Fact-checking US gun crime statistics

Summary

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More or Less – Fact-Checking US Gun Crime Statistics

BBC Radio 4
Host: Tim Harford
Original Air Date: December 21, 2012

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Episode Overview

This episode of More or Less explores the statistics surrounding recent debates about gun crime in the United States, particularly following a tragic school shooting. The team dissects viral claims about international gun deaths, fact-checks figures cited by media personalities, and engages with questions around the reliability of death statistics. The episode also debunks misleading claims about the average age of first-time homebuyers, investigates the real risk of deer collisions in the UK, and delves into the mathematical art of juggling.

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Key Segments and Insights

1. Debunking Viral US Gun Death Statistics

[00:42 – 05:47]

• Context: In the wake of a school shooting in Newtown, Connecticut, viral messages comparing gun deaths internationally (e.g., "Handguns killed 48 in Japan, 10,728 in the US...") began circulating.
• Investigation:
  • The quoted numbers do not match official statistics from the UN or the FBI.
  • FBI data for the previous year:
    • 12,664 firearms homicides in the US (not 10,728).
    • England and Wales had 60 gun killings, not 8 as viral claims suggest.
    • Handgun-specific deaths also differ: e.g., 6,200 in the US (not 11,000), 94 in Canada (not 52), 30 in England and Wales (not 8)—with many countries not reporting complete or up-to-date data.
• Source of the Numbers:
  • Joseph O’Leary from Full Fact traced the viral figures back to a 1980s poster titled “Stop handguns before they stop you,” based on 1979 statistics.
  • Quote:
    • Joseph O'Leary: “There’s a very, very small print on the poster that says based on 1979 statistics.” [03:32]
  • The figures were accurate for their time but are now over three decades old.
• Key Point:
  • While proportions between countries remain similar, using outdated figures distorts current debate. “If we’re going to be having a debate about this, we should be using the right figures, or else these Chinese whispers will continue and eventually we’ll just have a completely distorted impression of how serious the problem is.” — Joseph O’Leary [04:21]

Notable Moment

• Ben Fogle’s viral misleading tweet was retweeted over 3,600 times, but his correction reached only three people. Tim Harford: “I’m a Twitter fan myself, but I’m not sure it should be the first port of call for statistical truths.” [04:44]

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2. Interpreting "Gun Violence" Statistics

[05:22 – 05:47]

• Claim: Arianna Huffington tweeted “about 30,000 Americans alive right now won’t make it to 2014 because of gun violence.”
• Fact-check:
  • Ruth Alexander clarifies that "gun violence" includes both homicides and suicides. There are ~19,000 gun suicides and 12,500 gun homicides annually in the US, totaling about 31,500.
  • Quote:
    • Ruth Alexander: “Almost 19,000 people a year kill themselves with guns. Add that to 12,500 firearms homicides and you get to Arianna Huffington’s number.” [05:36]

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3. Reliability of Death Statistics

[05:47 – 08:04]

• Deaths in Official Statistics:
  • Deaths reported to a coroner (sudden or unexplained) in England/Wales/Northern Ireland aren’t registered until after inquests, causing delays—affecting accurate, timely statistics.
  • Medical statistician Professor Sheila Bird highlights delays in registering drug-related and young person deaths.
  • Quote:
    • Sheila Bird: “For somebody who has died from a drugs-related death, half of those deaths will have a delay of at least six months...” [06:44]
    • “Children and young adult deaths, one in five... is not registered for at least six months after the death has occurred.” [07:08]
  • In Scotland, all deaths are registered within eight days.
  • Importance: Delays matter for urgent research, such as trials to reduce deaths among ex-prisoners.
  • Quote:
    • “I should be able to check the deaths register at about 12 weeks after they’ve been released from prison... I’ll actually have to wait two years to be sure.” — Sheila Bird [07:26]

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4. Fun with Statistics: Chocolate and Intelligence

[08:22 – 13:42]

