasn't really grown for the past decade.

[A]

Is there a particular market or a particular industry you think really typifies Italy's woes?

[E]

When I was doing research for the Special report for the Economist, I spent a lot of time standing out on the street in Milan getting rained on and wondering why it was taking such a Long time for a taxi to come and pick me up. And so I became rather fascinated with the market for taxis in Italy and in Milan in particular. And taxis are really interesting because they typify, in a way, a problem with Italy and with its labor market. There was a study done that showed that In Milan in 2003, the cost of a taxi badge, so the kind of official license to be a taxi driver in Milan was €200,000. In Florence in 2006, it was €300,000 to become a taxi driver. And essentially what happens is the number of taxi driving permits is held down for the benefit of the people who have them already. And then when they retire, they sell them on to someone else, and it acts as their sort of pension potential. And so as a result, there's a strong incentive built into the system not to create more jobs for taxi drivers. And the result of that is a shortage of taxi drivers and frustrated journalists like me standing in the rain, getting soaked. If you multiply that across an economy, you get high unemployment and a system that favors insiders who do very nicely from these arrangements and are able to sort of protect their wages and have a comfortable retirement, and outsiders who are doing very badly out of this arrangement. And I think that's a big problem for Italy and one that the government will have to tackle, but it will be very unpopular when it starts to do so.

[A]

John Prideaux of the Economist and the immaculate and resourceful chauffeur of our show, Wesley Stevenson. You're listening to More or Less with me, Tim Harford, in association with the Open University. Now let's turn to cakes. Our colleague Jennifer Clark arrived at the office in a state of great excitement on Monday. Jen, tell us the story.

[B]

Well, great excitement, I don't think begins to cover it. I had to come and talk to more or less, because on Saturday at the weekend, my friend Lindsay was staying with me. She's a great baker. She offered to make profiteroles.

[A]

So I promised cakes. Are profiteroles a cake?

[B]

I would say profiterole is a cake like substance.

[A]

Okay, fine.

[D]

Yep.

[B]

I wouldn't wish to go to the wire on whether they're cakes or not, but for these purposes, I think they'll do as cakes.

[A]

Fine. Making profiteroles.

[B]

When she offers to make profiteroles, you say, yes, please. We went to the fridge to get some eggs, and away she went, cracking 1, 2, 3, 4, as per the recipe. And we were absolutely astonished because every single one of those four eggs cracked in sequence was a double yolker. So although we're both very keen bakers, and although you do quite often see a single double yolked egg in a box of eggs, neither of us could ever remember seeing four. So of course the question was, what are the odds of that and who are the people to answer it? More or less.

[A]

Yes, the magic words, what are the odds? So here to help me on my quest for egg clarity is Fiona Woods. Welcome, Fiona. And you've been speaking to the British Egg Information Service.

[F]

Yes, Tim, believe it or not, there is such a thing. They've informed me that one in every thousand eggs on average is a double yolker. Unfortunately, they couldn't tell me how they get to that figure.

[A]

This is not the kind of statistic we like here on more or less.

[F]

I know, I know. I think we have to give them the benefit doubt though, Tim.

[A]

I suppose so. It would be a minor tragedy if the British Egg Information Service was unable to supply useful information about British eggs, wouldn't it?

[F]

A minor tragedy it would be. So let's assume they're right, that one in a thousand eggs are double yolkers. The obvious next step is to say that if the probability of finding one egg with two yolks is one in a thousand, then to find the likelihood of discovering four in a row, you would simply multiply the probabilities together 4 times 1000 to the power of 4 brings us to the grand total of 1 trillion.

[A]

This is a new school American style trillion. Yes, with 12 zeros. Not an old school British trillion with 18 zeroes.

[F]

Yeah, new school, Tim. And by the way, it's called short scale. And the UK switched to short scale trillions in 1974.

[A]

It was a bit recent for me, but okay. You learn something every day on more or less. Wow, one in a trillion. Pretty unlikely, Jen.

[B]

Yeah, I mean, I've certainly not cracked a trillion eggs, but four out of that trillion seems like quite a high number. But I know the way you work on more or less and I doubt very much that's the end of the story.

