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Zeroes and ones, part five

13 Apr

This week on Journalists’ Adventures in Maths: percentage changes are not reversible, or why a 75% rise from 4 to 7 is not a 75% fall from 7 to 4.

Dutifully checking the numbers* in the copy as they come up, I first get a result at variance with the reporter’s:

and then, by swapping the numbers around, get one that agrees:

However, the minus sign at the start of the second answer is the clue: the numbers in that sum are declining from over 400,000 to less than 300,000. But the copy talks about a rise.

The same thing happens with the second pair of numbers: the percentage rise is calculated as though it were a percentage fall.

Why is it not the same? The difference between 8,276 and 12,092 is always constant: 3,816. But in a percentage, of course, you can relate that constant difference to different comparators, and 3,816 is a much larger proportion of 8,276 than it is of 12,092.

This will hardly come as news to people who can do maths. But for arts-heavy newsrooms, this is slightly more perilous territory than the answer just being wrong – it is wrong, but it seems right if you do the sum the wrong way round. You need the strength of mind to remember which number you’re starting with and stick with it. It seems somewhat analogous to the evergreen error of mistaking ancestors for descendants, or confusing “overestimating” and “underestimating”. It’s not just the relationship between the two things that’s important, but the direction of travel too.

*Use of a percentage calculator is highly recommended, of course; I like this one, with its clear, question-based approach.

Box-office figures

25 Jun

Thanks, Google. Actually, I was just checking titles and release dates of films for a piece about how the sex scene is dying out in cinemas. But thanks.

I’m quite impressed that it even saw a sum it could calculate in that search. It’s not like I was looking for the French arthouse romance 5×2. Thank goodness I didn’t need to check From Here To Eternity.

Zeroes and ones, part four

27 Nov

Q: Looking at the selected paragraphs below, and before doing any Googling, is there anything wrong with this article that can be determined simply from the evidence in front of you? Answers below

A: Not a particularly difficult one by the standards of what HeadsUp calls “implied mathematics“. If Hella Pick is 90 next spring, she’s 89 now. That means she was born in 1929. If she was born in 1929, she can’t have been 37 in 1980: she would have been in her 50s. So either her age or the date of Tito’s death is wrong. A quick bit of Googling would then tell you Tito indeed died in May 1980; so Ms Pick’s age at the time can be quietly removed from the copy. “… then 51 and working for the Guardian” somehow sounds much less glamorous.

Zeroes and ones, part three

11 May

One of the occupational hazards of being a journalist is that when a howler appears in the paper, all your friends know exactly who to call. Especially when they’re highly qualified science and maths graduates, and especially when the howler in question is a pretty glaring failure to check the sums.

So when this the first paragraph appeared in an article from the US office:

Screen Shot 2016-04-27 at 10.04.07

Followed by this information in the third paragraph:

Screen Shot 2016-04-27 at 10.04.25

Followed by this handy graphic as an explainer:

Screen Shot 2016-04-27 at 10.04.16

It wasn’t long before this appeared on my Facebook page:

Screen Shot 2016-05-09 at 12.51.30

Fortunately, because they’re all highly qualified science and maths types, when the bumbling former English student has questions, they have the explanations ready to hand:

Screen Shot 2016-05-09 at 12.51.43

So, for future reference: any percentage increase from 0% to any higher percentage is an infinite increase; but any percentage-point increase from 0% to a higher percentage is as simple a sum as can be: <higher percentage> – 0.

Meanwhile, the web news production editor has just sent this chastening email round to all subs:

A common error has popped up again so I just wanted to remind everyone that converting differences in temperatures is different to converting actual temperatures.
For example:
A temperature of 2C is 35.6F
but …
a difference in temperature of 2C is 3.6F.
 Thank goodness my friends didn’t see that story before it was corrected.


Marginal differences

14 May

Screen Shot 2015-05-10 at 17.00.15

Screen Shot 2015-05-10 at 17.01.12

It’s not all that hard to count to 331, but, as we can see above, there’s more than one way to get there.

In the aftermath of the general election, it fell to me to check the paper’s giant map of the seats won and lost across Britain on 7 May. In particular, the graphics department wanted to know how many gains – gross gains, that is: gains before losses – had actually been made, so that they could list them all around the map. Out of a total of 650 parliamentary seats, that seemed like an elementary request. Or so I thought, until I found that two reliable sources (the Guardian, top, and the BBC, above) were giving completely different figures.

To take the Conservatives as an example, both sources have them winning 331 seats in total. But the Guardian has them gaining 38 seats from other parties (and losing 10), while the BBC has them gaining 35 (and losing 11). How can that be? No wonder graphics was puzzled: I was too.