• Headline Claims: News stories suggested a link between chocolate consumption and Nobel Prize wins, based on a study published in The New England Journal of Medicine.
• Study Method:
  • Compared per capita Nobel laureates with per capita chocolate consumption for 22 countries.
  • Prof. Franz Messerli (study author): “...correlate the two... it had a p value of 0.0001.” [09:49]
• Interviews with Nobel laureates revealed mixed views:
  • Christopher Pissarides: “Chocolate that makes you feel good might contribute a little bit. Of course, it’s not the main factor.” [10:41]
  • Rolf Zinkernagel: “I never have eaten more than maybe half a kilogram of chocolate per year.” [11:03]
  • Eric Cornell:
    • Initially joking: “I attribute essentially all my success to the very large amount of chocolate that I consume. Personally...milk chocolate makes you stupid. Dark chocolate is the way to go.” [11:22]
    • Later, tongue-in-cheek retraction: “We scientists should strive to maintain objective neutrality and refrain from declaring our affiliation either with milk chocolate or with dark chocolate.” [11:48]
• Debunking the Study:
  • Prof. John MacInnis points out the “ecological fallacy”—national data can’t infer individual outcomes. Furthermore, Nobel prizes represent achievements over decades, but the chocolate data is current.
  • Quote:
    • “...causation to operate backwards in time... as measured in 2010, explaining people winning the Nobel Prize 100 years ago. Not highly likely.” — John MacInnis [13:34]

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5. The Myth of First-Time Buyers’ Average Age

[13:42 – 17:32]

• Claim: Politicians claim the average age of a first-time homebuyer is nearly 37.
• Reality:
  • Ruth Alexander reports the Council of Mortgage Lenders puts the median age at 29, steady for at least seven years.
  • Quote:
    • Bob Pannell (Council of Mortgage Lenders): “The median age of first time buyers has remained remarkably steady at 29 years...” [14:41]
    • The statistic about age 37 originated from previous research that excluded buyers under 30 who received parental help, inflating the average. The figure lingers as a “zombie statistic.” [17:31]

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6. The Real Risk of Hitting a Deer

[17:57 – 21:54]

• Listener query: Are “High risk of deer” road signs accurate?
• Data:
  • Jochen Langbein, National Deer Vehicle Collision Project:
    • Estimated 7,000–10,000 deer-related vehicle collisions annually in Scotland (risk of one collision per 300–400 vehicles).
    • In the UK: Possibly 42,000–75,000 deer killed annually.
    • More deer hit in England, but risk to individual drivers is higher in Scotland due to less traffic.
    • Langbein Paradox: “...higher number of deer collisions in England, but riskier for drivers in Scotland.” [20:27]
• Sign Wording:
  • Transport for Scotland's Steen Connolly says “high” (vs. “higher”) is used due to sign space limitations. [21:39]

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7. The Mathematics of Juggling

[22:11 – 27:45]

• Spotlight: Mathematician Colin Wright discusses his development of a number-based notation system for juggling tricks—a blend of math and performance.
  • Method: Uses sequences of numbers to encode juggling patterns (e.g., “4440” or “3-3-4-2-3-3”).
  • Quote:
    • “There are magazines published about juggling, and none of them had descriptions of juggling tricks...a certain restricted class of juggling trick.” — Colin Wright [23:01, cond.]
  • Insight: The notation system enabled discovery of new tricks and revealed hidden mathematical patterns in juggling.
  • Notable discovery: The “fake five,” a trick no one had performed before the notation revealed its possibility. [27:13]

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Memorable Quotes

• Tim Harford on social media statistics:

  • “I’m a Twitter fan myself, but I’m not sure it should be the first port of call for statistical truths.” [04:44]

• Joseph O’Leary on using out-of-date numbers:

  • “We should be using the right figures, or else these Chinese whispers will continue and eventually we’ll just have a completely distorted impression of how serious the problem is.” [04:27]

• Sheila Bird on delays in death registration:

  • “One in five [child and young adult deaths] is not registered for at least six months after the death has occurred.” [07:08]

• John McInnis on ecological fallacy:

