Who earns more?

Summary

More or Less – "Who earns more?"

BBC Radio 4 | September 17, 2010 | Hosted by Tim Harford

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Episode Overview

In this engaging episode of "More or Less," Tim Harford takes on three provocative statistical questions dominating public debate:

• Who earns more — public sector or private sector workers?
• How accurate are statistics about Catholic Mass attendance in England and Wales?
• Are high street clothing labels lying about trouser sizes?

Blending rigorous analysis with Tim Harford’s characteristic wit and clarity, the episode exposes the complexities behind the numbers, challenges oversimplified narratives, and brings data to life by speaking with experts and conducting hands-on investigations.

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Key Discussion Points & Insights

1. Public vs. Private Sector Pay – The Real Story

(Main segment: [00:36] to [08:03])

• Trigger: The Office for National Statistics (ONS) published a review igniting headlines claiming the "myth of the underpaid public sector worker."
• Headline claims [01:22]: "Myth of the underpaid public sector worker" (Daily Telegraph), and calls for pay reform (Daily Mail).
• Key guest: Sarah Levy, Head of Pensions Analysis at the ONS, report's lead author.

Main Findings

• Total Reward Concept: ONS used 'total reward', combining gross pay and employer pension contributions ([02:16]).
  • Sarah Levy: "We've put the two together... to create a measure called Total reward."
• Initial Result: At first, public sector workers seemed "better off" than private sector ([02:47]).
• Like-for-Like Adjustment:
  • Many private sector jobs (57%) have no employer pension. Only 10% of public ones lack pension.
  • When comparing only those with pensions, results flip: private sector workers are actually "better off" ([03:45]).

Debate Over Methodology

• Tim Harford challenges: "If you haven't got a pension, you haven't got a pension... why would you not count those private sector jobs that don't have pensions?" ([03:45]).
• Sarah Levy explains: Including zeros (no pension) skews averages; it’s about comparing similar roles ([04:08]).
  • Uses analogy: "If... we wanted to give you an average value of people's homes... we probably wouldn't include all the people who rent... we're trying to... compare like with like."

Complexity and Nuances

• Occupational breakdowns show much bigger differences within professions than between public and private sectors ([06:36]).
  • Sarah Levy: "If you look at managers and senior officials... the private sector is coming out better. If you look at elementary occupations, then the public sector is coming out better."
  • Gender and pay distribution matter: "Men at the top end... big gap in favour of the private sector. For women at the lower end... they're better off in the public sector." ([07:06])

Broader Statistical Perspective

• Once you adjust for things like job type, education, and experience, the supposed public sector “pay premium” drops sharply ([08:03]):
  • Tim Harford: "The Institute for Fiscal Studies... reckoned that while the unadjusted pay premium for public sector workers was about 15% for men and 22% for women, once you adjusted... the premium fell to between 2 and 4%. Those numbers, however, don't take pensions into account."

Memorable Thought Experiment

• Changes in sector (e.g., nationalizing the Royal Bank of Scotland, outsourcing council cleaners) shift average wages dramatically—without changing individual pay, highlighting the limitations of aggregate statistics ([08:03]).

• Tim Harford conclusion: "It doesn't matter how closely you look, the data from the Office for National Statistics won't give you the answer." ([09:21])

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2. How Many Catholics Go To Mass?

(Segment: [10:28]–[13:22])

• Context: Pope’s UK visit triggers scrutiny of Catholic Church attendance figures.
• Conflicting claims:
  • Catholic Church cited at 1.3 million Mass attendees.
  • National Secular Society says it’s only 840,000.

Investigation Summary

• The 1.3 million figure comes from a survey (Ipsos Mori for CAFOD), but is unreliable: "people tend to over claim when asked about virtuous behaviour" ([11:07]).
  • Wesley Stevenson: "The Catholic Church Press office tell us that journalists were never briefed with this number."
• The 840,000 is a projection from 2006 that may be too low ([11:47]):
  • "Latest figures... for 2008... showed Catholic attendance at just under 920,000. This suggests... attendance has stabilised..."
• Attendance counts are done in October, possibly inflating numbers as families seek Catholic school places ([12:38]).