Clearly, since they imply net gains of 28 and 24 seats respectively, the two sums can’t even be working from the same base figure of constituencies held before the election. So what figures are they using? Subtracting the net gains from the total of seats now held – 331 – is an obvious place to start. That reveals that the Guardian (331 – 28) is working on a basis of 303 Conservative seats already held, while the BBC (331 – 24) is working on a basis of 307.

Hmm. Odd. Can we relate either of those two figures to data about the previous election? Time for a quick trip to the Electoral Commission’s website, where we find that … oh:

Screen Shot 2015-05-13 at 15.13.38

Now we have a third figure for seats won in 2010: 306. What’s going on? Can we not even agree on a figure for the number of seats the largest party in the country holds from one general election to the next?

And then, after slightly longer than one cares to admit, the light began to dawn. The clue to the Electoral Commission figure is down at the bottom of the graphic: “Speaker (1)”. The Speaker of the House of Commons is an apolitical figure who votes only in the most exceptional of circumstances; nonetheless, he or she is still notionally an MP who stands for election as a representative of one of the parties. And the current Speaker, John Bercow, is a Conservative: the Tory MP for Buckingham. So if you add him to the Conservative total, you get 307: the same as the BBC’s figure. And then it all starts to become a lot clearer.

Clearly, the BBC is using the data from the 2010 election as its basis point. So what is the Guardian using? One obvious possibility is that it is factoring in changes to the makeup of the Commons that have taken place since 2010. Can we account for the discrepancy by looking at byelection results in the last parliament?

According to, there were 21 byelections in the last parliament. Three of them resulted in the Conservatives losing a seat, and all three are still reasonably memorable events for political wonks: author Louise Mensch’s unexpected resignation from her seat in Corby in 2012, which resulted in a Labour win; and the high-profile defections of Douglas Carswell and Mark Reckless from the Tories to Ukip in the runup to the election, when both incumbents won their seats back under new colours.

That reduces the number of seats the Tories held in parliament from 307 to 304, which is getting closer to the Guardian’s figure. Could it be that the Guardian is simply discounting the Speaker’s seat? It seems not: the election interactive is clear that it is talking about all 650 seats in the country, not 649 as would be the case if Buckingham were excluded.

It’s only when, exploring the interactive, you discover the striking fact that ultra-safe Tory seat of Kensington is described as a “gain” that you find the last missing piece. Sir Malcolm Rifkind, the former foreign secretary and MP for Kensington, was suspended by the Conservative party, and ultimately decided not to stand for re-election, after being caught in a cash-for-access newspaper sting in February. Technically, therefore, as a sitting MP who has had the party whip withdrawn, he counted as a seat lost before the election, and therefore a Tory “gain” (from an “independent”) when his successor duly won. So the Guardian’s total, omitting Mensch, Carswell, Reckless and Rifkind, is also correct: 303.

So who’s right? In short, everyone. The BBC is working on a previous-election basis, using unmodified figures from the 2010 ballot. The Guardian is using eve-of-election figures, reflecting the actual position of the parties on the day before the country voted in 2015.

Both approaches have their strengths and weaknesses. If you work on an eve-of-election basis, you’re using running totals based on the quality of your own electoral research and arithmetic. If you work only on the official previous-election numbers, the maths is simpler, but you have to remember the “byelection factor”: some triumphant regainings of marginals lost in midterm will actually be “holds” for your purposes, and some routine victories for the winners of half-forgotten byelections actually “gains”.

If you’re wrestling with British electoral totals (and you might not be for another five years … although who knows?), here’s a table covering four of the most likely problems you may encounter (click to enlarge). As to how 2020’s calculations will go, if the major boundary changes and seat reductions planned by the Tories go through in this parliament – heaven only knows.

Screen Shot 2015-05-13 at 17.06.57


Please show working

10 Jun

The chief revise sub isn’t quite sure about this paragraph:

Picture 42

He immediately saw what we all see when he calls us round to look at it: that doesn’t sound like 18% less. That sounds like a lot more than that. And he’s right: £250 is almost 40% less than £415, not 18%. And in the second calculation, £204, compared with what men with no qualifications earn per week (£354), is 42.3% less, not 14.3% less.

The nervousness that descends upon all journalists when numbers appear in a story starts to cloud the collective mind as we stare at it. The percentage figures are per hour, but the amounts in pounds are per week. Is that what the problem is? Does the hourly rate difference accumulate to create a larger gap at the end of the week? But a simple thought experiment rules that out. If one worker is paid £8 an hour and other is paid £10, the difference in hourly rate is 25%. After a six-hour shift, one has earned £48 and the other £60 – still a 25% difference. At the end of a five-day week, one has earned £240 and the other £300 – still a 25% difference. No: if a woman earns 18% less in the course of an hour, she should earn 18% less in the course of a week. Something’s wrong.