  • “You can make statements that are perfectly true about individuals, but which are not true of the collectives to which those individuals belong, and vice versa.” [12:43]

• Bob Pannell on first-time buyers:

  • “The median age of first time buyers has remained remarkably steady at 29 years for a considerable period...” [14:41]

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Key Takeaways

• Viral statistics about US gun deaths are often severely outdated, distorted by unclear sourcing, or misrepresented (especially differentiating between handguns and all firearms).
• Memorable statistics in the media (e.g., the 30,000 annual US gun deaths or the average age of first-time homebuyers) often neglect vital context or nuances.
• Even seemingly hard-and-fast facts, such as death statistics, can be subject to delays or data limitations, impacting research and policy.
• Fun statistical stories, like the supposed chocolate-Nobel Prize link, are usually spurious or rest on elementary errors in correlation and causation.
• Listener-driven questions reveal how easily risk perceptions can be skewed (e.g., the likelihood of hitting a deer), and how signs sometimes sacrifice accuracy for brevity.
• Mathematics and creativity can blend in surprising ways—a case in point being juggling notation.

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[End of Content Summary]

For more episodes or to submit questions, listeners are invited to email [e-mail]. Merry Christmas from the More or Less team!

Transcript

[A]

Thank you for downloading this edition of More or less from BBC Radio 4. Here's Tim Harford.

[B]

Hello and welcome to More or Less, the brandy fuelled flame on top of your statistical Christmas pudding this week. So this is 4440, the strange mathematical art of juggling the real average age of first time buyers. And could chocolate make make you more intelligent? But first, the massacre of 20 children and six women at a school in the United States has reopened the debate on gun ownership in the U.S. here's President Barack Obama speaking at a vigil in Newtown, Connecticut a few days after the killings.

[C]

Are we really prepared to say that we're powerless in the face of such carnage? That the politics are too hard? Are we prepared to say that such violence visited on our children year after year after year, is somehow the price of our freedom?

[B]

The debate hasn't just been taking place in the U.S. but all around the world and across social media. A popular message that's been posted and reposted has been last year handguns killed 48 in Japan, 8 in Great Britain, 34 in Switzerland, 52 in Canada, 21 in Sweden, 10,728 in the United States. Gun control. Now it does look plausible. After all, the US Is a big country and we know there are a lot of murders there. But, well, we thought we'd check out the numbers all the same. And the numbers turn out to be quite a puzzle. Well, Ruth Alexander's here. What did you find out, Ruth?

[D]

Well, my first port of call was the United Nations Office on Drugs and Crime. It's got figures on firearms homicide for lots of countries. But. But not for last year. But I found the FBI keeps more up to date figures. Those numbers show that there were 12,664 firearms homicides last year. But that doesn't match the statistic everyone's been posting. It's actually almost 2,000 more deaths. The figure for Britain also doesn't match. Everyone's been saying there were eight gun killings last year, but the Home Office says there were 60 for just England and Wales.

[B]

Well, that's firearms homicides. But the Post specifically mentions handguns, so maybe that explains the mismatch.

[D]

Yes, I thought this and I discovered that you can get data on this for some countries.

[B]

I can see from your face that the numbers don't add up.

[D]

No handguns were used to kill just over 6,200 people in the US last year, not almost 11,000. In Canada it was 94, not 52. And the latest figures for England and Wales show 30 people died from handgun wounds, not eight. But that data relates to 2009-10, not last year. And the data for other countries is either not available or is also out of date.

[B]

So these endlessly retweeted numbers are very roughly the right magnitude, but they don't seem to have come from official sources. So where did they come from? Joseph o', Leary from Independent Fact Checkers Full Fact thinks he's tracked the source down.

[E]

Well, we've got a very good idea. With viral claims like this, it's very difficult to pinpoint the source, but we think we've tracked it down to a poster from the early 80s. It was even broadcast in an advert. Stop handguns before they stop you. It was titled and it has exactly the same figures as was being tweeted about in the last few days.

[B]

Now, the poster, were the figures made up for the poster or were they once accurate?

