Pension Charges

Summary

More or Less — "Pension Charges"

BBC Radio 4 | Host: Tim Harford | Date: January 3, 2014

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Episode Overview

In this episode, Tim Harford and the More or Less team tackle the numbers and assumptions behind government claims concerning workplace pension charges. They systematically examine the impact of pension fund management fees, debunk widespread statistics on global Christian martyrdom, and explore the statistical significance of cycling deaths in London. The episode also features lighter moments, including a tongue-in-cheek defence of imperial measurements.

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1. Pension Charges: Do Small Percentage Changes Really Matter?

Timestamps: 00:08–08:04

Key Discussion Points

• Government Proposal:
  The UK government claims that halving annual workplace pension management charges from 1.5% to 0.75% could boost a hypothetical pension pot by £100,000—a surprising statement given only £55,000 in contributions over a working life.

• Listener Skepticism:
  Listener Geoff Pearce is invited to question these calculations:

  “It was that figure, 100,000. It’s a lot of money and it seemed a bit of a headline.” [01:22, Geoff Pearce]

• Compounding Charges Explained:
  Moneybox presenter Paul Lewis demonstrates, with spreadsheet in hand, how annual charges erode savings dramatically through compound interest:

  “These charges don’t just come off your money once. They come off every year... That first year’s contribution, 46 times one and a half percent is 69% of your money will disappear in charge.” [02:06, Paul Lewis]

• Assumptions Critiqued:
  Only under the government’s optimistic assumptions—46 years of saving, £100/month contribution, and 8% annual growth—is the £100,000 savings claim valid:

  “This is the maximum the Financial Conduct Authority allows a firm to assume growth. So if you put in 8% growth and 1 1/2 or 3/4% charges, you come to this magic, you’ll save £100,000 over the course of your working life figure.” [04:25, Paul Lewis]

• The Power and Pitfalls of Compound Interest:
  Behavioral economist Matt Levy explains why most people underestimate these effects:

  “People do linear growth. They have a sense that it’s going to grow quicker than linear, but they just have no idea how much quicker it’s going to grow.” [07:21, Matt Levy]

• Summary Takeaway:
  Even conservative growth assumptions show charges can greatly undermine savings. The government’s headline figure is possible—but only with optimistic growth; lower growth means less outright savings but higher proportional cost.

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2. Imperial versus Metric Measurements: A Humorous Detour

Timestamps: 08:24–11:54

Memorable Moments

• YouTube Apology:
  Matt Parker humorously recants his criticism of the imperial measurement system and explains its “logic” through an increasingly absurd chain of conversions.

• Notable Quotes:

  “Meters are vastly superior to inches.” [08:54, Matt Parker]
  “So nautical miles are the same as ordinary miles?”
  “They’re like normal miles, but wetter, basically.” [10:03, Matt Parker]

• Segment Tone:
  This riff lampoons imperial measures, illustrating absurd complexity by tracing units from barleycorns up to leagues and back, culminating in fictitious extremes.

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3. Fact-Checking: 100,000 Christian Martyrs Annually?

Timestamps: 12:38–21:06

Key Discussion Points

• The Statistic in Question:
  Claims that 100,000 Christians are killed for their faith each year have become prevalent in politics and the media.

• Source Examination:
  Ruth Alexander traces the figure to research at the Center for the Study of Global Christianity (CSGC), which extrapolated from deaths largely in the Democratic Republic of Congo’s civil war—most of which were not specifically religiously motivated.

• Major Findings:

  • Around 90% of the “martyr” deaths in the 2000–2010 estimate occurred during the DRC’s civil wars, which were not primarily about religion.
  • Earlier calculation methods have been repeated and remain unupdated, meaning the annual figure is now inaccurate.

• Expert Perspectives:

  • Professor Thomas Schirrmacher:

    “So when you hear that 100,000 Christians are dying for their faith, you need to keep in mind that the vast majority, 90,000 of the 100,000 martyrs a year, are people who were killed in the Democratic Republic of Congo.” [14:45]

  • Ian Linden:

    “It had nothing to do with the beliefs or the worship of the people who were killed. … It’s very difficult to describe any of that killing as creating martyrdom.” [16:12]

• Alternate Views:
  John Allen (author, The Global War on Christians) defends broader definitions, citing individuals killed for faith-related actions (e.g., a catechist in Congo):

  “If you go to the center … their standard is a death that occurs in what they define as a situation of witness.” [16:48, John Allen]

• Statistical Weakness and Revision:
  CSGC’s Todd Johnson acknowledges the method is outdated and the number should likely be lower, with current rough guesses in the 7,000–10,000 per year range.