Trends and Causes

• Attendance has dropped dramatically since 1990 (from 1.4 million to above 900,000), but decline seems to have stabilized since 2005 ([12:53]).
  • Wesley Stevenson: "Stabilization... in part at least due to the influx of Eastern Europeans into the UK." ([13:11])

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3. Are Trouser Sizes Honest? Vanity Sizing on the High Street

(Segment: [13:51]–[19:28])

• Prompted by: A US Esquire article reveals "vanity sizing"—where labelled trouser sizes are smaller than the actual measurements.
  • Esquire quote: "Your pants have been deceiving you for years." ([13:51])

UK Experiment

• Tim visits renowned tailor John Hitchcock for a scientific measurement of his waist.
  • John Hitchcock: “If I relax, it's 36. If I breathe in... 35. But you're going to need a 36.” ([16:16])
• Tim compares his labelled 34" trousers (from Gap, Next, etc.) to actual measurements.
  • All come up 36–36.5 inches despite 34” label ([18:14]).
  • John Hitchcock explains: Most men now wear trousers lower on the hips; sizing hasn't kept pace, making 36" trousers labelled as 34" ([18:42]).
    • “...somebody’s told you along the line, you're 34 waist, you go into the shop, you buy a 34, so you're happy. The fact that you decide now to wear them much lower, the cut has been rectified because it's worn a lot lower than you used to wear them.” ([19:08])

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4. Age, Gender, and Who Runs Faster: The Great North Run Handicapping

(Segment: [19:28]–[26:56])

Premise:
Who would run a half-marathon more impressively—a 28-year-old woman, or a 52-year-old man?

Expert:
Alan Jones, retired IBM engineer, expert in age-grading athletic performances.

Method:

• Compile best performances at each age; fit a curve (“bathtub” shape) ([20:21]).
• Use "percentage performance factor" to compare runners of any age/gender.
  • Alan Jones: "You take the person's time divided into [the open-class best]... and you get a percentage." ([21:17])
• Age and gender are both major factors in running performance ([22:14]).

Application to Presenters:

• Lucy Proctor (28F) vs David Lewis (52M) running the Great North Run ([24:43]).
• If David runs in 1:36:00, Lucy must finish roughly 3 minutes and 13 seconds faster for her time to be considered equally impressive ([25:46]).

Playful banter about fair handicapping and personal bests, but no 'trash talk':

• Tim Harford, joking: "This is great. I was expecting trash talk, but actually both of you are managing expectations." ([25:16])
• David Lewis: “Well, I am 52, but I like to think I'm not 52, but sometimes my body tells me I am 52.” ([26:37])

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Notable Quotes & Memorable Moments

• Sarah Levy (ONS):

  • On pension comparisons: "If we're going to compare like with like, we need to compare the people who have this sort of coverage." ([05:02])
  • On sector differences: "...the differences between professions are far greater than the differences between the public versus the private sector." ([07:06])

• Tim Harford:

  • "It doesn't matter how closely you look, the data from the Office for National Statistics won't give you the answer." ([09:21])
  • On vanity sizing: "I'm already interested because this pair of trousers I'm wearing, I'm told by the shop is a 34 inch... Am I wearing them wrong? Are they miss selling me?" ([16:23])

• John Hitchcock (Tailor):

  • "We don't always call out the measurement if we think we're going to upset you. We just write it down." ([16:08])
  • “If you sat down you're going to tear my tape measure.” ([16:47])
  • On modern sizing: "The cut has been rectified because it's worn a lot lower than you used to wear them." ([19:08])

• Alan Jones (Running Expert):

  • "For each distance there is what we call an open class time... you get a percentage performance factor. That's what you look at." ([21:17])
  • "A 48 year old man and a woman running [a half marathon]... if they're both good runners, they should run about the same speed." ([22:49])
  • On adjusting for Tim's own performance: “No, all we do is do it on age and then you'll have to just take whatever comes out.” ([24:01])