[E]

We believe they were once accurate. There's a very, very small print on the poster that says based on 1979 statistics. And if you look a bit further into all sorts of US publications, magazines, et cetera, they all talk about the FBI's 1979 Uniform Reform Crime Report, which we believe is the source of the figures themselves. So These are essentially 33 year old figures.

[B]

The actual figures are somewhat in proportion. It's outrageously out of date. However, the most recent statistics do tell a similar story.

[E]

Well, to an extent. I mean, populations have changed since the 1970s. Obviously in the US there are 100 million more people. Even so, the actual rate of homicides will have changed. So we can't just look at the numbers themselves, even if they're in the same proportion. But that said, yes, the point still stands. There are a huge number of people killed by guns in the US compared to the rest of the world, population aside. But if we're going to be having a debate about this, we should be using the right figures or else these Chinese whispers will continue and eventually we'll just have a completely distorted impression of how serious the problem is.

[B]

Joseph o' Leary from Full Fact. One of the people who tweeted the disco era claim about gun deaths was the TV presenter Ben Fogle. His tweet was then retweeted by others over 3,600 times. The next day he I have discovered the handgun fact wasn't from last year, but the sentiments remain the same, which I suppose is one way of making the correction. This second tweet was retweeted by three people. I'm a Twitter fan myself, but I'm not sure it should be the first port of call for statistical truths. And Ruth, before you go, from what we've learned, I think we need to take issue with another statistic. Arianna Huffington of Huffington Post fame has also misspoken on this issue.

[D]

On Twitter, she said about 30,000Americans alive right now won't make it to 2014 because of gun violence.

[B]

In other words, guns kill 30,000 people a year in the U.S. which they don't.

[D]

Well, actually they do, because almost 19,000 people a year kill themselves with guns. Add that to 12,500 firearms homicides and you get to Arianna Huffington's number.

[B]

Gosh. Although probably not what most people think of when they hear the phrase gun violence. Thank you, Ruth. Now, whether you're looking at crime statistics or the effectiveness of hospitals, we've long argued on more or less that death is the one hard fact that it's very hard to fudge. So imagine how surprised we were to find out it's not a hard fact at all.

[D]

At least not in England or Wales or Northern Ireland.

[B]

Thank you, Ruth. Deaths which are reported to a coroner, for example, sudden deaths, violent deaths, accidental deaths, or ones where the cause is unkn, are not registered until the inquest has taken place and a verdict is delivered. This means the deaths don't turn up in the official statistics for some time. This only affects 2% of the half a million deaths which take place every year in England. But it affects some groups to a much larger degree. According to medical statistician Sheila Bird from the Medical Research Council's biostatistics Unit.

[F]

For somebody who has died from a drugs related death, half of those deaths will have a delay of at least six months for those who are aged five to 44 years. So children and young adult deaths, one in five of those deaths is not registered for at least six months after the death has occurred.

[B]

In Scotland, by contrast, all deaths are registered within eight days of discovery, without exception. You'd be forgiven for thinking that the delays south of the border are untidy but not terribly important. But they do matter, Sheila Bird argues, because they're delaying important and potentially life saving research.

[F]

We are presently conducting a randomised controlled trial to see if we can reduce drugs related deaths of prisoners soon after release from prison. And so we are trying to find out whether we reduce their deaths within the first four weeks following release from prison. I should be able to check the deaths register at about 12 weeks after they've been released from prison to find out whether they were alive or dead at four weeks following release. I'll actually have to wait two years to be sure. And here we're talking about people's lives and interventions that may reduce public health problems.

[B]

Professor SHEILA Bird we went to the home Office about this. It told us that the present system ensures death records are reliable and accurate and that there are no plans to change the way things are done. You're listening to More or less. Christmas is coming. Time to switch our focus to something delicious.

[A]

Does chocolate make you smarter? A study suggests it might.

[G]

Chocolate produces brain power.

[A]

Study links eating chocolate to winning Nobels.