• Final Conclusion:

  “The idea that 100,000 Christians have been killed because of their faith every year over the past decade is thankfully unfounded.” [21:06, Tim Harford]

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4. Railway Satisfaction: UK—Europe's "Most Improved"?

Timestamps: 21:34–24:10

Key Discussion Points

• Billboard Claims:
  The UK is declared “Europe’s most improved railway” based on customer satisfaction gains from 1997 to 2012 (from 34% to 55%).

• Contextual Nuance:
  France leads in absolute satisfaction (59%). Despite the UK’s relative improvement, it only rises from 13th to 10th out of 15 in the EU15 rankings.

• Skepticism:
  Comparisons to countries like Luxembourg (with very limited rail) highlight the limitations and possible irrelevance of such rankings.

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5. Cycling Deaths in London: Statistical Significance of Sudden Clusters

Timestamps: 24:10–27:11

Key Discussion Points

• Listener Investigation:
  Statistics student Jody Aberdeen investigates whether the cluster of six London cyclist deaths in 14 days in 2013 is a meaningful anomaly.

• Methodology:
  Avoiding statistical traps, Jody looks at all possible 14-day periods over 8 years, not just standard calendar fortnights.

• Findings:
  Clusters of six deaths in two weeks are rare (only 1 in 40 such periods over eight years), so the incident was indeed unusual, though not necessarily indicative of a trend.

• Benefits of Cycling:
  Despite occasional tragic clusters, cycling still massively benefits mortality risk compared to not cycling:

  “The ratio of benefit to harm is almost 100 in favour of cycling over driving because of the massive benefit to cardiovascular health of regular exercise.” [26:42, Jody Aberdeen]

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Notable Quotes & Memorable Moments

• “These charges don’t just come off your money once. They come off every year.” [02:06, Paul Lewis]
• “People do linear growth...they just have no idea how much quicker [compound growth] is going to grow.” [07:21, Matt Levy]
• “They’re like normal miles, but wetter, basically.” [10:05, Matt Parker]
• “When you hear that 100,000 Christians are dying for their faith, you need to keep in mind that the vast majority, 90,000 of the 100,000 martyrs a year, are people who were killed in the Democratic Republic of Congo.” [14:45, Prof. Thomas Schirrmacher]
• “The ratio of benefit to harm is almost 100 in favour of cycling over driving because of the massive benefit to cardiovascular health.” [26:42, Jody Aberdeen]

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Useful Timestamps

• Pension Charges Explained: 00:08–08:04
• Imperial vs. Metric Rant: 08:24–11:54
• Christian Martyrdom Figures Debunked: 12:38–21:06
• UK Railways’ Satisfaction Claim: 21:34–24:10
• Statistical Analysis of Cycling Deaths: 24:10–27:11

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Tone & Style

The episode maintains Tim Harford’s signature blend of accessible statistical analysis and dry wit, consistently aiming to debunk misleading public figures and explain the nuances behind the numbers with clarity, empathy, and occasional levity.

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Recommended for:
Anyone who wants to understand how apparently small costs and big statistics can have outsized impacts—or be misleading—when compounded over time, and for those who appreciate an entertaining, critical approach to widely circulating claims.

Transcript

[A]

Thank you for downloading More or Less from the BBC. This is the version of the programme first broadcast on BBC Radio 4. Here's Tim Harford.

[B]

Hello and welcome to More Or Less the programme which welcomes the New Year with the same resolution as always to seek and destroy zombie statistics everywhere. Today we'll be looking at some tragic Christians being martyred for their faith and cyclists being killed on the roads. But we'll have some lighter moments too, notably an abject apology from an Australian. And before all that, let's talk about pensions. The Government recently announced proposals to cap management fees on workplace pension schemes. The Department for Work and Pensions stated that if the annual fee was halved from 1.5% to 3/4 of a percent, this could boost a hypothetical pension pot by £100,000, or which sounds like a big saving from a small tweak, especially since that hypothetical pension pot had only received about £55,000 worth of contributions. Well, a number of listeners emailed us to say they simply didn't believe the numbers being quoted. So we invited one of them, Geoff Pearce, into More Or Less Towers to show him how the numbers do add up. Geoff, you very kindly agreed to join us. Why were you suspicious of this figure?