The chief revise sub goes over to the reporter and ask to see the data on which the story is based. (The appearance at one’s desk of a member of production staff asking to see source documents is never a good sign for a reporter, of course, but they always seem to take it with remarkable stoicism.) He returns with this (click the image to magnify):


Pay data main NEW

As usual, some of the highlighting and circling seems to have been done with a completely different story in mind, but the data is there. Take a look at the last column, four rows down. There’s the 18% median pay gap figure (well, 17.9% – close enough for newspaper work). Read left, back along that row, and there are the gross weekly pay figures for men and women: £415 and £250. And the second-bottom row, for unqualified men and women, is also just like the reporter wrote it: 14.3%, £204, £354. What’s on earth’s going on? Is the table just completely innumerate?

And then someone has a bright thought. The problem women face in the workplace is not just lower pro-rata pay: it’s also less opportunity to work, whatever the rate. What if the gross pay figure reflects not only a lower hourly rate, but also a lower number of hours overall? It doesn’t explicitly say so anywhere in the table or the story, but what if the women’s working week in the study is shorter than the men’s?

The figures are there to work it out quickly: divide the gross weekly pay by the median hourly rate to get number of hours. For the men, that’s £415 divided by £10.02, or 41.4 hours per week – a full-time job. For the women, though, it’s £250 divided by £8.23, or 30.4 hours a week – a full 11 hours less. That’s why it doesn’t add up. No wonder it struck everyone as strange.

It’s fairly easy fix in the article, too. There’s no space to explore the issue of unequal hours – it’s only a 250-word downpage slot– so you have to lose the easy-to-grasp pound figures and go with the percentages. But at least it’s right now, and at least it was fixed before publication.

Thank goodness for multi-stage editing. The common cry when a mistake gets into print, from readers or readers’ editors, is “didn’t any of you notice?” Well, this time, somebody did. Maybe the chart shouldn’t have been taken out of context, or divorced from its explanatory notes. Maybe it didn’t have any notes at all, and silently included undeclared data that would have thrown anyone off track. Maybe it shouldn’t have got all the way through to the revise desk before it was spotted.

But that’s editing. That’s how it works. It’s not a discrete, finite task: it’s a process. There will always be mistakes on first proof. There will always be mistakes on second proof. More often than not, you’ll find something horrible on a final read even after hours of work on a story. That’s why the Tribune’s production editor insists on press-reading every page of the paper: even if it’s right on deadline, even if that means tearing the proof up and hurriedly handing individual stories round the room. Nothing beats multiple revisions and multiple pairs of eyes. It doesn’t matter how good you are: you won’t spot everything. But maybe someone else will see what you missed.

Zeroes and ones, part two

31 Oct

I love it when our media commentator goes off on a theme. Editing writers who have let themselves off the leash is always enjoyable, and his stream-of-consciousness style is at its best when he’s got hold of a metaphor and is running with it.

This piece – only a 240-word sidebar to his main column – is about the BBC payoffs row: the large amount of licence-payers’ money given as golden goodbyes to departing executives and the furious backlash that has resulted from them. That money could have been spent on all sorts of worthwhile things, the media has chorused, using the usual benchmarks: Downton Abbey episodes, schoolbooks, hospital beds etc. Last week, though, the BBC came out fighting, and countered the criticism with a comparison of its own. As the media commentator puts it:

Picture 17

And that’s all the media commentator needs to mint a new currency of comparison, the unit of exchange being the cost of televising Sunderland v Newcastle at the Stadium of Light: one match equals one “Light”.

Picture 18

When writers have got the bit between their teeth, the standard advice for editors is to keep out of their way and let them flow. And that’s good advice on the whole: intervening to correct fragmented sentences or very long paragraphs can kill the whole experience, and bring “correctness” and “readability” at the expense of enjoyment. But mistakes – actual mistakes – are a different matter. Maybe it’s my dorkish sub-editor’s soul, but I can’t fully enjoy a comic or passionate rant when a dangling modifier points all the ire in the wrong direction or there’s a glaring malapropism in the punchline. A greengrocer’s apostrophe can spoil a joke almost as much as it spoils an editorial. So the skill, actually, is to intervene just enough – to unobtrusively correct a fact or a timeline, say. Or, in this case, to correct the arithmetic.