[B]

These headlines from around the world are reporting a study published in the New England Journal of Medicine. The author of the study, a professor of medicine at Columbia University in the United States, Franz Marcelli, says the starting point was some research which suggested that cocoa had health benefits.

[H]

There was a study published in the Journal of Hypertension looking at cognitive function in elderly subjects who did actually have mild impairment. And they put these patients on regular coca intake and they concluded that regular consumption of coca, flavanols might be effective in improving cognitive function. There is data in the rats actually showing rats live longer and have better cognitive function when they eat chocolate. And even in snails, you can show that the snail memory is actually improved by chocolate as well.

[B]

This got him thinking. Could chocolate make you smarter? Short on any official measures, he took the number of Nobel Prize winners in a country as an indicator of general national intelligence and compared that with with the level of chocolate consumption. He did this for 22 countries and the results were striking.

[H]

When you correlate the two the chocolate consumption with the number of Nobel Prize laureates per capita, it had a p value of 0.0001.

[B]

That means that assuming there's no real correlation between Nobel Prizes and chocolate, there's less than a 1 in 10,000 probability of getting results like these by chance. Following a sugar rush brought on by too many chocolate biscuits eaten with abandon. To try to bring you the best quality programming, we conducted our own entirely unscientific survey of Nobel Prize winners.

[I]

My name is Christopher Pizaridis and I won my Nobel Prize in Economics in 2010. And throughout my life, in fact, ever since I was a young boy, it's one of the things that I did to cheer me up. To win a Nobel Prize, you have to produce something that others haven't thought about, you know, something different. And chocolate that makes you feel good might contribute a little bit. Of course, it's not the main factor. Don't get me Wrong.

[J]

I'm Rolf Zinkenagel and I have been educated mostly in Basel and in Switzerland.

[K]

Me personally, I am an outlier because

[J]

I never have eaten more than maybe

[K]

half a kilogram of chocolate per year.

[B]

So, mixed views there. But it's possible that not every Nobel laureate feels able to fully disclose their chocolate habit. More or less has discovered that this subject is not without controversy. Here's what American physicist Eric Cornell, who won the Nobel Prize in 2001, told Reuters.

[L]

I attribute essentially all my success to the very large amount of chocolate that I consume. Personally, I feel that milk chocolate makes you stupid. Dark chocolate is the way to go. It's one thing if you want, like a medicine or chemistry Nobel Prize, okay. But if you want a physics Nobel Prize, it pretty much has got to be dark chocolate.

[B]

But when More or less contacted Eric Cornell for further comment, this was the response we received.

[L]

I deeply regret the rash remarks I made to the media with respect to the chocolate controversy. We scientists should strive to maintain objective neutrality and refrain from declaring our affiliation either with milk chocolate or with dark chocolate. Now, I ask that the media kindly respect my family's privacy in this difficult time.

[B]

So, look, this is all nonsense. Here's Professor John McInnis from Edinburgh University. He's an advisor to the Economic and Social Research Council on Quantitative Methods.

[K]

The data on winning Nobel laureates is about individuals. The data about chocolate consumption is about countries. And the explanatory mechanism that the article proposes about flavonids and their relationship to intelligence is one that you'd expect to operate at the individual level. And yet his data is about countries switching inappropriately between the individual level and collective or global level. Like that's known as statistics, as the ecological fallacy, because you can make statements that are perfectly true about individuals, but which are not true of the collectives to which those individuals belong, and vice versa. Another problem is the number of Nobel laureates is a number that measures a country's kind of intellectual performance, if you like that over about the last hundred years, during which time the prizes have been awarded. And yet chocolate consumption data is for the current year or recent years. Now, I'm not aware of any scientific theory that allows causation to operate backwards in time. We usually want causes to precede effects. And yet here we've got causes as measured in 2010, explaining people winning the Nobel Prize 100 years ago. Not highly likely.