[C]

My first thought was it was that figure, 100,000. It's a lot of money and it seemed a bit of a headline.

[B]

Nice round number. A nice round number.

[C]

Everyone wants to save £100,000. But then I looked at what was being said in terms of the contribution of £100amonth for a working life of 46 years. And I looked at that and I thought, well, there must be some growth assumptions in there, because on that basis you're only paying in £55,000. So I couldn't see where the charge of 100,000 came from.

[B]

If only we had a financial guru in the studio with us. Unfortunately, Paul Lewis is here, presenter of Moneybox.

[C]

Hello, Paul.

[D]

Hello, Tim.

[B]

Thank you for coming in. Fancy meeting you here.

[D]

I just happen to be passing the studio.

[B]

Tim, could you please explain this to me and Geoff?

[D]

Yes, Geoff, can I say first, I think there's something you've perhaps misunderstood. If you'll forgive me. These charges don't just come off your money once. They come off every year. And that means that when you pay in your twelve hundred pounds in year one, you'll see I've got a spreadsheet here which explains it all. You've got £1,200 going in. One and a half percent of that is £18 which comes off. Then you get growth on your fund because it's invested. And at the end of the year, on these assumptions, which I'll explain in a minute, you've got £1,276 in your fund, so that's carried forward to the next year and you pay in another 1,200 pounds. But the 1.5% charge doesn't just come off the money from the next year, it comes off the first year's money as well. So if you're in a fund for 46 years, which is the assumption here, then you're going to find that that first year's contribution and the growth on it are taxed, if you like, by this charge 46 times. So in other words, that first contribution 46 times one and a half percent is 69% of your money will disappear in charge.

[C]

So by the time I take my pension money that I contributed in the early years has almost disappeared.

[D]

Yes, a lot of it has gone in charges. And what this spreadsheet does, by showing you that, and I've set it up to compare 1 1/2% charges here and 3/4 of a percent there. So that's half as big. Now, you see, at the end of year one, it makes almost no difference. Your charges are just nine pound difference. But as we scroll down, we find this quite extraordinary thing. And they assume that you're going to work for 46 years, so age 25 to, say, 71. And the difference between those two charge scenarios in this spreadsheet is actually 103,500 pounds. So with one and a half percent charges, you have 346,000 pounds in your pension fund. With three quarters of a percent charge, you have nearly 450,000 pounds in your pension fund, and that means you've got another £103,000. And that's because these charges come off every year. Now, I have to say I've taken one big assumption here, which is the only one that would give me £100,000 assumption, and that is that your pension fund, unlike most people's in the real world, will grow at 8% a year. Now, this is the maximum the Financial Conduct Authority allows a firm to assume growth. So if you put in 8% growth and 1 1/2 or 3/4% charges, you come to this magic, you'll save £100,000 over the course of your working life figure.

[B]

Paul, just looking at. We've accepted the government's assumptions here, so we've started this pension pot at the age of 25. Two interesting moments one is at the age of 34 where the pension pot starts to earn more than your contributions. So you're contributing £100amonth. The pension pot is, is contributing more than 100 pounds a month just by growing at 8%, which as we've discussed, 8% is a pretty optimistic growth rate, but it's not completely out of the question. And then there's a second interesting moment, and that comes at the age of 51. And at the age of 51, the charges being levied on the total pot, the charges of 1.5% are more than the money you're putting in. So your pension pot is now about £85,000. It is growing at 8% a year. That is over £6,000. And the 1.5% annual management charge is over £1,200. And by this time, Geoff, your £1,200 a year contribution is starting to be swamped by the action of the pension pot itself.

[C]

It still seems a large figure. I think the thing is you don't actually ever really sit down and think about what am I being charged for having this pension. I think the thing that has, has surprised me the most, again, probably my own fault for not looking into my own pension in that great detail, is this constant charging of your early years contributions throughout the scheme.