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Timestamps for Key Segments

• Public/Private Pay Statistics: [00:36] – [08:03]
• Fake Averages Thought Experiment: [08:03] – [10:28]
• Religious Attendance Figures: [10:28] – [13:22]
• Trouser Sizing Investigation: [13:51] – [19:28]
• Age/Gender Handicapping in Running: [19:28] – [26:56]

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Tone & Style

Intelligent, witty, and accessible. Tim Harford keeps things brisk and light-hearted, even when exploring technical statistical nuances. Frequent analogies, playful skepticism, and real-world experiments make numbers come alive for a broad audience.

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Conclusion

"Who earns more?" is a classic "More or Less" episode—debunking easy answers and exposing the layered realities behind headlines and received wisdom. Whether contemplating the fairness of public versus private pay, the accuracy of religious statistics, or the ego-softening world of high street trousers, Tim Harford and his guests remind listeners: data may clarify, but it rarely settles the debate.

Transcript

[Tim Harford]

Thank you for downloading this week's More or Less podcast. Here's Tim Harford.

Hello and welcome to More or Less, the Top gear of Radio 4 programmes about numbers. This week, the National Secular Society and the Catholic Church clash over how many Catholics regularly go to Mass. We ask whether a 28 year old woman should be able to run a half marathon faster than a 52 year old man. More importantly, are your trousers lying to you?

[John Hitchcock]

Just staying naturally.

[Tim Harford]

See, if I relax, it's 36. If I breathe in, we can get it down to 35.

[John Hitchcock]

Yes, but you're going to need a 36.

[Tim Harford]

But first, on Tuesday, the Office for National Statistics published their monthly economic and labour market review. Bear with me. This is about to get interesting because it's all about that age old statistical question, who's more hard done by and underpaid private sector workers or public sector workers? The ONS Review contains a chapter which tries to answer that question. Its first paragraph.

Some commentators have argued that, taking account of pensions as well as pay, public sector employees in the UK receive better remuneration than their counterparts in the private sector. This article analyses the evidence from the annual survey of hours and earnings of the Office for National Statistics and finds that the answers are more complex than such claims suggest.

Predictably, perhaps, given these straitened times, the report triggered a wave of headlines and comments such as, this from the Daily Telegraph, myth of the underpaid public sector worker. And this from the Daily Mail. The calculation will pile pressure on the

[Alan Jones]

coalition to rein in the cost of the public sector, fattened by 13 years

[Tim Harford]

of labour government through pay freezes, church job cuts and reform of the pension system. But did the stories reflect the complexity the ONS's report's authors wanted to get across? I spoke to Sarah Levy, head of Pensions Analysis at the ONS and the report's lead author.

[Sarah Levy]

I think it's very difficult in newspaper coverage to look in detail at the sort of issues that we're looking at. It's a very complex area and not one that is easy to summarise.

[Tim Harford]

Your main measure is something called total reward. So what does that mean?

[Sarah Levy]

What we've done here is we've looked at both gross pay and the employer's pension contribution, because a lot of people, if you ask them how much they earn, they're likely to quote you their gross pay. But in fact, the employer pension contribution can be a very significant part of overall remuneration. So we've put the two together, gross pay plus employer pension contributions, to create a measure called Total reward.

[Tim Harford]

Now you said this defies an easy summary, but let's try for an easy summary. So what did you find then? We can talk about the details later.

[Sarah Levy]

Okay, well what we found was that if we look at all full time employees, the basic conclusion is that the public sector is better off than the private sector. But we then realized that in fact that was not really a like for like comparison because the total reward is made up of both gross pay and pension contributions from the employer. And for the private sector, a large proportion, 57% of full time jobs don't actually have any pension contributions, whereas in the public sector that's only 10%. So if we were to compare all full time employees, we would not be comparing like with like. So what we then did was to exclude the people who don't have any pension contributions so that when we're comparing total reward, we are comparing getting closer to a like for like measure. And we then found a completely different result which was that in fact the private sector was better off than the public sector.