[A]

No, it isn't, Fiona.

[F]

How right you are, Jen. The point is that you can't just multiply a thousand together four times and say the chance of getting four straight double yolked eggs is one in a trillion.

[A]

Right. And the reason you can't is because that ignores the possibility that double yolked eggs might be coming in clusters. Now, I've been talking to an expert to explain where double yolked eggs come from. So his name is Richard Kempsey. He's agriculture director at Stonegate, which supplies eggs to supermarkets. And he says double yolked eggs almost always come from a particular kind of hen. A hen of a certain age, a young hen, one that's 20 to 28

[E]

weeks old in reality. It gets its mechanics just slightly wrong. You've got a young bird and it comes to lay its first egg, and it releases more than one eg. So it's the ovicle coming out of the ovaries, and there's two egg yolks which are released. So two ovicles released at the top of the oviduct. With a hen, it takes about 20 hours for it to descend down the oviduct. So in that process, those two egg yolks go down the oviduct, and at the end, which is quite natural, it forms a shell around the egg and out pops a rather large egg with two egg yolks in it.

[A]

Wow. So we've determined these young birds, they're far more likely to lay double yolked eggs. And in fact, our expert says that one in every hundred of these birds eggs are double yolkers. And that's a lot more common than the one in the thousand figure we started with.

[F]

And Tim, I've also found out that the eggs in a box are very likely to come from the same flock, and that flocks are usually around the same age.

[A]

Okay, interesting. So if that's true, we can say that while the chance of finding one double yolk egg, maybe one in a thousand, the chance of finding a second is quite a lot more likely. It's more like one in a hundred. And the same goes for the third egg and the fourth egg. So taking all that into account, we can do the sum. It's a thousand times a hundred times 100 times 100, and that's a billion. The probability of finding four eggs in a row is one in a billion,

[F]

which, to be fair, is still a very big number.

[A]

Well, yeah, but a trillion's a thousand times bigger. And there are a lot of egg cartons in the world. I mean, the. The difference we've just discovered there is the difference between something happening, say, roughly every week and roughly every 20 years.

[F]

And there's another big factor we need to consider the size of the egg. Double yolk eggs are far more likely to be of the large variety. Yet the birds that lay these eggs, young hens, don't usually lay large eggs. Most are small.

[A]

So if you find a large double yolked egg, and, you know, the other large eggs are from the same flock, then the chance that the other large eggs are also double yolkers becomes a lot more likely. I guess in the most extreme case, you'd say if the first eggs are double yolker, all the eggs are double yolkers.

[F]

I think that's taking it a bit too far, Tim. But this is the perfect moment to put our theory to the test and crack the remaining eggs.

[A]

Fiona, I think you're right. And I didn't mention that Jen actually has brought the carton with the two remaining eggs with her. So, just to recap on the naive reading, Jen, the chance that that fifth egg is a double yolk is just one in a thousand. And it will make your double yoke streak a one in a quadrillion chance. If it's a double yoker, and if they're both double yokers, the chance they're both double yokers is one in a million. And that would make your six double yoke streak a one in a quintillion chance. In other words, there's absolutely no chance. But actually, based on what Fiona and I have been learning, well, I wouldn't be totally surprised. Do you want to do the honours?

[B]

I'll tell you what, hearing those numbers, I'm rather wishing I'd placed some bets before I came into the studio. Okay, here we go. This is egg number five.

[A]

Okay, come on.

[B]

Are we ready?

[A]

One in a thousand Chills.

[B]

I need a drum roll.

[A]

Yeah, okay.

[B]

Okay, here we go. It's a double yolk.

[A]

It's a double yolk. Excellent. That's one in a. One in a quadrillion. You just hit.

[B]

I should go and buy a lottery ticket, shouldn't I? This is absolutely what I should do today. Okay, this is the final. This is egg number six.

[A]

This is all live, folks. We had no idea it was going to be a W cut. Okay, six egg.

[B]

Are we ready?

[F]

We're ready.

[B]

Okay, here we go. This is quite tense. It's a double yoker.

[A]

There you go. The amazing beauty of statistics. Thank you very much. Jen, any thoughts on that?