[B]

By the way, if you make a less optimistic assumption about the growth rate of your pension pot, charges won't cost you anywhere near £100,000, but they will cost you even more as a percentage of your pension. So the government is quite right to say that if annual charges did fall from 1.5% to three quarters of a percent, that would be a big deal. Jeff still couldn't quite believe the numbers, even though he saw them in black and white on Paul Lewis's rather beautiful spreadsheet. But underestimating the power of compound interest is something a lot of people do. As Matt Levy, behavioral economist at the London School of Economics, explains, rather than

[E]

doing the compound interest, people try to calculate the simple interest. So rather than having the 4% interest and then the 4% interest on the 4% interest and keep repeating it, if I put 100 pounds in an account, I'll get 4% this year, 104 pounds next year, I'll get 4%, 108 pounds. And so rather than doing exponential growth, people do linear growth. And that's sort of the extreme version. And then sort of the other extreme would be to do this exactly right. So we asked how much variation is there in how people perceive Exponential growth. And it turns out that there's certainly far more people who do this full linearization than than there are people who get it exactly right. So this is for the US population, which is probably similar here we found something like 10% of the population gets it right, about a third gets it completely wrong in terms of this linearization. And most people are somewhere in between. So you can sort of calibrate this and a lot of people fall in between. They have a sense that it's going to grow quicker than linear, but they just have no idea how much quicker it's going to grow.

[B]

Matt Levy from the London School of Economics and before him Paul Lewis of Moneybox and loyal listener Jeff Pearce. But don't forget, it's my world, I just let Paul Lewis play in it. Now, we're no strangers to controversy on more or less, but even we were shocked when we saw this video on YouTube on a channel called NumberHub.

[F]

We have no idea where US letter size came from. The main argument I've heard is, is that if you get a guy's arm right, that is four times that length. Because then if you.

[B]

Now there's nothing shocking in the posting of a video critiquing paper sizes per se. No indeed. We were enjoying Matt Parker's comparison of the US paper sizing system to the A4 system. But then, well, Matt, the stand up mathematician and friend of more or less, he overstepped the mark.

[F]

Meters are vastly superior to inches.

[B]

Unbelievable.

[F]

I mean the official original definition of an inch is that it's three barleycorns.

[B]

What do you expect from a measurement that was developed? I'll spare you any more. We've asked Matt Parker to come on and justify himself. Matt?

[F]

Yes, I. I have come a long ruler between my legs. Very, very apologetic. I have gone too far. I overstepped the mark and I was unnecessarily mean and critical of the imperial unit system. And so what I thought I could do is to now praise the merits and kind of promote the imperial measurement system for all of its wonder.

[B]

Where would you start?

[F]

So I mentioned the barleycorns in my video and what I didn't say is that if you get three of these barleycorns you get an inch. If you then get 12 of those inches you get a foot. And if you get three of those feet you get a yard, which is all very straightforward. And this carries on nice and systematically because 1760 yards gives you a mile. You take an eighth of that mile, you get a foot furlong, you divide the Furlong. In tenths, you get a Gunter's chain. If you divide the Gunter's chain into elevenths, you get a fathom. If you have 15 fathoms, you get a shackle. Or alternatively, if you take 100 fathoms, you get a cable. Now, each cable, if you have 10 of those, you get a nautical mile. If you take each nautical mile.

[B]

So nautical miles are the same as ordinary miles.

[F]

They're like normal miles, but wetter, basically.

[D]

Right.

[F]

So if you have three nautical miles, you get a league. Or alternatively, you can take a nautical mile and split it into 6,080ft, which means that the film 20,000 Leagues under the Sea should be 40,530 3,333ft under the sea.

[C]

Catchy.

[F]

Yeah, exactly. Now, each foot, if you divide that into thirds, you get a hand. Well, of course, three hands to the feet makes sense. Each hand. If you cut that in half, you get a stick. If you take a stick and snap it in half, you get an inch. If you take three inches, you get a palm. If you divide it into four, you get digits. You take three digits, you get a nail. You take four nails, you get a span. If you take two spans, you get a cubit. Now that cubit. If you divide that into thirds, you get a Chapman, which is a slightly insulting unit. And if you are actually keeping track, Tim, that would be 243.2 million shapments under the sea.

[B]

I knew that.

[F]

It's a much catchier title. Now, five chapmets in a row is a pace. If you take two paces, you've taken one step. If you take four steps, you've just walked along a rope. If you take five ropes, you get a Ramsden's chain. Because Ramsden didn't want to use gunters, he's got his own chain. You take 50 Ramsden's chains in a row, you get a Roman mile.

[B]

Is that similar to the nautical mile?

[F]

It is similar, but subtly different to all the other miles. Because you don't want just one mile. Why not have more than one? For different occasions? A Roman mile is exactly 60,000 inches. That's nice and straightforward. Whereas a standard mile is a slightly messier 63,360.

