Do the maths

How sta­tis­ti­cally likely is the pi na co­lada song? We in­ves­ti­gate

The Guardian - Weekend - - News -

You’ll know the song. That lop­ing 70s riff, fa­mil­iar from child­hood, a par­ent’s mix­tape or the Magic FM playlist. The singer’s bright, breezy de­liv­ery. And then the ir­re­sistible hook: “If you like pina co­ladas, and get­ting caught in the rain. If you’re not into yoga, and you have half a brain… ”

I re­dis­cov­ered Es­cape (The Pina Co­lada Song) in 2014 while watch­ing Guardians Of The Galaxy. I was even more en­rap­tured by the sound­track than the film. And this par­tic­u­lar track – a US No 1 on its re­lease in 1979 (al­though it recharted in 1980, mak­ing it the only pop song to hold the top spot in dif­fer­ent decades) – soon wormed its way into my psy­che, partly be­cause it was so catchy, partly be­cause it was so an­noy­ing.

If, like me, you’re the sort of per­son who sings along to a song de­spite hav­ing only the vaguest grasp of the lyrics (“Na-na-na PINA CO­LADA!”), it’s pos­si­ble the in­tri­cate plot­line of Ru­pert Holmes’s hit has passed you by. So let me sum­marise: Holmes sings of be­ing bored with his girl­friend, and read­ing the lonely hearts ads in bed as she sleeps next to him (we can leave aside the cal­lous­ness of that un­til later). One ad catches his eye: a mys­tery woman is look­ing for a man who likes pina co­ladas, get­ting caught in the rain, who isn’t in to yoga, and “has half a brain”. She also, get­ting spe­cific, wants some­one who “likes mak­ing love at mid­night, in the dunes of the cape”. Any man match­ing these re­quire­ments, she says, should write to her “and es­cape”.

Our pro­tag­o­nist, de­cid­ing this de­scrip­tion fits him per­fectly, places a per­sonal ad in re­sponse, sug­gest­ing they meet at a bar at noon. De­spite this unusual time for a first date, she walks in – and, what do you know, it’s “his own lovely lady”. Rather than break­ing into a flurry of mu­tual re­crim­i­na­tion, they laugh at the co­in­ci­dence and talk about all the in­ter­ests they never knew they shared – in­clud­ing an affair, pre­sum­ably.

This story first mad­dened and then in­trigued me. I am a data jour­nal­ist and found it hard to get past the sheer un­like­li­ness of this se­quence of events. Not only does Holmes’s pro­tag­o­nist hap­pen to see his girl­friend’s se­cret ad in a lo­cal pa­per, but he’s the first to see it and ar­range a meet­ing (we can as­sume, be­cause she’s still avail­able). And when they un­cover each other’s in­fi­delity, they just laugh it off. I won­dered, what were the chances?

I’ve spent the past decade as an in­ves­tiga­tive re­porter, digging through the num­bers be­hind ev­ery­thing from off­shore fi­nan­cial records to the in­tel­li­gence agency doc­u­ments leaked by Ed­ward Snow­den. What if I ap­plied my sta­tis­ti­cal skills to this ques­tion? OK, whether or not the pina co­lada cou­ple would have an­swered each other’s ads – and then rec­on­ciled – might not be the most press­ing is­sue on the planet, but as soon as the idea oc­curred, I found it hard to let go.

My search for an­swers be­gan with try­ing to work out how many peo­ple might be el­i­gi­ble for the song’s “lovely lady”. This was made slightly chal­leng­ing by Holmes’s de­ci­sion not to men­tion where the song is set at any point in the lyrics. Given the ab­sence of in­for­ma­tion to the con­trary, I opted for Holmes’s home­town of North­wich, a small town in Cheshire dat­ing back to Ro­man times. A pedant might note that Holmes moved to a sub­urb of New York as a child, but the song ti­tle – Es­cape – had al­ways evoked small­town Eng­land, at least to me. I grew up a few dozen miles from North­wich. I knew ex­actly why, liv­ing there, the lure of pina co­ladas and a fum­ble on a far-flung beach would be ir­re­sistible. Plus, the UK has much bet­ter archival data.