[Tim Harford]

I have to admit when I saw that you'd done that, I was a bit baffled. If you haven't got a pension, you haven't got a pension. And isn't the whole point of many people's worries about public sector pay that they say, well, these public sector jobs come with great pension pensions. A lot of private sector jobs don't have pensions. Why would you just say, well, let's just not count the private sector jobs that don't have pensions?

[Sarah Levy]

Well, I see them as two different issues. I think there's an issue of lack of pension coverage in the private sector. But if we're trying to compare like for like, you can do it for gross pay. But if you're looking at gross pay plus employer pension contributions and you include a lot of zeros, it makes it very difficult to make that comparison. If you think of similar examples, if for instance, we were wanting to give you an average value of people's homes, looking at home ownership, we probably wouldn't include all the people who rent their home and therefore have zero value of home ownership. So we're trying to make a measure here which actually reflects what the composition of the two sectors is. And compare like with like.

[Tim Harford]

Isn't that a bit like saying bankers aren't paid that much as long as you don't count the bonuses, Whereas in fact the bonuses are a central component of bankers pay.

[Sarah Levy]

Well, this is a different area from the one I work in. What I'm interested in is pensions. And from that perspective. It seems to me that if we're going to compare like with like, we need to compare the people who have this sort of coverage. As I say, there's a separate issue and that is that we've got 57% of full time jobs in the private sector with no pension. But the comparisons that have been made tend to be ones which don't take into account the similarities or dissimilarities between the sectors.

[Tim Harford]

I'm just wondering what the point of this whole comparison is. I mean, we have alluded to this like for like question. People don't enter the job market and simply have a choice of two jobs, either just generic public sector or generic private sector. They're looking for specific jobs. They're looking for a job as a police officer or a teacher or an accountant or a radio presenter. I mean, the whole comparison between these two entirely dissimilar chunks of employment seems a bit bizarre.

[Sarah Levy]

It is always very difficult. If you're generalizing, you're going to lose some of the complexities. I think the issue is whether we can make any comparisons and we feel that we've done something here which adds to the discussion. Up until now, the only evidence that we've had is about gross pay. We haven't been looking at gross pay plus employer pension contributions. And we think this is helping. But I agree with you. By no means does it answer all of the questions and there's still much more to be done.

[Tim Harford]

So I see the graph that you have on page 27 of your report which does start to break down. So you have public sector versus private sector managers and senior officials, public versus private professionals, public versus private admin and secretarial, public versus private personal services. Trying to break things down. And I guess the overall impression looking at this graph is that the differences between professions are far greater than the differences between the public versus the private sector.

[Sarah Levy]

Certainly that is the case. And this is why it's very difficult to compare the two sectors. Because the makeup of the two sectors is different in terms of occupations. But you can notice some interesting things from this graph. For instance, if you look at managers and senior officials or professionals, then the private sector is coming out better. If you look at elementary occupations, then the public sector is coming out better in terms of total reward. And I think there are some differences as well between men and women and between the higher paid and the lower paid. So for instance, if you look at distribution from the lower paid to the higher paid in terms of the total reward indicator, then men at the top End of the distribution, there's a big gap in favour of the private sector. Whereas if you look at women, particularly at the lower end of the pay distribution, they're better off in the public sector. So we do have a number of variations. We've got an overall conclusion, but it is more complex than that.

[Tim Harford]