[B]

For when you just need that little bit more.

[F]

Yeah, yeah. So if a Roman goes the extra mile for you, you get less value for money. Now, each inch, if you divide that into sixths, you get a picker. If you take a picker and divide it into twelfths, you get a point. You take a point and divide into 20th you get a twip, the smallest unit I will be mentioning. You then take six points. That gives you a poppy seed. And now four of those poppy seeds takes us right back to where we started, the barleycorn. So as you can see, it's a nice, consistent, straightforward system of measurement units.

[B]

Matt Parker, Apology accepted. Thank you. Did I ever tell you about the time I met the kilogram?

[F]

Don't start.

[B]

And you can watch Number Hub with Matt Parker on YouTube or you can visit our website pbc.co.uk Morealls One of the things we've placed there is a slightly more balanced take on the imperial versus metric systems that we recorded for more or less a few years ago. Our email address for your questions and comments is moreallesbc.co.uk. now every day around the world, Christians are dying for their beliefs. Police in Pakistan say at least 75 people have been killed in a double suicide bombing at a church in Peshawar.

[A]

Three people, including an eight year old girl, were killed in the Egyptian capital Cairo, when gunmen on motorcycles opened fire on a wedding party outside a Coptic Christian church.

[B]

These two attacks hit the headlines within just a month of each other and they're by no means isolated incidents. In November, Jim Shannon MP of the Democratic Unionist Party made this claim in parliament. 100,000 Christians will be killed in the world this year. One every day, one every hour. I should say Mr. Shannon isn't the only one saying this. In May, Vatican spokesman Archbishop Silvano Maria Tomasi made a radio address to the United Nations Human Rights Council.

[F]

Credible research has reached the shocking conclusion that every year an estimate of more than 100,000 Christians are killed because of some relation to their faith.

[B]

More than 100,000 Christians killed because of their faith every year. This statistic has been repeated many times in news reports on the Internet. It's taken on a life of its own, popping up all over the place, sometimes with an additional detail that the lives are taken by Muslims. Listener C. Collingridge asked us to do some fact checking, which Ruth Alexander has been helping with. Hi, Ruth.

[A]

Hi, Tim. The number comes from the center for the Study of Global Christianity at Gordon Conwell Theological Seminary in the United States. To get this figure of 100,000, they've estimated the number of Christians who've died as martyrs between the year 2000 and the year 2010, about a million by their reckoning. And they've divided that number by 10 to get an annual number, 100,000, which they're still using today.

[B]

Now, on one level, that seems like a reasonable calculation. But when you dig into the figures, you see that the majority of the million Christian martyrs they've captured for the period 2000 to 2010 died in the Democratic Republic of Congo. Professor Thomas Schiermaker from the International Society for Human Rights has been interrogating these numbers. The largest number comes from the civil war in the Democratic Republic of the Congo. And they take about 20% of those people having died as martyrs. And that means that 90% of the number, 100,000, actually are people that died in Congo. So when you hear that 100,000 Christians are dying for their faith, you need to keep in mind that the vast majority, 90,000 of the 100,000 martyrs a year, are people who were killed in the Democratic Republic of Congo. So we can say right away that the Internet rumours of Muslims being behind the killing of 100,000 Christian martyrs are nonsense. The DRC's a Christian country. In the civil war, Christians were killing Christians. But the fact that this number is largely based on deaths from a civil war is puzzling, because this wasn't a war about religion. Looking at previous calculations made by the Centre, it has in the past included in its estimate of martyrs deaths which occurred during the Rwandan genocide. And again, this is puzzling. Rwanda was not a conflict about religion. It was Hutus killing Tutsis. Both sides were Christian. Ian Linden, associate professor in the Study of Religion at the School of Oriental and African Studies in London, and and author of Church and Revolution in Rwanda, can give us some context. The genocide in Rwanda was based on the systematic killing of an ethnic group in an attempt to completely wipe them out. And it had nothing to do with the beliefs or the worship of the people who were killed. The civil wars in the Democratic Republic of the Congo were the consequences of a failed state disintegrated military force, so that militias had almost full power because of the weapons they had. They were indiscriminately killing and raping and plundering. And it's very difficult to describe any of that killing as creating martyrdom.

