Advertising fail: the case of parship.de

Winter can be a hard time for singles. It’s cold outside, there’s nobody to cuddle with and it sucks to go to family parties all alone. Perfect time for dating websites to flood the city with advertising. These posters by parship.de, who claims to be the largest online meeting point for singles in Germany, can be found everywhere these days:

Every 11 minutes a single using their website falls in love, they claim. The number is based on a consumer survey from 2013 and should probably suggest that your chances of finding your life partner online is very high. But if you think about it just for two more seconds it feels odd. Every 11 minutes someone using the website falls in love. If your not extremely altruistic you should not care about others falling in love (except of your prospective life partner, of course) but rather about you falling in love. So what are the odds for me personally? Do 11 minutes really suggest a good deal? It turns out that I was not the first to be bothered by the slogan. Researchers from the RWI Essen, a German economic research institute, even called it the “non-statistic of the month”. Let’s do the math:

For simplicity, the RWI researchers assume that every 10 minutes 2 singles fall in love. This means 6 per hour, 144 per day, or 52,560 per year (if users were 24/7 active on the website; you see the assumptions are actually quite favorable for the dating portal). With an estimated number of 5 million users per year the probability of being among the two lucky ones is $\frac{2}{5,000,00}$ every ten minutes. Per year this amounts to:

$1 - (\frac{4,999,998}{5,000,00})^{52,560} = 0.0208$

Not so great, huh? 2% chance of finding a partner per year. How long then will it take until Cupid’s arrow will finally pierce you? You can model these time-to-event probabilities with a discrete geometric distribution. Its mean is equal to $\frac{1 - p}{p}$ with $p$ being the probability of an event every period. Consequently, you will wait on average for 47 years until you  meet somebody. With a monthly fee of EUR 39.90 you will have spent EUR 22,503.60 until then. Great advertising!

You could argue that 5 million users is overestimated. Only paying users should be considered because the usability for non-paying users is reduced substantially after a trial period. But even with only 750,000 active users the calculation would yield a yearly probability of not more than 13%. To have a 50% chance to fall in love in the first year, not more than 150,000 competitors, who could snatch the precious ticket to love before you, should be active.

Here’s again the link to the original source: “Liebestrunken – Vermittlungsbörse schießt statistisches Eigentor”