[B]

It's been an absolute pleasure. And I am just going to place a bet, something I don't normally do, but it feels like it might just be that kind of day.

[A]

That's amazing. You know, only problem for you, you look in shock.

[F]

Actually, I am astounded. But, you know, I should always trust your math.

[A]

Well, I wasn't terribly convinced they were both going to be double yolkers, but there you go. Our main problem now is going to be Convincing anybody that that wasn't a setup. And it really wasn't.

[F]

We promise.

[A]

And we will put Jen's friend's profiterole recipe as a special treat for our podcast subscribers. By the way, the podcast is available from BBC.co.uk more or less. Actually, we were wondering, what with the porcini and lemon risotto last week and the profiteroles this week, do any loyal listeners have any recipes they'd like to share which have some numerical or statistical connection? As we've demonstrated, the connection is allowed to be extremely tenuous. So please send in your recipe ideas. And Fiona, Jen, thank you. And we just have time to settle a domestic dispute between listeners, Andy and Renner.

[E]

We were watching the television the other day when the results were coming up for the draw of the football and saw that Manchester United had been drawn against Manchester City. And the young lady on the television said, what are the odds of that happening? And I thought, that must be pretty massive odds for those two teams to be drawn against each other. And I said, well, that must be pretty big.

[B]

But my wife, I said that it's not that big at all, because if there's 64 teams, then the chances of it happening are one in 63, because the second team has only a choice of 63 other teams.

[E]

And I said, no, no, no, it was longer than that. So we ended up basically agreeing to disagree just to keep the peace.

[A]

Well, Renner, in my view, your only error was to agree to disagree. You are Precisely correct. With 64 teams in the draw, the chance that any particular team will face Manchester United is 1 in 63. And therefore the chance that Manchester City face Manchester United is also 1 in 63. Not that likely, but not that unlikely. And of course, there's a much larger chance that the draw throws up at least one tie with some kind of significance. For instance, Arsenal matched with local rivals Tottenham. My sense is that the probability Andy is trying to calculate is Manchester United vs Manchester City in a particular spot in the draw. For instance, United at home as the first team out of the bag. The chance of that is 1 in 64 times 1 in 63, or about 1 in 4,000. But why that might be an interesting number is beyond me, Andy. And that's all the marriages we have time to undermine this week. But we'll be back next week with all the statistics behind the Occupy the City movement and a man who's trying to corner the world market in a particular 1980s plastic toy and much more besides. Do please send us your numerically inspired kitchen creations by dropping into our [e-mail] more or less or emailing us directly at more or lessbc.co.uk even if you don't have the recipe for some kind of delicious cake, we'd still love to hear from you. Until next week, Goodbye. More or less was presented by me, Tim Harford of the Financial Times. It was produced by Ruth Alexander and the editor was Richard Varden. And as promised, here's Jen with her friend's recipe for profiteroles.

[B]

Lindsay's Chocolate Profiteroles yum yum yum. 150 grams of plain flour, a pinch of salt, 300 milliliters of water, 100 grams of butter and four standard eggs well beaten, although double yolkers work just fine. First, sift the flour and salt together. Place the water and butter in a saucepan and heat gently until the butter melts, Then increase the heat and bring to the boil. Remove the pan from the heat and quickly pour in all the flour. Beat well for about 30 seconds, or until the paste is smooth and leaves the sides of the pan clear, but don't over beat. You'll know when it looks right. Cool slightly and add the eggs, gradually beating well until the mixture is smooth and glossy. Cover the pan and leave until cold. Place the mixture in a piping bag and pipe 36 equal amounts of choux pastry in ball shapes well apart on greased baking trays. Or just use a spoon and dollop the number of profiteroles you want well apart on greased baking trays. Bake in a hot oven 200 degrees centigrade or 400 degrees Fahrenheit for about 10 minutes. Then reduce the temperature to 180 degrees centigrade or 350 degrees Fahrenheit for a further 20 minutes, or until the profiteroles are crisp, golden and puffed. Remove from the oven, make a small slit in each bun to release the steam and return to the oven for a further five minutes to dry out. Let them cool on a wire tray. Once they're cool, fill with whipped cream, drizzle with chocolate sauce and enjoy.