[A]

Someone who disagrees with that is John Allen, author of a book called the Global War on Christians, in which he uses the 100,000 statistic.

[G]

Well, I think that begs the question of what definition of being killed because you're a Christian, do you want to adopt? If you go to the center for the Study of Global Christianity, which is where that figure comes from, they will tell you that their standard is a death that occurs in what they define as a situation of witness. That is somebody was doing something on the basis of their faith that put them in the firing line. Let me give you a specific case. A female catechist in Congo who is having success persuading young people in her area not to sign up with the militias. And she is killed by one of those forces because they don't want to see their sources of recruits dried up. Now, is that anti Christian violence or isn't it?

[A]

And it doesn't seem unreasonable to count that woman as a martyr.

[B]

Yes, and Ian Linden did also make the point that there were Hutus in Rwanda who wouldn't leave their Tutsi colleagues because of their Christian faith and they were slaughtered and could be called martyrs. But do we know that there were 900,000 people being killed in the name of their faith in, in the Democratic Republic of Congo?

[A]

No, we don't. It's just an estimate. The man behind the number at the center for the Study of Global Christianity, Todd Johnson, told me that he's estimated that 20% of the people who died in the Congo died as martyrs because that's how many people there are thought to be practicing Christians. Now, this is based on research published in an early 1980s edition of the World Christian Encyclopedia, which estimated that usually the 20% of African populations were actively practicing Christians. Now, Todd has taken that number and applied it to the death toll in the Democratic Republic of Congo, although he says this statistic is something they've abandoned in their other work. And you know, there's another issue with including the Congo civil war deaths in the annual count of Christian martyrs. Much of the violence there has now ended. So how can it be forming the main basis for the number of Christian martyrs in this year? Here's Todd Johnson.

[G]

That's a weakness of this approach because Even in the DRC, things are not as intense as they were 10 years ago. That every year now it probably should go down, but then I've got to keep my eyes open for other situations around the world. So it's probably decreasing year by year right now. But the method is not exact enough to be doing that. So I've just kept it at 100,000 the last couple of years. But I'm likely going to have to lower it unless something comes to our attention.

[B]

And by the way, if you think that number's big, the centre publishes enormous numbers for the martyrs it says will be made around 2050. Why is that? Well, for the sake of their martyr estimates, that's the year they've taken to be the end of the world.

[A]

And you know, we haven't seen the Vatican quoting those statistics.

[B]

No. So back to the more tangible present. If you take out the 90,000 deaths in the Democratic Republic of Congo in a war that is now finished, that leaves 10,000 martyrs a year. And that, Thomas Schermacher from the International Society of Human Rights reckons is probably about the actual number of Christians who are killed because they're Christian each year. One has to see there is no scientific number in the moment. It has not been researched, and all experts in this area are very hesitant

[C]

to give a figure.

[B]

We are starting a research project with several universities worldwide on this topic, and there we start with a guess of 7 to 8,000 Christians killed as martyrs each year.

[A]

But to some extent, this number crunching is besides the point. For John Allen, author of the Global War on Christians. We asked him whether he thinks it matters whether the number of Christian martyrs is in the order of 10,000 or 100,000.

[G]

I think it would be good to have reliable figures on this issue. But I don't think it ultimately matters in terms of the point of my book, which is to break through the narrative that tends to dominate discussion in the west that Christians can't be persecuted because they belong to the world's most powerful church. The truth is, 2/3 of the 2.3 billion Christians in the world today live outside the West. They live in dangerous neighborhoods. They are often poor, they often belong to ethnic, linguistic and cultural minorities, and they are often at risk. And ultimately, I think making that point is more important than being precise about

[B]

the deaths of it may be impossible to be precise about this important issue, but the one thing that is clear is that the idea that 100,000 Christians have been killed because of their faith every year over the past decade is thankfully unfounded. You're listening to More or Less, and as always, our email address is more or lessbc.co.uk. roaming around the railways of Britain, the More or Less elves noticed a rather

[A]

bold billboard claim we're Europe's most improved railway.