Let’s look at what a “Light” is worth again. If £3.8m is “about half of what of what other TV networks would pay for televising the first half of  a Premiership football match”, that’s £3.8m per quarter, in effect, or £7.6m per half. The total cost of a match would be £7.6m x 2; therefore one Light equals £15.2m.

But that doesn’t seem to be how it works in the article. If BBC News costs £61.5m, that’s nowhere near as much as 10 Lights: more like four. Same with BBC4: £70.2m is less than 5 Lights, not more than 10.

And hang on a minute: did Lord Patten really say “half of what of what other TV networks would pay for televising the first half of  a Premiership football match”? That’s a funny way to put it – a lot of halves. That’s actually strange enough to need some investigation.

And lo and behold, the original article proves that doesn’t appear to be what he said. Per the furniture:

Picture 19

Mystery solved. But wait – what’s this in the body text?

Picture 20

So, he did say half of a half? What’s going on here? I thought I was just on for a quick tidy-up of a 240-word sidebar. But now, out of nowhere, we’re into a full-blown re-investigation of a completely different article from another desk whose content is at variance with its furniture (and which is also short an apostrophe in the standfirst). Can’t just leave it like that. Sigh.

Right: further scrutiny of this new article has revealed an actual hard number we can work from:

Screen shot 2013-10-29 at 18.12.48

Aha. So, allowing for typical politicians’ numerical exaggeration (and journalists are not in much of a position to criticise anyone else about that), £3.8m is indeed, roughly, the cost of televising half a Premier League match. Good: just need to email the media desk with suggested corrections for this piece, go back to my piece and write around the quote to fix it.

Except that – dammit – we’re still not quite there. If £3.8m is right (ish), the sums still aren’t. Look at the maths once again. The cost of BBC News, £61.5m, isn’t exactly “less than 10 Lights” if you take “less than 10” to mean nine-point-something and one Light to be £7.6m: it’s barely over eight. But it is pretty close if you go with the real £6.6m figure – which is mentioned nowhere in this piece. Moreover, BBC4’s budget of £70.2m isn’t “10 Lights and a bit of injury time” if one Light is £7.6m; and if one Light is £6.6m, it’s closer to 11 Lights than 10 – not just a bit of injury time but almost a whole extra hour.

Never judge an article by its word count. Man, why did I pick this one up?

Zeroes and ones

2 Jun

And the fact box read:

Picture 9

That’s faithfully transcribed from the data, supplied from an authoritative-looking source. And this is inward investment into China, so we are talking about serious money. But look at the subheading, as provided in the original: “$bn”. Then look at the commas in the figures: commas, not points. That means that Japan’s investment position in China in 2010 was $106,303,000,000,000. One hundred and six trillion dollars.

That’s a sizeable chunk of inward investment. No wonder the Shanghai skyline is shooting up so fast. It’s also about seven times larger than the national debt of the United States, and approximately 30% larger than the GDP of the entire world. And that’s before you get to the US’s own contribution to the Chinese economy, apparently a healthy  63 trillion dollars. You begin to suspect that something might be wrong.

Of course – all together now – you know what they mean. They mean 106 billion dollars; the table needs to say $m, not $bn. But that’s not what they said. There’s no descriptivism in maths. Billion is not “widely understood to mean million in informal or conversational usage”. It means billion.

Numbers, notoriously, provoke a certain amount of fear in the journalistic profession, stuffed as it is with arts graduates who quail inwardly at the sight of a percentage sign. But in many ways, it’s actually comforting to find oneself working in a system of communication where clarity is still prized over ambiguity.

Ten years after

24 Apr

This is a post to echo a good point that’s been made at HeadsUp repeatedly in the past few years: that there’s a lot of hidden or implied maths in historical stories that can be checked. Not just, say, the simple recalculating of percentages in financial copy, but the more difficult-to-spot progression of dates in a timeline, or perhaps the comparison of a biographical piece against the fixed historical dates it mentions.

In one recent story, the raw copy began:

Picture 22

The events in question, we soon learn, took place in 1931:

Picture 23

And the way she found out about them was by finding a copy of a memoir about them under her bed – a memoir that her father didn’t want his teenage daughter to read:

Picture 25

But despite her father’s unhappiness, what she had read left a strong and lasting impression on her:

Picture 24

There’s quite a lot of data there: enough, in fact, that the information can be plotted on one timeline that ought to take us from the incident itself to the present day.

But it doesn’t. Not quite. The incident happened in 1931. “Almost three decades later”, the copy says, Ms Washington was born. Let’s say three decades exactly, to make it easier; that would be 1961. So when she was 17, it would have been 1978; but “25 years” after she found the book only takes us to 2003. Ten years have gone missing somewhere. Time to email the author.