[B]

Professor John MacInnis. This is more or less. I'm Tim Harford, and if you have a number Y question, do please Send your emails to more or [e-mail]. loyal listener Toby Lloyd has done just that. Here's a statistic he's suspicious of. Straight out of the mouth of Grant Shapps earlier this year when he was Housing Minister. The average age of a first time buyer in particular has gone up dramatically. It's nearly 37. The average age of first time buyers has been steadily climbing for years. It's not just Grant Shapps. Everyone says it and everyone knows it. Apart from we've discovered the people who actually calculate the figure. The Council of Mortgage Lenders. Ruth's back. Actually, Ruth feels like you've never been away. You've been sitting in the corner of the studio the whole time. So what's the real number?

[D]

The correct number, they say is 29.

[B]

29.

[D]

29. What's more, it's been 29 for the last seven years. Hear it from the horse's mouth. Bob Pannell, the Council of Mortgage Lenders chief economist.

[M]

The median age of first time buyers has remained remarkably steady at 29 years for a considerable period, certainly throughout the period of the credit crunch and for some period before that. In fact, the median age of first time buyers has only varied by sort of about three years either side of 29 for the whole of the past 40 years. So it's a remarkably stable statistic.

[D]

Bob Pannell told me the real average age of people you think of as

[B]

first time buyers, young couples starting out in life, that kind of thing.

[D]

Exactly. Their age is probably lower. It's probably 27 or 28. Because here's the second surprise. When the Council of Mortgage Lenders say first time buyers, they don't mean people buying a house for the first time.

[B]

They don't.

[D]

Well, if you think about it, Tim, how would they know? Mortgage lenders don't care whether you've bought a house before and they don't ask if you've bought a house before. The only people who ever really cared was Her Majesty's Revenue and Customs who needed to produce a definition so that they could exempt first time buyers from stamp duty a couple of years ago or so.

[B]

So if mortgage lenders don't ask, and they don't really care one way or another, how do they produce these numbers?

[D]

Well, what gets measured is whether you currently have a mortgage and whether you're living in your own home when you apply for a new mortgage. So if you sold your house and moved into rented accommodation because of a divorce or some time spent abroad, for example, or even paid off your previous Mortgage, you may well be counted as a first time buyer. It's actually estimated that about one fifth of so called first time buyers have previously bought a home.

[B]

And of course those people are going to be older on average. But it seems surprising that the average age of first time buyers, albeit with this wobbly definition, is much lower than most people think and that it hasn't been going up at all as most people think. I mean, houses are really expensive and credit is hard to get.

[D]

Well, there's been something else going on which that number doesn't capture. The number of first time buyers able to buy a property on their own without help from mum and dad has fallen sharply. There were 70,000 of them snapping houses up in second quarter of 2005, but only 16,000 six years later, again according

[B]

to the Council of Mortgage Lenders, who presumably are slightly guessing at these figures. And now, this still begs the question, where did Grant Shapps as Housing Minister get the average age of 37 from? Because the Council of Mortgage Lenders says this is categorically wrong.

[D]

Yes, they do.

[B]

So where did the stat come from?

[D]

From the Council of Mortgage Lenders.

[C]

What?

[D]

They did some research a few years ago which they say they now regret in in trying to capture the age of first time buyers who were buying without help from their parents, they excluded all the people under 30 who were getting assistance. This had the effect of removing Almost everyone under 30 from the first time buyer equation, which made the average look artificially high. 37. In a newsletter last year, they fessed up and said they could now consign this misleading figure to oblivion.

[B]

But instead it's turned into a zombie statistic that refuses to die. Thank you, Ruth. Driving around Britain, we're constantly warned about all the dangers we could encounter. Falling rocks, children crossing sharp bends and deer. One listener got in touch via more or lessbc.co.uk to raise the following point.

[N]

Road signs in Scotland now declare warning high risk of deer on roads. Sure, the risk is higher in the autumn, but it is still extremely small as a proportion of miles of road or vehicle miles travelled. I fear the warning message A should say hire not high and B distorts our sense of risk counterproductively.

[B]

Our reporter Wesley Stevenson has been looking into deer vehicle collision statistics. Welcome, Wes. How likely are we to hit a deer when we're driving in Scotland?