[B]

The sign has a graph at the bottom showing Britain first, France third, and Germany languishing in 15th place. We were a little curious about what this actually means. Do we now have the top railway in Europe, or were we just really bad to start with? Well, the data have been put together by the European Union, and they compare rail customer satisfaction in the EU15, and that's the 15 EU members before enlargement in 2004. And they're comparing surveys from 1997 and from 2012, and it's true data since 1997 show that the UK has the largest increase in the proportion of people saying they're either fairly or very satisfied. In 1997, 34% of people surveyed said they were satisfied. In 2012, that number rose to 55%. It's worth noting though that France, although they are in third place for satisfaction growth, more people in absolute terms are happy with their railway 59%. Now, what about the UK's position overall? How does this surge in satisfaction affect us in the EU15 standings? Well, we've managed to climb three places in the rankings from 13th to 10th out of 15. And I think we can ask a few questions of the countries getting the higher rankings. Take Luxembourg for example. It's not clear how much a comparison between Luxembourg and the UK tells anybody. I do hear rumours that Luxembourg may actually have a train. What is certain is that they only have 250 miles of rail track to maintain. You may remember that last series, I took a bike ride around London with David Spiegelhalter Winton professor for the Public Understanding of Risk at Cambridge University. Left turning lorry, David, you steer clear of that. You steer clear of that. We discussed the dangers of cycling, but also the much larger health benefits. But since that item was broadcast, six cyclists were killed on the capital's roads in just two weeks. Awful news. And news that sparked protests by cyclists and a debate over what had caused the accidents and how cyclists could be made safer in future. Up in Sheffield, a statistics student by the name of Jody Aberdeen read the news and wondered what to make of it and whether David Spiegelhalter had been crunching the new numbers.

[H]

I did a back of the envelope calculation to confirm to myself whether I ought to be surprised and realised that actually it's more complicated than it would first seem. So I then sent an email to David, expecting perhaps for him to take on a more thorough and professional analysis. However, he set me up with the task of reading some of the papers associated with this area and then I was able to crunch the numbers myself.

[B]

Just kind of like a kung fu master trains a new student.

[H]

I did a brief calculation to work out what the chance within just one 14 day period would be. And it turns out to be vanishingly small. But he rightly suggested to me, ah, but you haven't considered the total number of 14 day periods. And that's where I think our intuition falls down, because there are actually very, very many 14 day periods. The temptation is of course to just consider calendar fortnights sequential, so non overlapping and count the deaths in each of those. But if you do that, you're only counting a tiny subset of all of the possible 14 day periods.

[B]

And there is, there is a bias in the kind of events that get reported. I notice looking at the data, there was this period in 2010 from it looks like late summer through almost to Christmas, months and months where no cyclist died on the streets of London at all. And I don't remember seeing newspapers reporting still no cyclist deaths, still no cyclist deaths. That sort of thing just doesn't get mentioned. But it is also an important thing to bear in mind.

[H]

It's fundamental to the analysis of the overall risk to take into account these periods with no or fewer events.

[B]

Now, let's talk about this final answer then. What do the data tell us?

[H]

In fact, it is a surprise. I analysed an eight year period of data and found that less than one in 40 such eight year periods you would find a cluster of six deaths in 14 days.

[B]

Okay, so if it's bad luck, then it is very bad luck, yes. And what are the other explanations other than very bad luck?

[H]

The first and most important one to consider is that there's something in our statistical modelling that's incorrect. It could potentially be that there's something about the risk of cycling in London that has changed within that period, November 2013, and that could be to do with cycling behaviour or traffic behaviour or infrastructure or who knows, something else.

[B]

Jody, having done this analysis, has it changed your view of the risks of cycling?

[C]

No.

[H]

The most important thing to note about cycling is that it is often counterintuitively a massive benefit in terms of mortality risk. Overall, the ratio of benefit to harm is almost 100 in favour of cycling over driving because of the massive benefit to cardiovascular health of regular exercise. So although the risk of trauma is small and may have changed in London, it in no way outweighs the health benefit of cycling.

[B]

Jody Aberdeen. He's a doctor and when he's finished his Master's degree, I suspect he may have a future in statistics.

[A]

And you can read more about Jody's calculations in Significance magazine. There's a link on our website.

[B]

Well, thank you very much, Ruth. That's all we have time for this week. As always, you can download and have another listen or catch up on our Numbers of the Year programme from last week by visiting our website, BBC.co.uk more or less. You can email us at moreorlessbc.co.uk with your comments and your suspicions about shady statistics. Until next week, goodbye.

[A]

More or Less was presented by Tim Harford, the Financial Times undercover Economist. It was produced by Ruth Alexander and made in association with the Open University. You can Download many more Radio 4 programmes for free. Find these at BBC CO UK Radio 4.