Sarah Levy a of the Office for National Statistics. This question of like for like is absolutely crucial. There was a research paper released by the independent think tank the Institute for fiscal studies in 2008 which reckoned that while the unadjusted pay premium for public sector workers was about 15% for men and 22% for women, once you adjusted for the composition of the workers in question, the premium fell to between 2 and 4%. Those numbers, however, don't take pensions into account. And here's a thought experiment. Imagine we were to nationalise a bank with a large number of very well paid employees. Oh, I suppose we've already done that. Ok, well, Royal bank of Scotland's employees are now officially public sector workers. We've just raised average public sector wages and lowered average private sector wages. Next, we outsource the cleaning and the rubbish collection at local councils around the country. Apparently, we've done quite a bit of that too. The cleaners and rubbish collectors are now private sector workers. And we've just raised average public sector wages again by removing some workers at the lower end of the income scale. A couple of points about this. First, it's entirely possible to make all these changes without altering the pay or the conditions of a single worker. Second, we haven't altered what the taxpayer is paying for either. In my thought experiment, those Royal bank of Scotland pay packages aren't being paid for by the taxpayer. RBS made 1.1 billion pounds in profits in the first six months of this year. And the private sector bin men and cleaners are being paid using council taxpayers money. I should point out, by the way, that while this thought experiment does highlight the difficulties in making sense of the data, it's only a small part of the story. We've got a separate note from the Office for National Statistics which reckons that if you exclude financial services jobs, average pay in the public sector drops by £5 a week, or about 1%. It's noticeable, but the gap measured by Sarah Levy and her colleagues was closer to pound 100 or 20%. It varies depending on exactly what you measure. So I don't know what to think. Maybe public sector workers are overpaid, lazy and unsackable. Maybe there is plenty of room to get Better public services for less money. It's not for me to say, but what I do know is that it doesn't matter how closely you look, the data from the Office for National Statistics won't give you the answer. You're listening to more or less in association with the Open University and I'm Tim Harford. Now, you may have noticed that the Pope's in town. The National Secular Society certainly has, and they sent us an email which said that the Catholic Church were telling journalists that that Catholic Mass attendance in England and Wales was at a reasonably healthy 1.3 million people, when actually the real figure is closer to 840,000. Well, is that so? Our reporter, Wesley Stevenson, was tragically killed by a freak sound effect two weeks ago. But fortunately we've managed to find his long lost twin brother, also called Wesley. So, Wes, where are these numbers coming from and who's telling the truth?

[Wesley Stevenson]

Well, the 1.3 million figure comes from an Ipsos Mori poll which was commissioned by the Catholic Overseas Development Agency cafod, and it was quoted in an article in the Catholic newspaper the Tablet last November. But if you read the article, it does say that we should be cautious about the figures because people tend to over claim when asked about virtuous behaviour. This was also the only place where we can find the figure quoted. The Catholic Church Press office tell us that journalists were never briefed with this number and it certainly doesn't seem to have been printed anywhere.

[Tim Harford]

So no evidence that the Catholic Church has been spinning the number. But what about the National Secular Society claim that the figure is as low as 840,000, is that right?

[Wesley Stevenson]

Well, the figure of 840,000 is based on a projection of mass attendance in 2010, which was made in 2006 by an organisation called Christian Research. Now, this assumed that Mass attendance would continue to drop at the same rate it had done over previous years. However, the latest figures collected for 2008 were released last Friday by the same organisation, Mass, and showed that Catholic attendance stood at just under 920,000. This suggests attendance in the Catholic Church has stabilised and it seems in the short term at least, that the 840,000 figure may be a bit conservative. One interesting aside is that these official figures are gathered by counting church attendances at all churches, but the count takes place in October. Some point out that the figures might spike then, as parents work on getting their children into Catholic schools.

[Tim Harford]

So the figures might be somewhat flattering, but that shouldn't affect the trend. And the National Secular Society describe this trend in its email to us as the catastrophic decades long decline in Mass attendance. So are they right about that or not?

[Wesley Stevenson]

Well there has been a drop. In 1990 more than 1.4 million Catholics attended weekly Mass in England and Wales, so the figure has fallen by about a third over the last two decades. But there does appear to have been a stabilization since 2005 at just above the 900,000 mark.

[Tim Harford]

Do we know why that is?

[Wesley Stevenson]

Well one of the academics who studies this area, Professor David Wurs from the University of Manchester, said he suspected that the stabilization was in part at least due to the influx of Eastern Europeans into the uk.