First, I needed to know how many peo­ple might have seen the per­sonal ad and how many might match it. My start­ing point was the UK Cen­sus – a na­tion­wide ef­fort, ev­ery 10 years, in which ev­ery cit­i­zen is legally obliged to give the gov­ern­ment in­for­ma­tion about them­selves: their age, lo­ca­tion and other de­mo­graphic data.

Es­cape was re­leased in 1979, only two years be­fore the 1981 na­tional cen­sus, ac­cord­ing to which 17,098 peo­ple lived in the town­ship of North­wich. Af­ter elim­i­nat­ing women and chil­dren – we can as­sume our mys­tery ad was seek­ing a man – the cen­sus had the fig­ures I needed. About 21% of the pop­u­la­tion at the time were 15 and un­der, and about 18% were pen­sion­ers, leav­ing 10,430 work­ing age adults. Of those, slightly less than half would be men: while more male ba­bies are born than fe­male, the male pop­u­la­tion in 1981 was still af­fected by the se­cond world war and women live longer than men. My count of men tar­geted by the ad­vert dropped to 4,902.

There was more I could do to thin out this crowd. While a bi­sex­ual man could still suit our pina co­lada-lov­ing lady, a gay man sadly would not. There is lit­tle to sup­port the com­monly thrown-around fig­ure that about one in 10 of the pop­u­la­tion is gay. For­mal stud­ies come up with much lower fig­ures, of about 3%, though these are likely to be un­der­es­ti­mates – far higher rates are found among younger adults who have grown up with less stigma. We were talk­ing about 1981, though, so I ex­cluded 3% of men, tak­ing us to 4,755 can­di­dates.

To be able to read a per­sonal ad in a news­pa­per, you need to be a reader of that news­pa­per. As Holmes in­con­sid­er­ately doesn’t name the news­pa­per – it’s al­most as if he were de­lib­er­ately mak­ing this dif­fi­cult – I needed to do some de­tec­tive work.

Per­sonal ads make more sense in a lo­cal news­pa­per than a na­tional one; who wants to travel 200 miles to bond over a com­mon ha­tred of yoga? So I needed to know how many lo­cal news­pa­pers were sold when the song came out – a fig­ure which, use­fully, is col­lected and pub­lished on­line by the World Ad­ver­tis­ing Re­search Cen­tre. The in­ter­net might be killing jour­nal­ism, but it does come in handy some­times.

About 2.5 bil­lion lo­cal and re­gional →

daily news­pa­pers were sold in the UK each year at the time of the song’s re­lease, or about eight mil­lion news­pa­pers a day. News­pa­per ad­ver­tis­ing re­search tends to as­sume about 2.5 peo­ple read each copy, mean­ing 20 mil­lion peo­ple a day would look at a pa­per. Given the UK pop­u­la­tion at the time was 56.3 mil­lion that is 36.1%, sug­gest­ing that of our 4,755 po­ten­tially el­i­gi­ble men, 1,689 would have seen the ad­vert.

Hang on a minute, you may say. How the hell do we know which ones liked pina co­ladas? Let alone get­ting caught in the rain, and the feel of the ocean? Sadly, there is no his­tor­i­cal re­search about North­wich that ad­dresses these ques­tions – leav­ing me with only one re­course: a rig­or­ous sci­en­tific poll of to­day’s Bri­tish pub­lic, in the hope that tastes haven’t shifted too rad­i­cally in the past 39 years.

Mirac­u­lously, I was able to per­suade the polling com­pany YouGov to put these ques­tions to the pub­lic in a way that would gen­er­ate se­ri­ous an­swers. This is ro­bust data, ex­plains YouGov po­lit­i­cal re­searcher Chris Cur­tis: “Un­like the ‘polls’ you see on Twit­ter, when con­duct­ing re­search we en­sure we are in­ter­view­ing a rep­re­sen­ta­tive sam­ple of the Bri­tish pub­lic. This means we ask the cor­rect num­ber of old, young, mid­dle class, work­ing class [peo­ple].”

He dis­cov­ered that women are more likely than men to en­joy pina co­ladas ( by 44% to 34%). These are low fig­ures for an iconic cock­tail: the sweet pineap­ple, rum and co­conut drink is also the sig­na­ture cock­tail of Puerto Rico, with its own na­tional day. But, sadly, the polls don’t lie.