[A]

Well, this was a question we put to Jochen Langbein, head of the National Deer Vehicle Collision Project, which records and monitors deer vehicle collisions.

[B]

Surprisingly enough, sounds like we talked to the right man. Although I am still scarred by the fact fish based controversy.

[A]

Don't worry. Jochen knows his deer accidents from his elbow and he's been studying the problem for nine years.

[O]

Well, our best estimates are that in Scotland, somewhere in the region of 7 to 10,000 vehicles per year will collide with a deer. So give a very rough estimate of the average likelihood per vehicle hitting a deer. We would need to actually divide the 43 billion vehicle kilometers covered by all the two and a half million vehicles into that figure, which would give a figure of around 1 in 300 to 1 in 400 vehicles actually being involved in a collision with the deer.

[B]

Which raises the question, how many miles would you have to drive before you could expect to hit a deer?

[A]

No, no,

[O]

that would come out as a figure of about three and a half million kilometers needing to be driven before you're one of the ones hitting a deer.

[A]

Deer collisions are a problem in the uk, especially if you're a deer. Not all the collisions are reported, but Jochen Langbein reckons that a conservative estimate would be that 42,000 deer are hit and killed in the UK each year. The true figure could be nearer 75,000. There's a peak in accidents in May when young roebucks are dispersing, and another in October, November, time associated with the increased movement of fallow red and seeker deer around the rut.

[B]

Now, we began with an email from a listener in Scotland, and I understand that despite England's larger area and much larger population, England actually only has as many deer as Scotland does. So is this largely a problem for Scottish drivers?

[A]

Well, that's an interesting question, Tim. Allow me to introduce what I like to call the Yochan Langbein paradox. Here's the man himself explaining it.

[O]

We actually have four times as many deer hit in England as we have in Scotland. But in terms of risk to individual drivers, because we have tenfold as much traffic in England as in Scotland, the individual risk per driver is actually lower in England, even though we have much higher number of deer being killed on the roads in England. On the point of view of the deer, it's clearly a much riskier life living in England because of the very much higher levels of traffic. But from view of a driver, it's a riskier business in Scotland driving on Scotland's roads because we've got a higher number of deer in relation to the traffic.

[B]

So the paradox is that deer collisions are more of a problem for Scottish drivers, but they're more of a problem for English deer. But look, the Risk of hitting a deer is still quite small, regardless of whether you drive in England or in Scotland. So why do the signs say high risk? I put this question to the man in charge of the variable message signs throughout Scotland. He's Transport for Scotland's Steen Connolly. Why do his signs say high risk instead of the more accurate higher risk? Time to discover the answer. The reason it's cut to high risk

[H]

is because those extra two letters doesn't allow you to put the full wording on the signs. On some of the signs, I have no problem. If we can fit higher on, we'll fit higher on, but it's just to be consistent with the signs.

[B]

We can fit higher on some signs

[H]

and not in others.

[B]

So we're being consistently put in high risk. Oh, right, ok, Fair point. And by the way, Jochen Langbein told us that according to research conducted in the United States, these variable message signs do help reduce accidents. Time for some juggling, I think.

[P]

So this is 4, 4, 4, 0,

[B]

because juggling is a mathematical art, really. Colin Wright is a mathematician who abandoned the traditional see and repeat approach to learning how to juggle and instead developed a sort of sheet music for juggling, where sequences of numbers represent particular juggling moves.

[P]

So I do three vertical throws. A four from the left hand, a four from the right hand, a four from the left hand. I've run out of juggling balls. I've got none left. That's a zero, click the fingers.

[B]

He came into the studio with his juggling balls, which he introduced to us as George, Oliver, Penelope, Yolinda, Greg and William. Well, do you not name your balls? I have names for mine. To explain how this mathematical system has helped him discover new juggling possibilities, I started our conversation by asking why he decided to do this in the first place.