[Tim Harford]

Well thank you Wes. If you'd like to send us emails about the Pope, public sector pay or anything else, our email address is more or less bc.co.uk. you can follow me on Twitter. I'm Tim Harford and our website with archive, podcast and all sorts of other goodies is BBC.co.uk more or less now are High street labels All Mouth and no Trousers? The US edition of Esquire magazine has recently asked the question, are your trousers lying to you?

[Unidentified Male Narrator (Esquire segment)]

The devastating realization came in H and M, specifically in a pair of size 36 dress pants. I'd never bought pants at H and M before and suddenly asked myself, how could a 36 inch waist suddenly be so damn tight? So I immediately went across the street, bought a tailor's measuring tape and trudged from shop to shop trying on various brands casual dress pants. It took just two hours to tear my self esteem to smithereens and raise some serious questions about what I later learned is called vanity sizing. Your pants have been deceiving you for years. Alfonni's 36 inch garrette pant was 38 and a half inches. Dockers, meanwhile, teased leave yourself some wiggle room and they weren't kidding. Despite having a clear size listed, the 36 inchers were 39 and a half inches. However, the temple for wasted male self esteem is Old Navy, where I easily slid into a size 34 pair of the brand's dress pants. The final measurement five inches larger than the label.

[Tim Harford]

Could the same thing be true in the uk? We had to investigate. And now here it is, a rather impressive trouser package. I've come to an esteemed tailor's just off Savile Row, Anderson and Sheppard and I'm here in in an elegant changing room with the managing director John Hitchcock, who is going to tell me whether my trousers are lying to me or not.

[John Hitchcock]

Every customer we have, we take four measurements. You've got Douglas Fairbanks.

[Tim Harford]

Douglas Fairbanks.

[John Hitchcock]

That's in his own handwriting. I mean this is exactly. You can go through. And it's like an autograph book really.

[Tim Harford]

Is there any that you're particularly proud of?

[John Hitchcock]

Prefer to stare. I mean Fred Astaire was really something. He come in here and he used to dance in the fitting room and make certainly felt comfortable in his clothes.

[Tim Harford]

So what are the key measurements when you're measuring a pair of trousers? The outside leg, the inside leg, the

[John Hitchcock]

waist seat and obviously the leg when

[Tim Harford]

you're measuring the waist. Is this a sensitive topic for some customers, their waist measurement? Do some people prefer not to know?

[John Hitchcock]

We don't always call out the measurement if we think we're going to upset you. We just write it down.

[Tim Harford]

Now, should I be breathing in, breathing

[John Hitchcock]

out, just staying naturally.

[Tim Harford]

See, if I, if I relax it's 36. If I breathe in we can get down to 35.

[John Hitchcock]

Yes, but you're going to need a 36.

[Tim Harford]

Now I'm already interested because this pair of trousers I'm wearing, I'm told by the shop is a 34 inch. You know, I don't usually have to struggle to do the buttons up. Am I wearing them wrong? Are they miss selling me?

[John Hitchcock]

This is the tape measure.

[Tim Harford]

Yep.

[John Hitchcock]

Right. And if we put that round you.

[Tim Harford]

I believe you, the tape measure doesn't lie.

[John Hitchcock]

And we pour that in, that's 34 and I think you're going to be uncomfortable with that.

[Tim Harford]

That's a little bit of a bulge coming out.

[John Hitchcock]

Yeah, you've got a bulge coming out the top and I think if you sat down, you're going to tear my tape measure.

[Tim Harford]

Yeah, that's very kind of you to put it that way. Well, we're off to nearby Oxford street now. We're going to pop into some of the biggest trouser retailers, or jean retailers, if you prefer, John, and we'll buy a few pairs and we'll see whether they deliver on the promises on the label. I've braved Oxford Street, I've been to four high street shops and I bought four pairs of 34 inch trousers. Why 34 inch trousers? Because I always wear 34 inch trousers and they always seem to fit me. But John measured my waist as 36 inches and he measured my trousers 36 inches. So I've brought these four pairs of 34 inch trousers back here to Anderson and Shepherd for the moment of truth. Yeah, that would be great. I'm starting with Gap and they claim to be 34 by 34. Let's try them on. Not sure this is quite my style, but on the radio this is no time for vanity. They are very comfortable. They seem to fit perfectly. They're just sitting on my hips. Let's see how big they are.