Our poll had to be split into five dif­fer­ent ques­tions, re­worded from the orig­i­nal per­sonal ad, with an­swers pre­sented in ran­dom or­ders – mainly to make sure peo­ple gave a gen­uine re­sponse to each, rather than piec­ing to­gether the lyrics of the song. Some things needed a tweak. “While it may seem ob­vi­ous to many, it was im­por­tant we spec­i­fied that by ask­ing about hav­ing ‘half a brain’ we were not talk­ing lit­er­ally and in­stead re­fer­ring to in­tel­li­gence,” says Cur­tis.

Af­ter that, we just had to see how many men in our sam­ple matched each as­pect of the song. Not only did 34% of men like pina co­ladas, but also 27% liked get­ting caught in the rain. We got a much bet­ter hit rate for not be­ing into yoga – 81% of our sam­ple aren’t in­ter­ested – while 80% think they’re in­tel­li­gent (the near­est we could get to “have half a brain”). “Mak­ing love at mid­night in the dunes of the cape” is rather too spe­cific to poll, but the re­search did es­tab­lish that 34% of men say they like mak­ing love on a beach (a fig­ure re­garded scep­ti­cally by those who have done this).

As­sum­ing that each of these ques­tions was in­de­pen­dent from the oth­ers – for ex­am­ple, lik­ing rain makes you no more likely to be into pina co­ladas – we cal­cu­lated that ex­actly 2% of men (one in 50) would match the per­sonal ad in Holmes’s song. This gave us the an­swer to how many men liv­ing in North­wich and read­ing the pa­per would see the ad and be in­ter­ested: 34. So I had my an­swer: our song’s pro­tag­o­nist was mod­er­ately, but not spec­tac­u­larly, lucky to be the first per­son to re­spond to his girl­friend’s ad. I knew the ac­tual chances.

But this still didn’t feel like the end of my jour­ney. What about that im­prob­a­ble happy end­ing? In­stead of be­ing shocked and hurt by their mu­tual at­tempts at in­fi­delity, the pair sim­ply laugh about it. What were the chances of that?

Fun­nily enough, there is no study that cov­ers this ex­act sce­nario – but there is re­search into some­thing close. The Amer­i­can aca­demic Dr Nancy Kal­ish, based at Cal­i­for­nia State Uni­ver­sity in Sacra­mento, has spent decades ex­am­in­ing why some di­vorced cou­ples end up not only rec­on­cil­ing, but re­mar­ry­ing each other.

What per­cent­age of di­vorced cou­ples get back to­gether? The an­swer is 6%, or about one in 17 – not many, but per­haps more than you’d ex­pect. Sur­pris­ingly, these cou­ples had a strong chance of stay­ing to­gether for good; at 72%, well above the av­er­age. It seems there’s a case of se­cond-time-lucky, or an el­e­ment of for­give­ness makes you stronger, which might bode well for the char­ac­ters in our song.

So, roughly speak­ing, I had my an­swers. If we take all the statis­tics to­gether, the chances of Holmes’s story hap­pen­ing as de­scribed are one in 567. This is rel­a­tively un­likely – about the same chance as be­ing born with an ex­tra fin­ger or two – but in a coun­try with mil­lions of peo­ple, stranger things hap­pen ev­ery day.

My in­ves­ti­ga­tion, I was forced to con­clude, had roundly vin­di­cated Holmes’s song­writ­ing. But it kick­started a habit – fact-check­ing pop mu­sic, and learn­ing about the world as I did. For in­stance: a 1980s study taught me that when un­der­grad­u­ate re­searchers asked a stranger “Voulezvous coucher avec moi, c’est soir?” three-quar­ters of men said yes (al­most no women did). Can you cry a river? Not re­ally: the av­er­age vol­ume of a hu­man tear is not great, and it would take bil­lions flow­ing ev­ery se­cond to match the flow of the Thames.

And, in an­swer to Bey­oncé’s ques­tion, “Who run the world?” I learned that, last year, out of a to­tal of 193 United Na­tions coun­tries, only 15 had a fe­male leader.

Tak­ing mu­sic far more se­ri­ously – and way more lit­er­ally – than any­one ever should do taught me that even the flim­si­est pop song can be a route to learn­ing some­thing deep about the world. Just don’t ask me what love’s got to do, got to do with it. 

James Ball’s Should I Stay Or Should I Go? And 87 Other Se­ri­ous An­swers To Ques­tions In Songs is pub­lished by Box­tree at £9.99

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