[P]

When I was attempting to learn five, I gave up very quickly because it's phenomenally difficult. And I discovered that nobody in the juggling club actually juggled five. Well, very few juggled five. But what they were doing were a variety of tricks with just three. So I said to people, yeah, show me. Show me a trick with three. So some of them were really clean and obvious, but then they also started to do weird shapes in the air and patterns. And there was one in particular, which is called mills mass. And when I went to try and write it down, I couldn't. It was almost impossible to describe. And when I finally did get a description after a few days of working with one of the chaps, it took two and a half sides of afol. And I thought, for a juggling trick that lasts for one second, there must be an easier way. But it turned out that there wasn't. There are magazines published about juggling, and none of them had descriptions of juggling tricks. So the other guys and I decided we would try and figure out how to write down juggling tricks. And we worked and worked and worked on this over a period of 18 months or more, and finally emerged this simple and elegant way of describing a certain class of juggling trick. Not everything possible, but a certain restricted class of juggling trick.

[B]

What does juggling notation look like on the page? Is it diagrams? Letters, Numbers?

[P]

The first one that we came out with is actually a diagram. But then we realized that if you do stick to a perfectly metronomic beat and you don't move your hands around, then the only thing that matters about the juggling balls is when they come down, the amount of time that they've been in the air. And so we could abstract away from the diagram and turn it into a string of numbers.

[B]

So if I give you a string of numbers, so 3, 3, 4, 2, 3, 3. Is that a juggling trick?

[P]

That is a juggling trick. Now, not every string of numbers is a valid juggling trick. And so that became an interesting piece of mathematics. Then, if given a random string of numbers or a string of numbers from some other source without actually juggling it, is there a way of telling whether or not it corresponds to a juggling trick? And the one that you've just given me does. It corresponds to doing the normal three ball cascade, which is like an infinity sign, a figure of eight lying on its side. Then the four is a vertical throw from one hand, and the two is hang on to the ball for a beat and then pick up where you left off. So 3, 3, 3, 4, 2, 3, 3, 3.

[B]

And why is the 4 throwing the ball high in the air, and why is the two holding onto the ball?

[P]

Well, if you're juggling four balls and you're juggling a ball on every beat, and all of the throws are the same, then the balls will take it in turn. So that means you do red, green, blue, orange, red, green, blue, orange, red, green, blue, orange. And the red ball is thrown every fourth time.

[B]

So that would just be 4, 4, 4, 4, 4,.

[M]

4, 4.

[P]

Exactly. So, and then if you're only juggling two balls, then you throw. Well, you don't actually throw it, but you have a ball in the right hand, then a ball in the left hand, and the balls don't actually get thrown, they just stay in the hands. And so that corresponds to a 2. And similarly, a 1 is just take a ball and transfer it at speed from one hand to the other, kind of zipping it across, zipping it across, zipping it across. And so a zip from one hand to the other with no air time at all is described as a one. The amazing thing was that when we were developing this, we had several ideas that didn't work. And so when we finally got this one with the string of numbers, we thought, this looks quite promising. We started to write down all of the tricks that we knew to stress the system to see if it would work. And we noticed patterns between the different tricks. And when we arranged it in just the right way on the paper with the courage to leave gaps, we spotted that there was an overarching pattern to the juggling tricks, one which the physical juggling didn't expose, but the notation did. And then we thought, hang on a minute, there are gaps here. There are obvious things that should go in the gaps. So we would write that down and say, well, that should be a juggling trick. If there is any justice in the world, that should be a juggling trick.

[B]

And it just this string of numbers that fits the.

[H]

The pattern.

[P]

That fits the pattern.

[B]

And is it a juggling trick?

[P]

Not only that, the one that we found at the time was an utterly superb juggling trick. It's known as the fake five. It's a four ball pattern and nobody had ever done it, as far as we can tell.

[B]

Colin Wright. And there's a video of Colin juggling on our website, BBC.co.uk more or less. If you've spotted any statistical sins or just have a number you want us to take a look at, please email More or Less at BBC Co UK until next week. Merry Christmas and goodbye.

[A]

More or Less was presented by Tim Harford, the Financial Times undercover Economist. It was produced by Ruth Alexander and the editor was Richard Varden.