[John Hitchcock]

If you measure from there to there, it measures 18 across. Double 18 is 36.

[Tim Harford]

Next is next. Did you see what I did there? I would say that they were a

[John Hitchcock]

little loose, but do you see they're just, just over 36 again.

[Tim Harford]

So again, you measured them at 36 and a half maybe? Yes, they're advertised at 34. John, it seems pretty open and shut. You've measured my waist, it's 36 inches and yet they're advertised as 34. So are my trousers lying to me?

[John Hitchcock]

No, what it is, where I've measured you is halfway from your waist to your hips. That's where you're 36. If you actually measured your waist, then you're only 34. But because you've chose to wear the trousers on your hips, you need it that little bit larger.

[Tim Harford]

But they are still 36 inch trousers, advertised as 34. So are the retailers adjusting because they know that I'm going to wear my trousers low because I'm a fashionable kind of guy?

[John Hitchcock]

That's really it. Really. You know, somebody's told you along the line, you're 34 waist, you go into the shop, you buy a 34, so you're happy. The fact that you decide now to wear them much lower, the cut has been rectified because it's worn a lot lower than you used to wear them. Maybe in the 70s.

[Tim Harford]

You're listening to more or less and your 34 waist, 34 leg presenter is Tim Harford. Now, have you ever wondered how you could go about handicapping a tennis match between Rafael Nadal and John McEnroe or between Usain Bolt and a horse, assuming you could get the horse to hold the tennis racket, or a fight between a shark and a toaster, or a half marathon race between a 28 year old woman and a 52 year old man this Sunday. Or if you're listening to the Repeat this morning, it is, or it was the Great North Run, the largest half marathon in the world. There are all sorts of people taking part. But how would we know, given people's sex and given their age, which performances are the most impressive? Well, Alan Jones is a retired engineer for IBM and as a hobby he's been thinking about this problem for a very long time. So I asked him, how does he do it?

[Alan Jones]

Well, what we do we take the best performance, not world records, because they're just best performance for each single age. So we have the best performance that a man has done and a woman's done say at age 36. And at age 37 we have these for all the ages up well into the 80s. And if you plot these on a piece of paper, you get kind of a bathtub curve. It goes up for the youngsters at 5 years age and it goes down to a flat area for ages around 25 through 35. And then it curves back up again as you get older. That is the times are longer and people get slower. And then we run a curve right underneath all those and that's how we create these tables.

[Tim Harford]

And how would you answer? You've got this curve, you've got these tables. So if I gave you a time for a 30 year old and for a 50 year old, how would you tell me which was the more impressive time?

[Alan Jones]

So what you do in addition, which I did not mention, for each distance there is what we call an open class time. That's the best we think anyone's has done or will do in the next few years. And so based on that time, you take the person's time divided into that and you get a percentage. And if the person was 25 years, like your example of a woman being 25, you just merely divide her time. Now say she's rather slow and just runs exactly half the speed of the other runner. It takes twice as long. Divide in, she has a performance factor of 50%. So that's okay if someone's in the age 25, 35, if they're older, there's this extra age factor that we put in that we've developed from these tables and we adjust it according to that. So that 25 year old woman and a 52 year old man, you develop what you call a percentage performance factor. And that's what you look at.

[Tim Harford]

I suppose some people will be wondering what matters more, age or gender?

[Alan Jones]

Well, it depends. And a man, you know, in his 50s is going to get a better benefit from these tables than a woman in her twenties. So it depends. You can't say if you're comparing a woman in her 20s with a man, say 40, then the man's definitely going to do better.

[Tim Harford]

Is there a particular age where you would say it's a fair race between a woman and a man if the woman is a young woman and the man is older or does that question not make sense?

[Alan Jones]

Yeah, you have to do that for each distance now we've been looking at the half marathon and that turns out to be the age 48. And the reason that is is because the open time between the very best open runner male and the open runner female is a factor of 8995. And that's also the age factor for a 48 year old man. So that is a, that's a wash. A 48 year old man and a woman running. If they're both good runners, they should run about the same speed.

[Tim Harford]

Have the shapes of these curves changed over time? Are older runners getting better relative to younger runners or are men getting slower or faster relative to women?

[Alan Jones]

Well, they haven't really changed very much for the men, partly because the men have been in this running business so much longer and the tables are just kind of tweaked. But the women, it's changed quite a bit. Back when they started this in 1989, they didn't have much data and to tell you the truth, the tables were very graded against the women. They were very hard for a woman to do.

[Tim Harford]

Well, could you adjust for someone like me? I mean, I'm mildly asthmatic, a little bit lazy, I'd much rather count things than run. Can you give me an adjusted factor?

[Alan Jones]

No, all we do is do it on age and then you'll have to just take whatever comes out. What we're showing is what the very best runners will do and then everyone else is just adjusted below that.

[Tim Harford]

Well, Alan, that's how it works in theory. But we've got a practical problem for you to solve. In fact, it's a bit of a grudge match. I've got Lucy Proctor. Hello, Lucy.

Hello.

And David Lewis. Hello, David.

[David Lewis]

Hello.

[Tim Harford]

Easily the two most serious runners on the current affairs staff and we're trying to work out if you did the age adjusted problem. And of course adjusted for gender. You may have noticed they do have different gender. Who would come out as the better runner. So Lucy, where are you going? To put this to the test.

We are both doing the Great North Run on Sunday, the biggest half marathon in the world. So it's a good place to test this out.

Are you feeling confident?

I was feeling confident until I discovered that David did a 15 mile fell run last weekend as preparation, which makes me incredibly nervous. And now I'm not feeling so full of bravado as I was before.

David, you've been practicing. That's not fair.

[David Lewis]

Well, no, I think Lucy's showing a bit of modesty there. I haven't run a road race for about 18 months. So I.

[Tim Harford]

This is great. I was expecting trash talk, but actually both of you are managing expectations. You're both absolutely convinced, at least you're both claiming to be absolutely convinced that the other person is going to do better. Alan, my understanding is that David and Lucy are both hoping to do this in about 1 hour 30 to 1 hour 40, that sort of time, if they were in that ballpark. Lucy is 28, David is 52. Well, first of all, who needs to beat whom and by how much?

[Alan Jones]

Well, let's take the hypothetical case of David running in one hour and 36 minutes. That will give him, adjusting for his age of 52, a performance factor of 70.95%. Well, then, working the tables backwards, I find that Lucy has to run 1 hour, 32 minutes and 47 seconds. That's about 3 minutes, 13 seconds faster.

[Tim Harford]

Lucy, David's an old man. That doesn't sound too hard.

But he's a man, you know, it makes a big difference. And he's also got the confidence of having done lots of races and the knowledge that he's done a PB way faster than that. Whereas my PB is one personal best. Sorry, I've gone into running jargon. My PB is 137, so I've now got a knockoff, apparently five minutes, which is a lot when you're running.

So, David, you should do it backwards or something, or wear a backpack to compensate.

[David Lewis]

Well, I am 52, but I like to think I'm not 52, but sometimes my body tells me I am 52. And I think as I'm getting older, you know, running is a bit more of a painful process. So hopefully, if I can keep everything together on the day and I don't ate too much, I'll give Lucy a run for her money.

[Tim Harford]

That's all we have time for this week, if you're listening to our Sunday repeat. Of course, Lucy and David have run their race already, but you'll have to wait until next week to find out what happened. Until then, our website, BBC.co.uk more or less is the place to find out more, to subscribe to the podcast, listen to archive episodes of the show, or to send us your comments and your tip offs about dodgy statistical stories in the news. Please do, because the show depends on your ideas. Goodbye.

More or Less was presented by Tim Harford, the FT's undercover economist. The producer was Richard Knight and the editor was Richard Varden. It was made in association with the Open University.